what is mediator variable in research

Mediator Variable / Mediating Variable: Simple Definition

Types of Variables >

A mediator variable explains the how or why of an (observed) relationship between an independent variable and its dependent variable .

In a mediation model, the independent variable cannot influence the dependent variable directly, and instead does so by means of a third variable, a ‘middle-man’.

In psychology, the mediator variable is sometimes called an intervening variable . In statistics, an intervening variable is usually considered to be a sub-type of mediating variable. However, the lines between the two terms are somewhat fuzzy, and they are often used interchangeably.

Mediator Variable Examples

A mediator variable may be something as simple as a psychological response to given events . For example, suppose buying pizza for a work party leads to positive morale and to the work being done in half the time.

• Pizza is the independent variable,
• Work speed is the dependent variable,
• The mediator, the middle man without which there would be no connection, is positive morale .

Although we may observe a definite effect on work speed when and if pizza is bought, the pizza itself does not have the power to affect work rates: only by affecting morale of the workers can it make an actual difference.

Full Mediation and Partial Mediation

Full mediation is when the entire relationship between the independent & dependent variables is through the mediator variable. If you take away the mediator, the relationship disappears. Since the real world is a complicated place with many interactions, this is less common than partial mediation.

Partial mediation happens when the mediating variable is only responsible for a part of the relationship between independent & dependent variables. If the mediating variable is eliminated, there will still be a relationship between the independent and dependent variables; it just won’t be as strong.

Mediational Hypotheses

Mediational hypotheses, by definition, include full (complete) mediation. In other words, the independent variable has zero effect on the dependent variable; the causal relationship depends entirely on the mediator.

Baron and Kenny’s Four Steps

Baron and Kenny (1986), Judd and Kenny (1981), and James and Brett (1984) outlined the following steps to identify the mediational hypothesis. If the steps are met, then variable M is said to completely mediate the X-Y relationship. The steps are

• Show that a the independent variable (X) is correlated with the mediator (M).
• Demonstrate that the dependent variable (Y) and M are correlated .
• Demonstrate full mediation on the process. The effect of X on Y, controlling for M (i.e. controlling for paths a and b in the image at the top of this page), should be zero. If the results for this step are anything but zero, then there is partial mediation.

The authors state that three regression analyses are needed:

• X as the predictor variable and M as the outcome variable .
• X as the predictor variable and Y as the outcome variable.
• X and M as the predictor variables and Y as the outcome variable.

The procedures come with some hefty explanations, which are beyond the scope of this article. I recommend reading Baron and Keny’s original text. Or, as an excellent (plain English) alternative, read Paul Jose’s Doing Statistical Mediation and Moderation: Methodology in the Social Sciences , which includes Baron and Kenny’s steps starting on page 20.

Mediator versus Moderator variables. Retrieved from http://psych.wisc.edu/henriques/mediator.html on June 26, 2018. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182. Retrieved June 26, 2018 from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.169.4836&rep=rep1&type=pdf on June 26, 2018 Butler, Adam. Mediation Defined. Retrieved from https://sites.uni.edu/butlera/courses/org/modmed/moderator_mediator.htm on June 26, 2018

15 Mediating Variable Examples

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A mediating variable is a factor that explains the process through which an independent variable affects a dependent variable.

Here is a scholarly definition from Veronica Hefner (2017):

“A mediating variable is a variable that links the independent and the dependent variables , and whose existence explains the relationship between the other two variables.  A mediating variable is  also known as a mediator variable or an intervening variable.”

For example, in a study exploring the link between exercise and mental well-being, self-esteem might serve as a mediating variable, meaning that exercise boosts self-esteem, which then enhances mental well-being. It is that hidden ‘middle step’.

Mediating Variable Examples

1. the link between social media usage and loneliness.

Independent Variable: Social media usage Dependent Variable: Feelings of loneliness Mediating Variable: Quality and frequency of face-to-face interactions

If social media usage reduces the amount or quality of face-to-face time with others, it can lead to feelings of loneliness. Therefore, the relationship between extensive social media usage and feelings of loneliness might be mediated by the diminished quality and frequency of in-person interactions.

2. The Link Between Physical Activity and Mental Health

Independent Variable: Physical activity Dependent Variable: Improved mental health Mediating Variable: Endorphin release

When an individual engages in physical activity, the body releases endorphins, which are known as “feel-good” hormones. These endorphins play a significant role in enhancing mood and reducing feelings of anxiety and depression. Therefore, the positive relationship between physical activity and improved mental health might be mediated by the release of endorphins.

3. The Link Between Sleep Duration and Academic Performance

Independent Variable: Sleep duration Dependent Variable: Academic performance Mediating Variable: Cognitive function and attention span

Adequate sleep duration is crucial for optimal cognitive functioning and attention span. When students get adequate sleep, their cognitive abilities like memory, decision-making, and problem-solving are enhanced, leading to better academic performance. Thus, the relationship between sleep duration and academic performance might be mediated by improvements in cognitive function and sustained attention span.

4. The Link Between Job Satisfaction and Employee Turnover

Independent Variable: Job satisfaction Dependent Variable: Employee turnover Mediating Variable: Organizational commitment

Employees who are satisfied with their job are more likely to develop a stronger commitment to their organization. This commitment often results in greater loyalty and a decreased likelihood to leave the company. Therefore, the relationship between job satisfaction and reduced employee turnover might be mediated by the increased sense of organizational commitment.

5. The Link Between Dietary Habits and Physical Health

Independent Variable: Dietary habits Dependent Variable: Physical health Mediating Variable: Nutrient intake

If someone consistently consumes a balanced diet, they intake essential nutrients that promote good health. The relationship between dietary habits and physical health might be mediated by the level of essential nutrients consumed, ensuring proper body function and preventing deficiencies.

6. The Link Between Classroom Environment and Student Engagement

Independent Variable: Classroom environment Dependent Variable: Student engagement Mediating Variable: Student’s perception of safety and belonging

A positive and inclusive classroom environment can make students feel safe and like they belong. When students perceive that they are in a safe environment where they are valued, they are more likely to engage actively in learning. Thus, the relationship between the classroom environment and student engagement might be mediated by the student’s feelings of safety and belonging.

7. The Link Between Work-Life Balance and Employee Burnout

Independent Variable: Work-life balance Dependent Variable: Employee burnout Mediating Variable: Stress levels

Employees with a poor work-life balance often experience heightened stress levels due to the overlapping demands of their job and personal life. Elevated stress levels over extended periods can lead to feelings of burnout. Therefore, the relationship between work-life balance and employee burnout might be mediated by the levels of stress an employee experiences.

8. The Link Between Urban Green Spaces and Mental Well-being

Independent Variable: Presence of urban green spaces Dependent Variable: Mental well-being Mediating Variable: Frequency of nature interactions

When urban areas have more green spaces, residents tend to interact more frequently with nature, either by walking, exercising, or simply spending time in these areas. These interactions with nature have been shown to reduce stress and increase feelings of relaxation. Therefore, the relationship between the presence of urban green spaces and mental well-being might be mediated by the frequency of nature interactions.

9. The Link Between Employee Training and Job Performance

Independent Variable: Employee training Dependent Variable: Job performance Mediating Variable: Skill acquisition and competence

Regular and quality employee training sessions equip employees with new skills and enhance their competence in their roles. As they become more skilled and competent, their performance at their job tends to improve. Thus, the relationship between employee training and job performance might be mediated by the level of skill acquisition and competence achieved.

10. The Link Between Plant Ownership and Reduced Stress

Independent Variable: Plant ownership Dependent Variable: Reduced stress Mediating Variable: Increased interaction with nature and nurturing behavior

Caring for plants allows individuals to interact with nature even in indoor environments. Additionally, the act of nurturing plants and seeing them grow can be therapeutic and rewarding. These interactions and behaviors can lead to relaxation and a reduction in stress levels. Therefore, the relationship between plant ownership and reduced stress might be mediated by the increased interaction with nature and the nurturing behavior associated with plant care.

11. The Link Between Music Lessons and Cognitive Development

Independent Variable: Music lessons Dependent Variable: Cognitive development Mediating Variable: Development of discipline and concentration

Engaging in music lessons often requires students to practice regularly, fostering discipline. Additionally, mastering an instrument necessitates concentration and focus. These attributes can positively impact other areas of life, including academic pursuits. Thus, the relationship between music lessons and cognitive development might be mediated by the enhanced discipline and concentration developed through musical practice.

12. The Link Between Outdoor Play and Physical Health in Children

Independent Variable: Outdoor play Dependent Variable: Physical health in children Mediating Variable: Physical activity levels

Children who engage in outdoor play are often more physically active than those who spend more time indoors, as they run, jump, climb, and engage in other physical activities. This increased level of physical activity is essential for cardiovascular health, muscle development, and overall physical well-being. Therefore, the relationship between outdoor play and physical health in children might be mediated by the levels of physical activity they engage in.

13. The Link Between Personal Financial Management and Life Satisfaction

Independent Variable: Personal financial management Dependent Variable: Life satisfaction Mediating Variable: Financial security and reduced monetary stress

Individuals who effectively manage their finances tend to achieve a higher degree of financial security. This security can alleviate stress and anxiety related to monetary concerns, leading to a more content and satisfied life. Thus, the relationship between personal financial management and life satisfaction might be mediated by the sense of financial security and reduced monetary stress achieved through effective financial practices.

14. The Link Between Reading Habits and Vocabulary Size

Independent Variable: Reading habits Dependent Variable: Vocabulary size Mediating Variable: Exposure to diverse words and contexts

Individuals who read regularly encounter a wide variety of words in different contexts. This repeated exposure enhances their vocabulary as they come across and internalize new words. Therefore, the relationship between reading habits and vocabulary size might be mediated by the degree of exposure to diverse words and contexts through reading.

15. The Link Between Community Involvement and Personal Well-being

Independent Variable: Community involvement Dependent Variable: Personal well-being Mediating Variable: Sense of belonging and purpose

Engaging with and contributing to one’s community can foster a sense of belonging and purpose. Feeling connected and knowing that one’s actions positively impact others can lead to enhanced personal well-being. Thus, the relationship between community involvement and personal well-being might be mediated by the heightened sense of belonging and purpose derived from active community participation.

Mediating vs Moderating vs Confounding Variables

Mediating, moderating, and confounding variables are three of the most common types of ‘ third variable ‘. They are similar in that they need to be observed or controlled in order to better understand the relationship between the independent and dependent variables (Stapel & van Beek, 2015).

However, the three differ in important ways.

Let’s start with some definitions:

• Mediating Variables: These explain the process through which an independent variable influences a dependent variable.
• Moderating Variables : These influence the strength or direction of the relationship between an independent and a dependent variable (Nestor & Schutt, 2018).
• Confounding Variables : These are external factors that, if not controlled, can cause a false perception of a relationship between the independent and dependent variables (Boniface, 2019).

The table below shows how they differ:

Boniface, D. R. (2019).  Experiment Design and Statistical Methods For Behavioural and Social Research . CRC Press. ISBN: 9781351449298.

Hefner, V. (2017). Variables, Moderating Types . In Allen, M. (Ed.) The SAGE Encyclopedia of Communication Research Methods . SAGE Publications.

Nestor, P. G., & Schutt, R. K. (2018). Research Methods in Psychology: Investigating Human Behavior . SAGE Publications.

Scharrer, E., & Ramasubramanian, S. (2021).  Quantitative Research Methods in Communication: The Power of Numbers for Social Justice . Taylor & Francis.

Stapel, B. & van Beek, R.J. (2015). Confounders, moderators and mediators. In Mellenbergh, G. J., & Adèr, H. J. (Eds.). Advising on Research Methods: Selected Topics 2014 . Johannes van Kessel Advising.

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 25 Number Games for Kids (Free and Easy)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 25 Word Games for Kids (Free and Easy)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 25 Outdoor Games for Kids
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 50 Incentives to Give to Students

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Mediator vs moderator—which is right for you?

Last updated

18 April 2023

Reviewed by

Miroslav Damyanov

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Including mediators and moderators in your research not only allows you to study the relationship between two variables but can also help you avoid biases that could occur without them. Read further to learn more about how to distinguish and apply mediators and moderators in research.  

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• What is mediation in research?

Mediators provide a way for independent variables (aka causal variables or intervention) to impact a dependent variable (aka an outcome or effect). They explain the how and why relationship between the two. A mediator is always caused by the independent variable and influences the dependent variable. Consider a mediator as the “middleman” between independent and dependent variables. 

When using mediators, you can learn how or why an effect takes place. When using mediation analysis, you’re testing a hypothetical causal chain. If variable A affects variable B, then it turns into variable C.   

Perhaps an easier way to understand it is mediation analysis gives us information about how or why the independent variable affects the dependent variable. Taking the mediator out of the model in complete mediation eliminates the relationship between the dependent and independent variables . This is because the mediator thoroughly explains the relationship between the dependent and independent variables, and without it, there’s no relationship.

You can use a mediator in your research to see if the influence of the mediator is stronger than the direct influence of the independent variable. A mediator carries an effect to the direct variable from the indirect variable. 

A mediation flow chart might read: the independent variable causes the mediator, the mediator must change the dependent variable, and the mediator changes the relationship or correlation between the independent and the dependent variables.   

• What is moderation in research?

While mediation answers the how and why, moderators look at interactions. Moderation analysis is the level that the relationship between the independent and dependent variables changes as a function of a third variable or the moderator. 

Moderator variables are sometimes referred to as interactions or products because they can affect the strength or direction of the relationship between the independent and dependent variables. They make the relationship stronger or weaker or change it from strong to moderate to no influence at all.

Moderators can be either quantitative or qualitative. Examples of quantitative moderators might be numerical values such as test scores, weight, age, IQ, etc. Examples of qualitative moderators would be factors with no numeric value, such as gender, race, or education. 

The moderator can also be changed to determine the amount of change in the relationship between the variables since it influences the level, direction, or strength of the relationship.  

The purpose of using a moderator in your research is to help you determine what categorical or quantitative variables change the relationship between your independent and dependent variables or to determine if there’s any validity to the moderator you have chosen and the changes predicted.

• Mediator vs moderator variables

Partial or complete mediation

We can talk about partial or complete mediation. 

In complete or full mediation, a mediator explains the relationship between the independent and dependent variables. If the mediator is removed, a relationship no longer exists, explaining why it’s called complete.  

With partial mediation, when the mediator is removed from the model, there’s still a statistical relationship between the independent and dependent variables, meaning the mediator only partially explains the relationship.

Strength and direction of the effect

Moderation in research refers to the extent to which the relationship between two variables changes depending on the level of a third variable, which is known as the moderator variable. A moderator can change the strength and direction of the relationship between the independent and dependent variables.  

Mediation analysis

Mediation analysis uses either an analysis of variance or linear regression analysis to test whether a variable is a mediator. As explained previously, mediation may either be partial or complete. Mediators are caused by the independent variable, and they also influence the dependent variable. 

Moderation analysis

Moderation analysis is a commonly used technique in statistical modeling to help understand the nature of the relationships between variables and to identify the conditions under which those relationships are strongest or weakest. Moderation analysis can be conducted using various statistical methods, such as multiple regression, ANOVA, and structural equation modeling. 

Moderators used in research can be categorical, such as race, gender, religion, etc., and are usually not quantifiable, or they can be quantitative, such as age, income, weight, etc. If a moderator is removed, a relationship will still exist between the independent and dependent variables—unlike when a mediator is removed from complete mediation.  

• Mediator vs moderator examples

A simple example of a mediator variable:

Exercise affects family relationships because it creates endorphins.

Exercise is the independent variable, and family relationships are the dependent variable.  Endorphins are the mediator.

Without the mediator, your variables don’t have a relationship with each other.  However, when looking at moderators, as in the next example, there would still be a relationship, but a moderator explains how the variables are affected.

A simple example of a moderator example:

Seniors are more likely to have accidents due to vision impairments.

Accidents are the independent variable, vision impairments are the dependent variable, and seniors are the moderator (age being the variable you use to create the group 'seniors').

What is the difference between a confounder and a mediator?

A mediator is the mechanism of a relationship between two variables: it explains the process by which they’re related. A confounder, however, is a third variable that affects variables of interest and makes them appear related when they actually are not.

Is a mediator an IV or DV?

IVs (independent variables) and DVs (dependent variables) are different from a mediator. The mediator variable is used to explain the relationship between the independent variable and the dependent variable. Without the mediator variable, there’s no relationship between the other two in the case of complete mediation.

How can you tell if a variable is a mediator?

When mediation is in place, there’s a correlation between the independent variable and the mediator variable, as well as a correlation between the mediator variable and the dependent variable. 

In other words, mediation occurs when the relationship between the independent variable and the dependent variable is partially or completely explained by the mediator variable, which in turn means that there is a correlation between the independent variable and the mediator variable and between the mediator variable and the dependent variable.  

Put simply, it’s seen as a mediator variable if the change in the level of the independent variable significantly accounts for the variation in the other variable. 

What is an example of moderation?

If work experience influences starting salary, how big a role does gender play? Work experience is the independent variable, salary is the dependent variable, and gender is the moderator. 

Can a variable be both moderating and mediating?

Yes, a variable can be both moderating and mediating, although the two roles are distinct and serve different purposes in statistical analysis. It’s dependent on the framing of the study and the independent variable and dependent variable you’re working with. 

Consider that a variable can be both a mediator and a moderator when it affects both the strength and the direction of the relationship between two variables and also explains the mechanism through which the relationship occurs. 

Is a moderator variable a confounder?

A confounder is a variable that’s related to both the predictor of interest and the outcome, but it’s not on the causal pathway. A moderator is a variable that changes the direction or strength of the relationship between the independent and the dependent variables.

How do you identify a moderating variable in research?

To identify a moderating variable in research, you must look for a variable that influences the direction or strength of the relationship between the independent and dependent variables. Overall, identifying a moderating variable requires careful consideration of the research question, theoretical framework, and data analysis techniques used in the study. 

What is a mediator relationship?

A mediator relationship is a type of relationship in which a third variable, called a mediator, explains the relationship between two other variables. More specifically, a mediator variable that acts as a “middleman” explains how or why two other variables are related to each other. 

What is a moderator relationship?

A moderator relationship, also known as an interaction or conditioning effect, is one where the independent and dependent variables have a relationship, but by adding the third, or a moderating variable, the relationship changes. Moderators point out the when, who, or under what circumstances.

Can a mediator be a moderator?

No, a mediator variable and a moderator variable are two distinct concepts in statistical analysis and cannot be the same variable.

A mediator variable explains the relationship between two other variables. A moderator variable affects the direction or strength of the relationship between two other variables.

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Mediator vs. Moderator

What's the difference.

Mediator and moderator are two statistical concepts used in research to understand the relationship between variables. A mediator variable explains the mechanism or process through which an independent variable affects a dependent variable. It helps to understand the underlying causal pathway between the two variables. On the other hand, a moderator variable influences the strength or direction of the relationship between an independent and dependent variable. It helps to identify the conditions under which the relationship between the variables is stronger or weaker. While a mediator explains why and how the relationship exists, a moderator explains when and for whom the relationship is stronger or weaker. Both concepts are crucial in understanding the complexity of relationships between variables in research.

Further Detail

Introduction.

When it comes to statistical analysis and research, two important concepts that often come up are mediator and moderator variables. These terms are frequently used in various fields, including psychology, sociology, and economics. While both mediator and moderator variables play crucial roles in understanding relationships between variables, they have distinct attributes and functions. In this article, we will explore the differences and similarities between mediators and moderators, shedding light on their unique characteristics and how they contribute to the research process.

Mediator Variables

A mediator variable, also known as an intermediate variable, is a variable that explains the relationship between an independent variable and a dependent variable. It acts as a mechanism or pathway through which the independent variable influences the dependent variable. In other words, a mediator variable helps to understand the underlying process or mechanism that connects the two variables of interest.

For example, let's consider a study examining the relationship between stress (independent variable) and job satisfaction (dependent variable). In this scenario, job engagement could act as a mediator variable. It explains how stress affects job satisfaction by influencing an individual's level of engagement at work. By including a mediator variable, researchers can gain a deeper understanding of the relationship between stress and job satisfaction.

Key attributes of mediator variables include:

• Mediators are influenced by the independent variable.
• Mediators influence the dependent variable.
• Mediators explain the underlying process or mechanism.
• Mediators are often tested using statistical methods such as mediation analysis.
• Mediators are essential for understanding the "why" or "how" behind a relationship.

Moderator Variables

A moderator variable, on the other hand, is a variable that influences the strength or direction of the relationship between an independent variable and a dependent variable. Unlike mediator variables, moderators do not explain the underlying process but rather affect the relationship between the two variables of interest.

Continuing with the previous example, let's say that the study also considers the role of social support as a moderator variable in the relationship between stress and job satisfaction. Social support could moderate the relationship by either strengthening or weakening the impact of stress on job satisfaction. By examining the moderating effect of social support, researchers can identify whether the relationship between stress and job satisfaction varies depending on the level of social support an individual receives.

Key attributes of moderator variables include:

• Moderators do not explain the underlying process but affect the relationship.
• Moderators influence the strength or direction of the relationship.
• Moderators are often tested using statistical methods such as moderation analysis.
• Moderators help identify boundary conditions or contexts where the relationship may differ.
• Moderators provide insights into when and for whom the relationship holds.

Comparing Mediators and Moderators

While mediator and moderator variables have distinct attributes, they also share some similarities. Both mediator and moderator variables are important in understanding the complexity of relationships between variables and contribute to the advancement of research in various fields. They both provide valuable insights into the underlying processes and conditions that shape these relationships.

However, the key difference lies in their primary functions. Mediator variables explain the mechanism or process through which the independent variable affects the dependent variable, while moderator variables influence the strength or direction of the relationship between the two variables. Mediators focus on the "why" or "how," while moderators focus on the "when" or "for whom."

Another difference is the statistical methods used to test mediators and moderators. Mediation analysis is commonly employed to examine mediator variables, while moderation analysis is used for moderator variables. These statistical techniques help researchers quantify and understand the specific effects of mediators and moderators, providing empirical evidence for their roles in the relationship between variables.

Furthermore, mediators and moderators can coexist in a single study. In some cases, a variable may act as both a mediator and a moderator, depending on the research question and context. For example, a variable could mediate the relationship between an independent variable and a dependent variable, while also moderating the strength of that relationship for certain groups or conditions. This highlights the complexity and interplay of these concepts in research.

Mediator and moderator variables are essential components of statistical analysis and research. While mediators explain the underlying process or mechanism between independent and dependent variables, moderators influence the strength or direction of the relationship. Both mediators and moderators contribute to a deeper understanding of relationships between variables, providing valuable insights into the "why," "how," "when," and "for whom" of these relationships. By incorporating mediator and moderator variables into research designs, researchers can enhance the validity and applicability of their findings, ultimately advancing knowledge in their respective fields.

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Article contents

Mediator variables.

• Matthew S. Fritz Matthew S. Fritz Department of Educational Psychology, University of Nebraska - Lincoln
•  and  Houston F. Lester Houston F. Lester Department of Educational Psychology, University of Nebraska - Lincoln
• https://doi.org/10.1093/acrefore/9780190236557.013.19
• Published online: 22 December 2016

Mediator variables are variables that lie between the cause and effect in a causal chain. In other words, mediator variables are the mechanisms through which change in one variable causes change in a subsequent variable. The single-mediator model is deceptively simple because it has only three variables: an antecedent, a mediator, and a consequent. Determining that a variable functions as a mediator is a difficult process, however, because causation can be inferred only when many strict assumptions are met, including, but not limited to, perfectly reliable measures, correct temporal design, and no omitted confounders. Since many of these assumptions are difficult to assess and rarely met in practice, the significance of a statistical test of mediation alone usually provides only weak evidence of mediation.

New methodological approaches are constantly being developed to circumvent these limitations. Specifically, new methods are being created for the following purposes: (1) to assess the impact of violating assumptions (e.g., sensitivity analyses) and (2) to make fewer assumptions and provide more flexible analysis techniques (e.g., Bayesian analysis or bootstrapping) that may be more robust to assumption violations. Despite these advances, the importance of the design of a study cannot be overstated. A statistical analysis, no matter how sophisticated, cannot redeem a study that measured the wrong variables or used an incorrect temporal design.

• mediator variables
• mediation analysis
• causal analysis
• temporal design
• Bayesian analysis
• bootstrapping

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Understanding and Using Mediators and Moderators

• Published: 06 June 2007
• Volume 87 , pages 367–392, ( 2008 )

Cite this article

• Amery D. Wu 1 &
• Bruno D. Zumbo 1  

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Mediation and moderation are two theories for refining and understanding a causal relationship. Empirical investigation of mediators and moderators requires an integrated research design rather than the data analyses driven approach often seen in the literature. This paper described the conceptual foundation, research design, data analysis, as well as inferences involved in a mediation and/or moderation investigation in both experimental and non-experimental (i.e., correlational) contexts. The essential distinctions between the investigation of mediators and moderators were summarized and juxtaposed in an example of a causal relationship between test difficulty and test anxiety. In addition, the more elaborate models, moderated mediation and mediated moderation, the use of structural equation models, and the problems with model misspecification were discussed conceptually.

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Wu, A.D., Zumbo, B.D. Understanding and Using Mediators and Moderators. Soc Indic Res 87 , 367–392 (2008). https://doi.org/10.1007/s11205-007-9143-1

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Chapter 14: Mediation and Moderation

Alyssa blair, 1 what are mediation and moderation.

Mediation analysis tests a hypothetical causal chain where one variable X affects a second variable M and, in turn, that variable affects a third variable Y. Mediators describe the how or why of a (typically well-established) relationship between two other variables and are sometimes called intermediary variables since they often describe the process through which an effect occurs. This is also sometimes called an indirect effect. For instance, people with higher incomes tend to live longer but this effect is explained by the mediating influence of having access to better health care.

In R, this kind of analysis may be conducted in two ways: Baron & Kenny’s (1986) 4-step indirect effect method and the more recent mediation package (Tingley, Yamamoto, Hirose, Keele, & Imai, 2014). The Baron & Kelly method is among the original methods for testing for mediation but tends to have low statistical power. It is covered in this chapter because it provides a very clear approach to establishing relationships between variables and is still occassionally requested by reviewers. However, the mediation package method is highly recommended as a more flexible and statistically powerful approach.

Moderation analysis also allows you to test for the influence of a third variable, Z, on the relationship between variables X and Y. Rather than testing a causal link between these other variables, moderation tests for when or under what conditions an effect occurs. Moderators can stength, weaken, or reverse the nature of a relationship. For example, academic self-efficacy (confidence in own’s ability to do well in school) moderates the relationship between task importance and the amount of test anxiety a student feels (Nie, Lau, & Liau, 2011). Specifically, students with high self-efficacy experience less anxiety on important tests than students with low self-efficacy while all students feel relatively low anxiety for less important tests. Self-efficacy is considered a moderator in this case because it interacts with task importance, creating a different effect on test anxiety at different levels of task importance.

In general (and thus in R), moderation can be tested by interacting variables of interest (moderator with IV) and plotting the simple slopes of the interaction, if present. A variety of packages also include functions for testing moderation but as the underlying statistical approaches are the same, only the “by hand” approach is covered in detail in here.

Finally, this chapter will cover these basic mediation and moderation techniques only. For more complicated techniques, such as multiple mediation, moderated mediation, or mediated moderation please see the mediation package’s full documentation.

1.1 Getting Started

If necessary, review the Chapter on regression. Regression test assumptions may be tested with gvlma . You may load all the libraries below or load them as you go along. Review the help section of any packages you may be unfamiliar with ?(packagename).

2 Mediation Analyses

Mediation tests whether the effects of X (the independent variable) on Y (the dependent variable) operate through a third variable, M (the mediator). In this way, mediators explain the causal relationship between two variables or “how” the relationship works, making it a very popular method in psychological research.

Both mediation and moderation assume that there is little to no measurement error in the mediator/moderator variable and that the DV did not CAUSE the mediator/moderator. If mediator error is likely to be high, researchers should collect multiple indicators of the construct and use SEM to estimate latent variables. The safest ways to make sure your mediator is not caused by your DV are to experimentally manipulate the variable or collect the measurement of your mediator before you introduce your IV.

Total Effect Model.

Basic Mediation Model.

c = the total effect of X on Y c = c’ + ab c’= the direct effect of X on Y after controlling for M; c’=c-ab ab= indirect effect of X on Y

The above shows the standard mediation model. Perfect mediation occurs when the effect of X on Y decreases to 0 with M in the model. Partial mediation occurs when the effect of X on Y decreases by a nontrivial amount (the actual amount is up for debate) with M in the model.

2.1 Example Mediation Data

Set an appropriate working directory and generate the following data set.

In this example we’ll say we are interested in whether the number of hours since dawn (X) affect the subjective ratings of wakefulness (Y) 100 graduate students through the consumption of coffee (M).

Note that we are intentionally creating a mediation effect here (because statistics is always more fun if we have something to find) and we do so below by creating M so that it is related to X and Y so that it is related to M. This creates the causal chain for our analysis to parse.

2.2 Method 1: Baron & Kenny

This is the original 4-step method used to describe a mediation effect. Steps 1 and 2 use basic linear regression while steps 3 and 4 use multiple regression. For help with regression, see Chapter 10.

The Steps: 1. Estimate the relationship between X on Y (hours since dawn on degree of wakefulness) -Path “c” must be significantly different from 0; must have a total effect between the IV & DV

Estimate the relationship between X on M (hours since dawn on coffee consumption) -Path “a” must be significantly different from 0; IV and mediator must be related.

Estimate the relationship between M on Y controlling for X (coffee consumption on wakefulness, controlling for hours since dawn) -Path “b” must be significantly different from 0; mediator and DV must be related. -The effect of X on Y decreases with the inclusion of M in the model

Estimate the relationship between Y on X controlling for M (wakefulness on hours since dawn, controlling for coffee consumption) -Should be non-significant and nearly 0.

2.3 Interpreting Barron & Kenny Results

Here we find that our total effect model shows a significant positive relationship between hours since dawn (X) and wakefulness (Y). Our Path A model shows that hours since down (X) is also positively related to coffee consumption (M). Our Path B model then shows that coffee consumption (M) positively predicts wakefulness (Y) when controlling for hours since dawn (X). Finally, wakefulness (Y) does not predict hours since dawn (X) when controlling for coffee consumption (M).

Since the relationship between hours since dawn and wakefulness is no longer significant when controlling for coffee consumption, this suggests that coffee consumption does in fact mediate this relationship. However, this method alone does not allow for a formal test of the indirect effect so we don’t know if the change in this relationship is truly meaningful.

There are two primary methods for formally testing the significance of the indirect test: the Sobel test & bootstrapping (covered under the mediatation method).

The Sobel Test uses a specialized t-test to determine if there is a significant reduction in the effect of X on Y when M is present. Using the sobel function of the multilevel package will show provide you with three of the basic models we ran before (Mod1 = Total Effect; Mod2 = Path B; and Mod3 = Path A) as well as an estimate of the indirect effect, the standard error of that effect, and the z-value for that effect. You can either use this value to calculate your p-value or run the mediation.test function from the bda package to receive a p-value for this estimate.

In this case, we can now confirm that the relationship between hours since dawn and feelings of wakefulness are significantly mediated by the consumption of coffee (z’ = 3.84, p < .001).

However, the Sobel Test is largely considered an outdated method since it assumes that the indirect effect (ab) is normally distributed and tends to only have adequate power with large sample sizes. Thus, again, it is highly recommended to use the mediation bootstrapping method instead.

2.4 Method 2: The Mediation Pacakge Method

This package uses the more recent bootstrapping method of Preacher & Hayes (2004) to address the power limitations of the Sobel Test. This method computes the point estimate of the indirect effect (ab) over a large number of random sample (typically 1000) so it does not assume that the data are normally distributed and is especially more suitable for small sample sizes than the Barron & Kenny method.

To run the mediate function, we will again need a model of our IV (hours since dawn), predicting our mediator (coffee consumption) like our Path A model above. We will also need a model of the direct effect of our IV (hours since dawn) on our DV (wakefulness), when controlling for our mediator (coffee consumption). When can then use mediate to repeatedly simulate a comparsion between these models and to test the signifcance of the indirect effect of coffee consumption.

2.5 Interpreting Mediation Results

The mediate function gives us our Average Causal Mediation Effects (ACME), our Average Direct Effects (ADE), our combined indirect and direct effects (Total Effect), and the ratio of these estimates (Prop. Mediated). The ACME here is the indirect effect of M (total effect - direct effect) and thus this value tells us if our mediation effect is significant.

In this case, our fitMed model again shows a signifcant affect of coffee consumption on the relationship between hours since dawn and feelings of wakefulness, (ACME = .28, p < .001) with no direct effect of hours since dawn (ADE = -0.11, p = .27) and significant total effect ( p < .05).

We can then bootstrap this comparison to verify this result in fitMedBoot and again find a significant mediation effect (ACME = .28, p < .001) and no direct effect of hours since dawn (ADE = -0.11, p = .27). However, with increased power, this analysis no longer shows a significant total effect ( p = .08).

3 Moderation Analyses

Moderation tests whether a variable (Z) affects the direction and/or strength of the relation between an IV (X) and a DV (Y). In other words, moderation tests for interactions that affect WHEN relationships between variables occur. Moderators are conceptually different from mediators (when versus how/why) but some variables may be a moderator or a mediator depending on your question. See the mediation package documentation for ways of testing more complicated mediated moderation/moderated mediation relationships.

Like mediation, moderation assumes that there is little to no measurement error in the moderator variable and that the DV did not CAUSE the moderator. If moderator error is likely to be high, researchers should collect multiple indicators of the construct and use SEM to estimate latent variables. The safest ways to make sure your moderator is not caused by your DV are to experimentally manipulate the variable or collect the measurement of your moderator before you introduce your IV.

Basic Moderation Model.

3.1 Example Moderation Data

In this example we’ll say we are interested in whether the relationship between the number of hours of sleep (X) a graduate student receives and the attention that they pay to this tutorial (Y) is influenced by their consumption of coffee (Z). Here we create the moderation effect by making our DV (Y) the product of levels of the IV (X) and our moderator (Z).

3.2 Moderation Analysis

Moderation can be tested by looking for significant interactions between the moderating variable (Z) and the IV (X). Notably, it is important to mean center both your moderator and your IV to reduce multicolinearity and make interpretation easier. Centering can be done using the scale function, which subtracts the mean of a variable from each value in that variable. For more information on the use of centering, see ?scale and any number of statistical textbooks that cover regression (we recommend Cohen, 2008).

A number of packages in R can also be used to conduct and plot moderation analyses, including the moderate.lm function of the QuantPsyc package and the pequod package. However, it is simple to do this “by hand” using traditional multiple regression, as shown here, and the underlying analysis (interacting the moderator and the IV) in these packages is identical to this approach. The rockchalk package used here is one of many graphing and plotting packages available in R and was chosen because it was especially designed for use with regression analyses (unlike the more general graphing options described in Chapters 8 & 9).

3.3 Interpreting Moderation Results

Results are presented similar to regular multiple regression results (see Chapter 10). Since we have significant interactions in this model, there is no need to interpret the separate main effects of either our IV or our moderator.

Our by hand model shows a significant interaction between hours slept and coffee consumption on attention paid to this tutorial (b = .23, SE = .04, p < .001). However, we’ll need to unpack this interaction visually to get a better idea of what this means.

The rockchalk function will automatically plot the simple slopes (1 SD above and 1 SD below the mean) of the moderating effect. This figure shows that those who drank less coffee (the black line) paid more attention with the more sleep that they got last night but paid less attention overall that average (the red line). Those who drank more coffee (the green line) paid more when they slept more as well and paid more attention than average. The difference in the slopes for those who drank more or less coffee shows that coffee consumption moderates the relationship between hours of sleep and attention paid.

4 References and Further Reading

Baron, R., & Kenny, D. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.

Cohen, B. H. (2008). Explaining psychological statistics. John Wiley & Sons.

Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological methods, 15(4), 309.

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological methods, 7(1), 83.

Nie, Y., Lau, S., & Liau, A. K. (2011). Role of academic self-efficacy in moderating the relation between task importance and test anxiety. Learning and Individual Differences, 21(6), 736-741.

Tingley, D., Yamamoto, T., Hirose, K., Keele, L., & Imai, K. (2014). Mediation: R package for causal mediation analysis.

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Mediator vs. Moderator Variables – Definition & Examples

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In the methodology of academic research, understanding the roles of mediators and moderators is crucial in exploring and explaining the relationships among variables. While mediators explain the process through which an effect occurs, moderators influence the strength or direction of these effects. In statistics, mediators and moderators help you understand the relationship between two variables. This article discusses the differences between mediator vs. moderator and a few examples.

Inhaltsverzeichnis

• 1 Mediator vs. moderator variables — In a nutshell
• 2 Definition: Mediator vs. moderator
• 3 Mediator vs. moderator variables
• 4 Mediator vs. moderator examples

Mediator vs. moderator variables — In a nutshell

When learning about mediator vs. moderator variables, you’ll discover that they offer more than a simple study. They give an insight peak into real-world issues. This is because the mediator vs. moderator variables do the followings:

• Compare correlations and causal relationships between two variables
• Emphasize the relationship between variables
• Judge the external validity of your research

Definition: Mediator vs. moderator

A mediator (mediating variable) explains the process in which two variables relate. In contrast, a moderator (moderating variable) affects the direction and strength of this relationship.

Mediator vs. moderator differ because of the following reasons:

• The mediator shows the connection between two variables. For instance, sleep quality (independent variable) affects the quality of your work (dependent variable) through alertness.
• The moderator may be acting upon two variables, changing the strength and direction of that relationship. For instance, mental health status can moderate the relationship between sleep and work quality. The relationship is stronger for people without mental health conditions than for their counterparts.

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Mediator vs. moderator variables

An analysis of mediator vs. moderator variables is essential to understand the distinction between the two better, as explained below:

Mediation analysis

Mediation analysis tests whether a variable is a mediator using one of the two main methods – Analysis of Variance (ANOVA) or linear regression analysis. Mediation may either be partial or complete.

Taking the mediator out of the model in complete mediation eliminates the relationship between an independent and dependent variable . This is because the mediator thoroughly explains the relationship between a dependent and an independent variable.

In partial mediation, the relationship between the dependent and independent variable still exists when you take the mediator out of the model. This is because the mediator partially explains this relationship.

When learning about mediator vs. moderator variables, understand that meeting the following conditions makes a mediation analysis feasible:

• The independent variable must cause the mediator
• The mediator must influence the dependent variable
• The mediator must cause a higher statistical correlation between dependent and independent variables

In simple linear regression, the models describe the connection between variables by fitting a line to the data you observe. Regression makes it possible to estimate how a dependent variable changes when the independent variable(s) change.

Simple linear regression is a parametric test estimating the relationship connecting two quantitative variables. In contrast, ANOVA is a statistical test that analyses the differences between the means of three or more groups. Both simple linear regression and ANOVA use the R program.

Moderation analysis

Moderation analysis tests the effects of a moderator variable on the relationship between a dependent and independent variable.

Multiple linear regression estimates the relationship between one dependent variable and two or more independent variables. You can perform multiple linear regression using the R program or conduct moderation analysis using Analysis of Moment Structures (AMOS).

Moderator variables are also called interactions or products. They may be qualitative (non-numeric values like education, gender, social status, etc.) or quantitative (numeric values like weight, age, test score, etc.) Moderator variables help judge your research’s external validity by identifying limitations when relationships hold.

Mediator vs. moderator examples

Here are some examples that identify the mediator vs. moderator variables as well as independent and dependent variables in research statements:

What is the difference between a mediator and a confounder?

A mediator variable shows the connection between two variables. However, another third variable may affect these two and make them seem related when this is not the case: this third variable is called a confounder variable.

What makes a mediator vs. moderator relevant to a study?

Mediators tell you why and how an effect happens, while moderators help judge the external validity of your research. Both variables are important in studying casual or complex correlational relationships.

How do you know that something is a mediator?

A mediating variable results when an independent variable influences the dependent variable and gives a higher statistical correlation between the dependent and independent variables.

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Mediator Variable

A mediator variable is the variable that causes mediation in the dependent and the independent variables. In other words, it explains the relationship between the dependent variable and the independent variable. The process of complete mediation is defined as the complete intervention caused by the mediator variable. This results in the initial variable no longer affecting the outcome variable. The process of partial mediation is defined as the partial intervention.

The mediation caused by the mediator variable is developed as a mediation model. This model that develops due to the mediation is a causal model. In other words, this means that the mediator variable has been assumed to cause the affect in the outcome variable and not vice versa. In the field of psychology, the mediator variable explains how the external physical events affect the internal psychological significance.

The mediation caused by the variable cannot be defined statistically. On the contrary, statistics can be utilized to assess an assumed meditational model developed by the mediator variable.

Baron and Kenny have given steps for conducting meditational hypotheses . A variable plays a role on the mediator variable under some specific conditions. The conditions are as follows:

If the change in the level of the independent variable significantly accounts for variation in the other variable, then the variable is considered a mediator variable.

If the change in the other variable significantly accounts for the variation in the dependent variable, then the other variable is considered a mediator variable.

If the other variable strongly dominates the significant relationship between the dependent and the independent variable, then the other variable is termed as a mediator variable. In other words, if the relationship between the dependent and the independent variable no longer exists and their variations are controlled by some other variable, then that variable is termed as the mediator variable.

In general, the mediation model examines the relationship between the dependent variable and the independent variable, the relationship between the independent variable and the mediator variable, and the relationship between the dependent variable and the mediator variable.

If the mediator variable is measured with less than perfect consistency, then the effects caused are likely to be biased. In other words, the effect of the mediator variable is likely to be underestimated and the effect of the independent variable and the independent variable is likely to be overestimated. This bias in the variation of the variable is generally due to measurement error. An Instrumental variable is then used to solve this problem of bias in the variability. If this approach does not work, then the researcher is required to explain that since the reliability of the mediator variable is very high, the bias caused is fairly minimal.

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If the mediation caused by the mediator variable is perfect in nature, then the independent variable and the mediator variable are correlated to each other. This correlation is termed as collinearity. If the independent variable explains all the variation caused by the mediator variable, there will not be any unique variation that would explain the dependent variable, and this will thus result in multicollinearity .

Multicollinearity is generally expected in the mediational analysis of the mediator variable and the dependent and the independent variable, and therefore it cannot be avoided by the researcher.

Related Pages:

• Baron & Kenny’s Procedures for Mediational Hypotheses
• Multicollinearity
• Take the Course: Mediation and Moderation

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Key Differences Between Mediating Vs Moderating Variables

Mediators: These are intervening variables that explain the process of how an independent variable (IV) influences a dependent variable (DV). They act as the mechanism, clarifying how the IV impacts the DV.

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Moderators: These are conditioning variables that alter the strength or direction of the relationship between the IV and DV. They act as the context, revealing under what conditions the effect of the IV on the DV is modified.

What Are Mediating Variables 

Mediating variables play a crucial role in understanding the mechanism or process through which an independent variable influences a dependent variable. In simpler terms, they help to explain why or how the relationship between the independent and dependent variables exists.

Mediating variables are often referred to as intermediate variables or mechanisms in dissertations and research papers , because they mediate or intervene in the relationship between the independent and dependent variables. They provide insight into the underlying processes or pathways that link the variables of interest.

For example, let’s say we’re studying the relationship between exercise (independent variable) and mental health (dependent variable). A mediating variable in this scenario could be self-esteem. Through self-esteem, exercise may positively influence mental health by boosting confidence and reducing stress levels. Therefore, self-esteem acts as a mediator in explaining the relationship between exercise and mental health.

How Mediating Variables Work

Mediating variables operate by transmitting the effects of the independent variable to the dependent variable. They serve as a bridge or mechanism through which the influence of the independent variable is conveyed to the dependent variable in a thesis or dissertation .

In statistical terms, mediating variables are often tested using mediation analysis techniques. These techniques assess the indirect effect of the independent variable on the dependent variable through the mediator.

The strength and significance of the indirect effect help researchers determine the extent to which the mediating variable explains the relationship between the independent and dependent variables.

Mediating variables can operate through various mechanisms, including cognitive processes, emotional responses, physiological changes, or behavioural pathways. Understanding how these mechanisms function is essential for accurately identifying and interpreting mediating variables in research studies.

Examples Of Mediating Variables

In a study investigating the relationship between socioeconomic status (independent variable) and academic achievement (dependent variable), the mediating variable could be parental involvement in education . Parental involvement may mediate the relationship between socioeconomic status and academic achievement by influencing factors such as parental support, access to educational resources, and motivation.

In research exploring the impact of job satisfaction (independent variable) on employee performance (dependent variable), a mediating variable could be organizational commitment. Organizational commitment may mediate the relationship by fostering greater engagement, loyalty, and effort among employees, thereby enhancing their performance.

In a study examining the effects of stress (independent variable) on physical health outcomes (dependent variable), a mediating variable could be coping strategies. Coping strategies, such as problem-solving or seeking social support, may mediate the relationship by influencing the body’s physiological response to stress and buffering against its negative effects on health.

What Are Moderating Variables 

Moderating variables, also known as interaction variables, serve to qualify or alter the relationship between an independent variable and a dependent variable. Unlike mediating variables, which explain why or how a relationship exists, moderating variables influence the strength or direction of the relationship under different conditions.

In essence, moderating variables answer the question: “When does the relationship between the independent and dependent variables change?”

Moderating variables introduce variability into the relationship between the independent and dependent variables by affecting the conditions under which the relationship holds or differs. They can highlight the circumstances under which the effects of the independent variable on the dependent variable are enhanced, attenuated, or even reversed.

How Moderating Variables Work

Moderating variables operate by altering the nature of the relationship between the independent and dependent variables across different levels or conditions of the moderating variable.

For instance, let’s consider a study examining the relationship between study time (independent variable) and academic performance (dependent variable), with motivation as a moderating variable. In this scenario, motivation may influence the strength of the relationship between study time and academic performance. Students with high motivation may demonstrate a stronger positive relationship between study time and performance compared to students with low motivation.

Moderating variables are often tested using interaction terms in statistical analyses, such as regression analysis. Interaction terms allow researchers to assess whether the effect of the independent variable on the dependent variable varies depending on different levels or conditions of the moderating variable.

Examples of Moderating Variables

In research investigating the impact of mentoring programs (independent variable) on career advancement (dependent variable) among employees, years of experience could serve as a moderating variable.

The relationship between mentoring programs and career advancement may be stronger for employees with fewer years of experience, as they may benefit more from guidance and support compared to seasoned employees.

In a study exploring the effects of parenting style (independent variable) on adolescent behaviour (dependent variable), family income could act as a moderating variable. The relationship between parenting style and adolescent behaviour may differ based on different levels of family income.

For example, here is a hypothesis based on the above statement, authoritative parenting may have a more positive influence on behaviour among adolescents from higher-income families compared to those from lower-income families.

In research examining the impact of advertising (independent variable) on purchasing behaviour (dependent variable), product relevance could serve as a moderating variable.

The relationship between advertising and purchasing behaviour may be stronger for products that are highly relevant to consumers’ needs or desires compared to products with low relevance.

Mediating variables intervene in the relationship between the independent and dependent variables, explaining the underlying mechanism or process through which the independent variable affects the dependent variable. They provide insight into why or how the relationship exists and are often referred to as intermediate variables.

Moderating variables, on the other hand, qualify or alter the strength or direction of the relationship between the independent and dependent variables under different conditions. They influence the circumstances under which the relationship holds or differs, rather than explaining why or how it exists.

The primary function of mediating variables is to elucidate the mechanism or process through which the independent variable influences the dependent variable. They help researchers understand the underlying pathways or intervening variables that transmit the effect of the independent variable to the dependent variable.

Moderating variables function to qualify or alter the relationship between the independent and dependent variables under different conditions. They introduce variability into the relationship and thesis statement by influencing the strength or direction of the relationship across different levels or conditions of the moderating variable.

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Relationship With The Independent And Dependent Variables

Mediating variables intervene between the independent and dependent variables, mediating or transmitting the effect of the independent variable to the dependent variable. They provide a deeper understanding of the causal mechanisms underlying the relationship between the independent and dependent variables.

Moderating variables interact with the independent and dependent variables, influencing the nature of their relationship under different conditions. They do not intervene in the relationship itself but instead modify or qualify the relationship based on different levels or conditions of the moderating variable.

Consider a study examining the relationship between job training programs (independent variable) and job performance (dependent variable), with skill acquisition as a potential mediator. In this scenario, skill acquisition mediates the relationship between job training programs and job performance by explaining how the acquisition of new skills enhances job performance.

Now, imagine the same study but with job satisfaction as a potential moderator. Here, job satisfaction may moderate the relationship between job training programs and job performance by influencing the extent to which employees benefit from the training programs.

For instance, employees with high job satisfaction may exhibit a stronger positive relationship between training programs and performance compared to those with low job satisfaction.

Frequently Asked Questions

What is the difference between moderating and mediating variables.

Mediating variables explain the mechanism or process through which an independent variable affects a dependent variable, while moderating variables influence the strength or direction of the relationship between the independent and dependent variables under different conditions.

What is an example of a mediating variable?

What is a moderating variable example.

In research on the impact of teaching methods (independent variable) on student performance (dependent variable), student engagement (moderating variable) may influence the strength of the relationship, with higher engagement enhancing the effectiveness of certain teaching methods.

What is the difference between intervening variables and moderating variables?

Intervening variables, like mediating variables, explain the relationship between independent and dependent variables. Moderating variables, however, influence the strength or direction of this relationship under varying conditions, rather than explaining the mechanism itself.

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Mediating and moderating variables explained.

What is the difference between a mediator and a moderator? One of my former academic advisors used to always say “be a walking laboratory”. I think it’s a very poetic way of describing a core feature of psychological research—to come up with theories or explanations for various phenomena we observe. Sometimes there isn’t a clear-cut relation between a dependent and independent variable. In those cases, a mediating variable or a moderating variable can provide a more illustrative account of how dependent (criterion) variables are related to independent (predictor) variables.

A mediating variable explains the relation between the independent (predictor) and the dependent (criterion) variable. It explains how or why there is a relation between two variables. A mediator can be a potential mechanism by which an independent variable can produce changes on a dependent variable. When you fully account for the effect of the mediator, the relation between independent and dependent variables may go away. For instance, imagine that you find a positive association between note-taking and performance on an exam. This association may be explained by number of hours studying, which would be the mediating variable. 

A moderator is a variable that affects the strength of the relation between the predictor and criterion variable. Moderators specify when a relation will hold. It can be qualitative (e.g., sex, race, class…) or quantitative (e.g., drug dosage or level of reward). Moderating variable are typically an interaction term in statistical models. For instance, imagine researchers are evaluating the effects of a new cholesterol drug. The researchers vary the participants in minutes of daily exercise (predictor/independent variable) and measure their cholesterol levels after 30 days (criterion/dependent variable). They find that at low drug doses, there is a small association between exercise and cholesterol levels, but at high drug doses, there is a huge association between exercise and cholesterol levels. Drug dosage moderates the association between exercise and cholesterol levels. 

Let’s look at some examples in psychological research.

A recent paper by Frank, Amso, & Johnson (2014) examined the developmental relationship between early perceptual abilities and face perception in infancy.  In the study, the authors tested visual search abilities of 3-, 6-, and 9-month-old infants. Infants were shown panels of red rods against a black background. One of the rods was either slanted at a diagonal or moved back and forth. Accuracy at looking at the slanted or moving rod was calculated as “visual search accuracy”. Infants also viewed excerpts from Charlie Brown and Sesame Street and relative amount of time spent viewing faces was measured. They found that infants looked more at faces and were more accurate at identifying a moving target with age. This effect was fully mediated by visual search accuracy for moving rods. That is, developmental improvements in visual search accuracy fully accounted for the amount of time infants looked at faces.

A great example of a moderator comes from Cohen and Willis, 1985. In that study, the authors proposed a stress-buffering hypothesis. Prior research had suggested a main effect of social support on quality of life. However, Cohen and Willis demonstrated that the relation between social support and quality of life depends on an individual’s stress level. Someone who experiences a lot of stress, but has good social support, will show better outcomes (fewer symptoms of depression, anxiety, fatigue…) than someone with low social support. Social support is the moderating variable. 

These examples should clarify the difference between mediating and moderating variables. Both types of variables provide interesting explanatory means to describe psychological phenomena.

Frequently asked questions

What’s the difference between a confounder and a mediator.

A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.

Frequently asked questions: Methodology

Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.

Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .

Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.

Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.

Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.

A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”

To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.

Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.

While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.

Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.

Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.

• Convergent validity indicates whether a test that is designed to measure a particular construct correlates with other tests that assess the same or similar construct.
• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related. This type of validity is also called divergent validity .

You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.

• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related

Content validity shows you how accurately a test or other measurement method taps  into the various aspects of the specific construct you are researching.

In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.

The higher the content validity, the more accurate the measurement of the construct.

If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.

Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.

When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.

For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).

On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.

A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.

Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.

Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.

Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .

This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .

Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.

Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .

Snowball sampling is best used in the following cases:

• If there is no sampling frame available (e.g., people with a rare disease)
• If the population of interest is hard to access or locate (e.g., people experiencing homelessness)
• If the research focuses on a sensitive topic (e.g., extramarital affairs)

The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.

Reproducibility and replicability are related terms.

• Reproducing research entails reanalyzing the existing data in the same manner.
• Replicating (or repeating ) the research entails reconducting the entire analysis, including the collection of new data . 
• A successful reproduction shows that the data analyses were conducted in a fair and honest manner.
• A successful replication shows that the reliability of the results is high.

Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.

The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).

Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.

A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.

The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.

Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.

On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.

Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.

However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.

In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .

It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.

While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.

Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.

Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.

Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.

Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.

You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .

When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.

Construct validity is often considered the overarching type of measurement validity ,  because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.

Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.

There are two subtypes of construct validity.

• Convergent validity : The extent to which your measure corresponds to measures of related constructs
• Discriminant validity : The extent to which your measure is unrelated or negatively related to measures of distinct constructs

Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.

The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.

Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.

You can think of naturalistic observation as “people watching” with a purpose.

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.

In statistics, dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation).

As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.

Overall, your focus group questions should be:

• Open-ended and flexible
• Impossible to answer with “yes” or “no” (questions that start with “why” or “how” are often best)
• Unambiguous, getting straight to the point while still stimulating discussion
• Unbiased and neutral

A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when: 

• You already have a very clear understanding of your topic. Perhaps significant research has already been conducted, or you have done some prior research yourself, but you already possess a baseline for designing strong structured questions.
• You are constrained in terms of time or resources and need to analyze your data quickly and efficiently.
• Your research question depends on strong parity between participants, with environmental conditions held constant.

More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.

This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.

The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.

There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.

A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:

• You have prior interview experience. Spontaneous questions are deceptively challenging, and it’s easy to accidentally ask a leading question or make a participant uncomfortable.
• Your research question is exploratory in nature. Participant answers can guide future research questions and help you develop a more robust knowledge base for future research.

An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.

Unstructured interviews are best used when:

• You are an experienced interviewer and have a very strong background in your research topic, since it is challenging to ask spontaneous, colloquial questions.
• Your research question is exploratory in nature. While you may have developed hypotheses, you are open to discovering new or shifting viewpoints through the interview process.
• You are seeking descriptive data, and are ready to ask questions that will deepen and contextualize your initial thoughts and hypotheses.
• Your research depends on forming connections with your participants and making them feel comfortable revealing deeper emotions, lived experiences, or thoughts.

The four most common types of interviews are:

• Structured interviews : The questions are predetermined in both topic and order. 
• Semi-structured interviews : A few questions are predetermined, but other questions aren’t planned.
• Unstructured interviews : None of the questions are predetermined.
• Focus group interviews : The questions are presented to a group instead of one individual.

Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .

In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Triangulation can help:

• Reduce research bias that comes from using a single method, theory, or investigator
• Enhance validity by approaching the same topic with different tools
• Establish credibility by giving you a complete picture of the research problem

But triangulation can also pose problems:

• It’s time-consuming and labor-intensive, often involving an interdisciplinary team.
• Your results may be inconsistent or even contradictory.

There are four main types of triangulation :

• Data triangulation : Using data from different times, spaces, and people
• Investigator triangulation : Involving multiple researchers in collecting or analyzing data
• Theory triangulation : Using varying theoretical perspectives in your research
• Methodological triangulation : Using different methodologies to approach the same topic

Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.

However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure. 

Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.

Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.

Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.

In general, the peer review process follows the following steps: 

• First, the author submits the manuscript to the editor.
• Reject the manuscript and send it back to author, or 
• Send it onward to the selected peer reviewer(s) 
• Next, the peer review process occurs. The reviewer provides feedback, addressing any major or minor issues with the manuscript, and gives their advice regarding what edits should be made. 
• Lastly, the edited manuscript is sent back to the author. They input the edits, and resubmit it to the editor for publication.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.

Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.

Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.

Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.

For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.

After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.

Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.

These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.

Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.

Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.

Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.

In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.

Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.

These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.

Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .

You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.

You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.

Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.

Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.

Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .

These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.

In multistage sampling , you can use probability or non-probability sampling methods .

For a probability sample, you have to conduct probability sampling at every stage.

You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.

Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.

But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .

These are four of the most common mixed methods designs :

• Convergent parallel: Quantitative and qualitative data are collected at the same time and analyzed separately. After both analyses are complete, compare your results to draw overall conclusions. 
• Embedded: Quantitative and qualitative data are collected at the same time, but within a larger quantitative or qualitative design. One type of data is secondary to the other.
• Explanatory sequential: Quantitative data is collected and analyzed first, followed by qualitative data. You can use this design if you think your qualitative data will explain and contextualize your quantitative findings.
• Exploratory sequential: Qualitative data is collected and analyzed first, followed by quantitative data. You can use this design if you think the quantitative data will confirm or validate your qualitative findings.

Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.

Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.

In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.

This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

Quantitative research designs can be divided into two main categories:

• Correlational and descriptive designs are used to investigate characteristics, averages, trends, and associations between variables.
• Experimental and quasi-experimental designs are used to test causal relationships .

Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.

A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.

The priorities of a research design can vary depending on the field, but you usually have to specify:

• Your research questions and/or hypotheses
• Your overall approach (e.g., qualitative or quantitative )
• The type of design you’re using (e.g., a survey , experiment , or case study )
• Your sampling methods or criteria for selecting subjects
• Your data collection methods (e.g., questionnaires , observations)
• Your data collection procedures (e.g., operationalization , timing and data management)
• Your data analysis methods (e.g., statistical tests  or thematic analysis )

A research design is a strategy for answering your   research question . It defines your overall approach and determines how you will collect and analyze data.

Questionnaires can be self-administered or researcher-administered.

Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.

Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.

You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.

Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.

Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.

Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.

While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

Random error  is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .

You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.

Systematic error is generally a bigger problem in research.

With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.

Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.

Random and systematic error are two types of measurement error.

Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).

Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).

On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.

• If you have quantitative variables , use a scatterplot or a line graph.
• If your response variable is categorical, use a scatterplot or a line graph.
• If your explanatory variable is categorical, use a bar graph.

The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.

The difference between explanatory and response variables is simple:

• An explanatory variable is the expected cause, and it explains the results.
• A response variable is the expected effect, and it responds to other variables.

In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:

• A control group that receives a standard treatment, a fake treatment, or no treatment.
• Random assignment of participants to ensure the groups are equivalent.

Depending on your study topic, there are various other methods of controlling variables .

There are 4 main types of extraneous variables :

• Demand characteristics : environmental cues that encourage participants to conform to researchers’ expectations.
• Experimenter effects : unintentional actions by researchers that influence study outcomes.
• Situational variables : environmental variables that alter participants’ behaviors.
• Participant variables : any characteristic or aspect of a participant’s background that could affect study results.

An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.

A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.

In a factorial design, multiple independent variables are tested.

If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.

Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .

Advantages:

• Only requires small samples
• Statistically powerful
• Removes the effects of individual differences on the outcomes

Disadvantages:

• Internal validity threats reduce the likelihood of establishing a direct relationship between variables
• Time-related effects, such as growth, can influence the outcomes
• Carryover effects mean that the specific order of different treatments affect the outcomes

While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .

• Prevents carryover effects of learning and fatigue.
• Shorter study duration.
• Needs larger samples for high power.
• Uses more resources to recruit participants, administer sessions, cover costs, etc.
• Individual differences may be an alternative explanation for results.

Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.

Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.

Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .

If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .

A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.

Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.

Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.

If something is a mediating variable :

• It’s caused by the independent variable .
• It influences the dependent variable
• When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered.

A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method.

Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.

However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.

There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.

• In single-stage sampling , you collect data from every unit within the selected clusters.
• In double-stage sampling , you select a random sample of units from within the clusters.
• In multi-stage sampling , you repeat the procedure of randomly sampling elements from within the clusters until you have reached a manageable sample.

Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.

The clusters should ideally each be mini-representations of the population as a whole.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.

Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .

If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.

• In a single-blind study , only the participants are blinded.
• In a double-blind study , both participants and experimenters are blinded.
• In a triple-blind study , the assignment is hidden not only from participants and experimenters, but also from the researchers analyzing the data.

Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .

A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.

However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).

For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.

In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).

The process of turning abstract concepts into measurable variables and indicators is called operationalization .

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organize your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organization to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

When conducting research, collecting original data has significant advantages:

• You can tailor data collection to your specific research aims (e.g. understanding the needs of your consumers or user testing your website)
• You can control and standardize the process for high reliability and validity (e.g. choosing appropriate measurements and sampling methods )

However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.

In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.

In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .

In statistical control , you include potential confounders as variables in your regression .

In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!

You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .

• The type of soda – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.

Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .

Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.

Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.

A sampling error is the difference between a population parameter and a sample statistic .

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.

The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).

The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.

Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .

Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.

Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.

Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.

The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .

Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.

Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.

There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .

Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .

External validity is the extent to which your results can be generalized to other contexts.

The validity of your experiment depends on your experimental design .

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Guidelines for the Investigation of Mediating Variables in Business Research

David p. mackinnon.

Department of Psychology, Arizona State University, Tempe, AZ 85287-1104, USA

Stefany Coxe

Amanda n. baraldi.

Business theories often specify the mediating mechanisms by which a predictor variable affects an outcome variable. In the last 30 years, investigations of mediating processes have become more widespread with corresponding developments in statistical methods to conduct these tests. The purpose of this article is to provide guidelines for mediation studies by focusing on decisions made prior to the research study that affect the clarity of conclusions from a mediation study, the statistical models for mediation analysis, and methods to improve interpretation of mediation results after the research study. Throughout this article, the importance of a program of experimental and observational research for investigating mediating mechanisms is emphasized.

This piece is the sixth in the Method Corner series featured by this Journal. This series focuses on some of the methodological issues encountered by business psychologists. Past pieces described aggregation of multidimensional constructs ( Johnson et al. 2011 ), methods to identify the importance of regression models ( Tonidandel and LeBreton 2011 ), polynomial regression ( Shanock et al. 2010 ), and method bias ( Conway and Lance 2010 ). The detection of mediators is also a methodological issue important to business psychology. Many theories in business research postulate a mediator ( M ) that transmits the effect of a predictor variable ( X ) to an outcome variable ( Y ) in a causal sequence such that X causes M and M causes Y. In more general terms, a mediating variable explains the process by which one variable causes another. Theories across many disciplines focus on mediating processes and many research questions lend themselves to these models. In intervention research, theory and prior empirical research determine which mediating variables are included as part of study design. If an intervention substantially changes a mediating variable that is causally related to an outcome, then a change in the mediator will produce a change in the outcome. For example, if organizational skills create more efficiency among employees, an employee program teaching organizational skills should increase organizational skills, resulting in greater employee efficiency.

Mediation theory is also applicable to studies that do not include an intervention. An observational variable can serve as a predictor or antecedent variable in a mediation model. For example, it has been suggested that the effects of psychological climate perceptions on performance are mediated by employee work attitudes ( Parker et al. 2003 ), where psychological climate does not represent an intervention but is an observed variable measured for each employee. Psychological climate is an observed variable and is not randomized, thus limiting conclusions regarding the causal nature of the mediating process. The lack of randomization makes it difficult to rule out alternative explanations of the relationship. Examples of alternative explanations include changes in employee work attitudes causing changes in psychological climate or that there is another variable causing changes in both psychological climate and employee work attitudes.

Since the classic articles on mediation by Alwin and Hauser (1975) , Judd and Kenny (1981) , James and Brett (1984) , and Baron and Kenny (1986) , thousands of articles have applied mediation analysis in many fields, including psychology (e.g., Fritz and MacKinnon 2007 ; Mackinnon et al. 2002 ), medicine ( Begg and Leung 2000 ), business ( Chiaburu and Byrne 2009 ; Hung et al. 2009 ), and many other fields (see MacKinnon 2008 ). The popularity of mediation analysis is growing because the method focuses on what is often the central scientific hypothesis: the process by which one variable affects another.

Mediators and Moderators and Confounders and Covariates

Before delving into the details of mediation analysis, we begin with definitions of several key terms that come into play when considering how three variables can be related. These potential relationships are important to understanding when mediation analysis is the appropriate choice for answering specific research questions. When considering the relationship of an independent variable ( X ) and a dependent variable ( Y ), an additional third variable ( Z ) may fill one of several roles. Each role for the third variable describes both a different theoretical model of the relationship between X , Y , and Z , as well as a different approach to the statistical analysis.

A third variable that is both unrelated to the predictor X and has little to no effect on the relationship between X and Y is called a covariate ; a covariate is not often of primary theoretical interest but is used to account for additional variation in the outcome Y. A third variable, Z , can be related to both X and Y in such a way that the inclusion of Z changes the relationship between X and Y. Such a variable is called a confounder , because it confounds or conceals the simple relation between X and Y (see Greenland and Morgenstern 2001 for information on confounders). A variable that is a moderator affects the direction and strength of the relationship between two variables such that the relationship between X and Y is different for varying levels of Z . A moderator is typically expressed as an interaction between the independent variable and the moderator, such that the effect of the independent variable on the dependent variable is conditional on the level of the moderator. A moderator may be a factor in an experimental manipulation with random assignment to varying levels (e.g., time between treatments) or a moderator may be a non-manipulated variable (e.g., age or gender). The understanding of a moderator effect is often a critical component to the generalizability of research findings to other populations, locations, and domains.

The focus of this article is on the third variable as a mediator variable. A simple mediation model is shown in Fig. 1 . A mediation relationship is one in which the independent variable causes the mediator which then causes the dependent variable ( Mackinnon 2008 ). Although variations of the definition of mediation exist in the literature (e.g., Holmbeck 1997 identifies terminological inconsistencies), we will assume a mediator to be a variable that transmits the effect of an independent variable to a dependent variable. Although the terms “mediator” and “mediated effect” will be used throughout this manuscript, other terms are used to describe these variables and effects in different areas of research. For example, the “mediated effect” is often referred to as the “indirect effect” because it represents the effect of the independent variable effect on the dependent variable effect via the mediator variable (i.e., indirectly rather than directly). The “mediator” is sometimes called the “intervening variable” because it is intermediate between the independent and the dependent variables.

Illustration of the mediation model using path diagrams

Though the primary focus of this article is mediation analysis, we feel obligated to spend some time comparing mediation and moderation effects. Both mediation effects and moderation effects are examined in psychological research with some frequency and involve a third variable. This often results in difficulties for researchers who are inexperienced in the nuances of these two types of effects; some may be confused about whether they should be performing a mediation analysis or not, while others may perform a mediation when their research question actually involves moderation (or vice versa). We would like to emphasize that determining whether to investigate a mediator effect versus a moderator effect depends entirely on the research question of interest. In general, moderators provide information on the circumstance under which effects are present , whereas mediators address the mechanisms by which an effect occurs . Mediation effects are exemplified by the question “How did it work?” because mediation examines the means by which the intervention affects outcomes. Moderation effects are exemplified by the question “Who did it work for?” because moderation examines which subgroups (e.g., boys vs. girls) show effects of the intervention on outcomes ( James and Brett 1984 ; Fairchild and MacKinnon 2008 ; MacKinnon 2011 ).

Mediation in Business Psychology

Theories across many substantive disciplines focus on mediating processes as explanations for how and why an antecedent variable is related to an outcome variable; business psychology is no exception. A casual review of the Journal of Business and Psychology found that between 2007 and 2010, over 30 articles purported to be addressing theoretical questions involving mediation or using mediation analysis. Of these, more than 20 articles cited classic mediation sources such as Baron and Kenny (1986) and Sobel (1982) .

Basic Mediation Model

A simple mediation model with one independent variable, X , one mediator, M , and one outcome variable, Y , provides information to investigate mediation by estimating three regression equations. The relationships between X , M , and Y are shown as path diagrams in Fig. 1 . Consider the study by Leach et al. (2009) , in which the relationship between meeting design characteristics ( design ) and perceived meeting effectiveness ( perception ) was mediated by attendees’ involvement during the meeting ( involvement ). In this example, design is the independent variable X , perception is the outcome variable Y , and involvement is the mediator M .

Equation (1) represents the relationship between the independent variable X and the dependent variable Y :

In terms of the example, this equation represents the relationship between design and perception , where the coefficient c represents the effect of design on perception , i is the intercept, and e 1 is the residual variance (i.e., the part of perception that is not explained by design ). Equation 2 represents the relationship between the independent variable X and the mediator M :

In the example, this equation represents the relationship between design and involvement . Equation 3 represents the somewhat more complex relationship between X , M , and Y :

This equation shows how perception can be predicted by both design and involvement . Since there are two predictors here, both c ′ and b are partial regression coefficients ; each regression coefficient is the effect of that predictor on the outcome, controlling for the effect of the other predictor. Using the example, the b coefficient is the effect of involvement on perception , controlling for design , and the c ′ coefficient is the effect of design on perception , controlling for involvement . There are several important assumptions of this single mediator model, including temporal precedence of the X → M → Y relationship and the assumption that no variables are omitted from the relationship; these assumptions, some of which are testable and some of which are not testable, are discussed later. As an aside, although we are presenting the mediation model in terms of three regression equations, regression is a special case of a structural equation model (SEM) and the methods described can often be done in either the regression or the structural equation model framework. However, structural equation modeling allows for more comprehensive modeling of measurement error, change over time, and multivariate dependent variables that are impossible or cumbersome with multiple regression analysis.

Decisions Prior to Mediation Analysis

Despite the extensive use of complex statistical modeling in the behavioral sciences, the quality of a research project is largely determined by the design decisions that are made before any analysis is done and even before the study is conducted. The conceptualization of a mediation analysis requires forethought about the relationships between the variables of interest and the theoretical meaning behind those relationships. Several other issues are important for researchers to consider prior to conducting a mediation analysis. Some of these decisions are common to all studies, but we will focus on the decisions that are of particular importance when planning a mediation analysis. In any study, a researcher must address the issues of manipulation versus observation, omitted variables that may be influencing results, reliability and validity of measures, and sample size to adequately detect effects. In addition, the theoretical task of choosing which variables will serve as mediators is critical. Table 1 summarizes some of the issues for consideration prior, during, and after mediation analysis.

Summary of issues before, during, and after mediation analysis

Randomization

Random assignment of subjects to experimental conditions is the gold standard for making causal inference about the relationship between two variables. In the case where X represents randomly assigned condition, the coefficients a and c represent causal effects under certain reasonable assumptions. The coefficients b and c ′ represent adjusted relations. Even though there is random assignment to experimental groups, the b and c ′ coefficients do not have a clear interpretation as causal effects because participants select their own value of the mediating variable. This ambiguity of self-selection to value of the mediator is a primary focus of modern causal inference approaches to mediation to be described later. Random assignment to the levels of X is common in many mediation studies but a second random assignment to the value of M (called “double randomization”) is rare and often difficult for ethical or logistical reasons. In double randomization studies, one randomized study evaluates the X to M relation and a second randomized study evaluates the M to Y relation adjusting for X ( MacKinnon 2008 ; MacKinnon and Pirlott 2011 ; Stone-Romero and Rosopa 2011 ; Spencer et al. 2005 ).

A second type of design to obtain some level of randomization of the mediating variable is called a blockage design. In this design, a manipulation is used to block or prevent the mediation process thereby demonstrating that the mediator was crucial ( MacKinnon 2008 ; Robins and Greenland 1992 ). If the blocking manipulation removes the mediation relation, this provides support for a mediational process. As an example of blockage design, return to the example in which the relationship between meeting design characteristics ( design ) and perceived meeting effectiveness ( perception ) was mediated by attendees’ involvement during the meeting ( involvement ). Using a blockage design, participants in the study may be assigned to a blocking treatment condition where deep involvement in the meeting was prevented (e.g., by a mildly distracting task or by not allowing communication with others at the meeting) in addition to the manipulation of the meeting design characteristics. If involvement is a mediator of the design-to-perception relationship, mediation effects should be related to the amount of involvement across groups and participants in the blockage treatment condition should not show as large of a mediated effect as participants in the control condition because the mediating process was blocked. A closely related type of design is the enhancement design which seeks to enhance (rather than eliminate as in the blockage design) the mediated effect in the treatment group. In the meeting perception example, participants in the study may be assigned to an enhancement treatment condition which creates even deeper involvement in the meeting (e.g., by telling them that a promotion will be offered to the person who learns the most from the meeting). If involvement is a mediator of the design to perception relationship, mediation effects should again be related to the amount of involvement across groups and participants in the enhancement treatment condition should show larger mediated effects than the participants in other examples (see other examples in MacKinnon 2008 ; Maxwell et al. 1986 ; Klesges et al. 1986 ).

Several options exist to strengthen causal arguments when randomization of X and/or M is not possible, including the selection of covariates before the study that may explain the X to M and the M to Y relations. Similarly, these covariates may be used in a propensity score model to address omitted variable explanations of mediated effects ( Coffman 2011 ; Jo et al. 2011 ). Instrumental variables may be used to estimate causal effects when randomization (particularly of X ) is not feasible ( MacKinnon 2008 , Chap. 13; Lockhart et al. 2010 ). In addition to statistical adjustments, experimental design methods such as the blockage and enhancement designs can strengthen causal interpretation by focusing on testing the consistency and specificity of mediation relations across different contexts, subgroups, and measures of the mediating and outcome variables ( MacKinnon and Pirlott 2011 ).

Omitted Variables

The term “ignorability” refers to the assumption that the relationship between two variables is unaffected by other variables (such as covariates, confounders, or moderators). Mediation analysis contains two major relationships that may be influenced by other variables: the X → M relationship and the M → Y relationship. Mediation therefore assumes a two part sequential ignorability assumption. There are many issues that arise in the causal interpretation of the single mediator model which stem from the two part sequential ignorability assumption ( Imai et al. 2010 ; Lynch et al. 2008 ; ten Have et al. 2007 ). The ignorability assumption for the X → M relationship can largely be addressed by randomizing the levels of X ; the ignorability assumption for the M → Y relationship is more difficult to justify and represents a challenging aspect of mediation analysis. Ignorability for the M to Y relation assumes randomization of participants at each level of X . In most research, this randomization is not possible and participants usually self-select their value of M. The extent to which sequential ignorability is a valid assumption may differ depending on the type of mediating variable. For example, if the mediators are selected because theory and prior empirical research suggest that they are causally related to the outcome variable, it may be reasonable to conclude that the b effect is known. Thus, it is only required that the levels of M be changed. In this case, the manipulation that changes the X to M relation will have the same expected change in the M to Y relation. Replication experiments can also further clarify the actual mediator from a host of other potential omitted variables. In this respect, replication studies with different manipulations are critical for identifying mediating variables.

Reliability

As in all research, the reliability and validity of proposed measures are best assessed prior to conducting the study. The reliability of a measurement is the extent to which a measure consistently reproduces values of the underlying true score. Valid measures measure the construct they are designed to measure. A program of research is typically needed to develop reliable and valid measures. Measurement is critical to mediation analysis and the search for mediating variables can be considered a measurement problem where science is advanced by more accurate measures of the mediating process ( MacKinnon 2008 ).

Studies on measurement error highlight the need for reliable measures when detecting a mediator. Hoyle and Kenny (1999) demonstrated that as the reliability of M decreases (i.e., as the reliability coefficient departs from one), the observed effect of M on the Y and b is underestimated and the observed effect of X on the Y and c ′ is overestimated. This results in an underestimation of the mediated effect and a decrease in the statistical power to detect the mediated effect. Due to the potential impact unreliability has on masking mediational effects, reliable mediating measures are crucial. One way to increase reliability is to obtain multiple indicators of the variable of interest and create a latent construct representing the variable of interest. The use of a latent variable model allows the estimation of associations between latent variables which are free of measurement error. However, using a latent variable model requires sufficiently large sample sizes and this is not always plausible. Modeling approaches which incorporate the effects of multiple methods such as multiple reporters or item types may yield more reliable relations than those ignoring method effects ( Geiser and Lockhart, under review ) and may provide promising tools for investigating mediation effects with more reliable measures.

Sample Size

Selection of sample size for adequate statistical power is an important part of designing any study. Although a large a sample size is ideal, sample size is often limited for reasons outside the control of a researcher, such as a small available population (e.g., local individuals of a specific age) or financial issues (e.g., excessive time or cost of measurements). However, even with an extremely large sample size, it will be important to obtain some measure of effect size to judge the importance or size of an effect. Mediation studies have traditionally been underpowered because the sample size requirements are much larger than those of simpler models, such as simple linear regression. Fritz and MacKinnon (2007) used simulations to determine sample sizes to obtain 0.80 power for small, medium, and large effect sizes in the single mediator model. A sample size of approximately 74 is required to detect a mediation effect when the path for the X to M relation and the M to Y relation is medium. A more complex mediation model would require a larger sample. The careful use of covariates can decrease the required sample size and repeated measures and longitudinal data can also improve the ability to detect effects. Required sample size and statistical power for more complicated mediation models has been outlined by Thoemmes et al. (2010) using a Monte Carlo approach in a covariance structure analysis program.

Choosing Mediators

The theoretical interpretation of the links in a mediation model can be thought of in terms of the theory for the process underlying the manipulations. These two processes are called the action theory and the conceptual theory ( Chen 1990 ; MacKinnon 2008 ). As shown in Fig. 2 , action theory corresponds to how the manipulation will affect the mediators (the relationship between X and M ) and conceptual theory focuses on how the mediators are related to the outcome of interest (the relationship between M and Y ). Consider an intervention designed to increase knowledge of the benefits of exercise and nutrition designed to increase employee well-being, which is measured as the number of sick days the employee uses. The action theory is that the program will increase the employees’ knowledge of exercise and nutrition. Conceptual theory says that knowledge of the benefits of exercise and nutrition will increase employee well-being, reducing the number of sick days. The use of action and conceptual theory can be used to demonstrate how a manipulation leads to changes in the dependent variable ( Ashby 1956 ; Lipsey 1993 ; MacKinnon 2008 ).

Action and conceptual theory

The informed choice of possible mediators often emerges from action and conceptual theory. Typically, conceptual theory is based on prior research that provides information about the relationship between a potential mediator and the outcome of interest. However, action theory can also inform the selection of mediators, based on what variables are able to be changed by experimental manipulation or intervention. For example, an experimental manipulation can change an individual’s beliefs about a product, but it typically cannot change aspects of an individual’s personality ( Table 1 ).

Table 2 summarizes six methods suggested by Mackinnon (2008) to choose mediators. Depending on the information available and the current state of a particular research area, any one of the six approaches may be a viable approach to choosing mediators. When the area of study is well-researched and a great deal of prior research is available on which to build, mediators can be chosen by performing a literature review to determine empirical relations between potential mediating variables and the outcome variable of interest, by targeting mediators based on an established theoretical framework in the area of substantive research, or based on prior mediation research. In particular, the “theory-driven” approach has received considerable support in the literature ( Chen 1990 ; Lipsey 1993 ; Sidani and Sechrest 1999 ). When the area of research is new and little prior research is available to guide the selection of mediator variables, different approaches to selecting mediators must be employed. Mediators may be identified by studying correlates of the outcome measure to identify mediators based on the conceptual theory of the outcome, using qualitative methods such as focus groups, or on the basis of common sense or intuition about what seems to be the best target of a program. Although these are less scientifically driven methods, they may be a good approach in newly developing fields.

Methods of choosing /mediators

Testing Multiple Mediators

Many studies include more than one mediator of an X – Y relationship. For example, Chen and Chiu (2008) examined several mediators of the relationship between supervisor support of employees and employee organizational citizenship behavior. They found that job satisfaction, person-organization fit, and job tension mediated the relationship between supervisor support and citizenship behavior. When there are multiple mediators, a simple approach is to evaluate one mediator at a time. Using the Chen and Chiu study as an example, one may initially examine the supervisor support → job satisfaction → citizenship behavior relationship. Looking at a single mediator at a time is a useful approach because specific theoretical hypotheses often focus on single mediators rather than groups of mediators. It is also wise to examine any potential moderator or interaction effects (discussed in more detail shortly) at the single-mediator stage. If the study involves many mediators, it will be necessary to implement some control for experiment-wise error due to multiple tests; the alpha or Type I error rate increases rapidly with multiple tests.

A model including all measured mediators should be estimated in addition to single mediator models. This is accomplished by expanding Eq. 3 to include all mediating variables. For example, in the case of three mediating variables, Eq. 3 can be reexpressed as:

Evaluating a model that includes all measured mediators is important because it is possible that the effect of a mediator may change in the presence of other mediators. Recall that the b and c ′ coefficients in these models are partial regression coefficients controlling for all other predictors, so the exclusion of some mediators could potentially change these values in the complete model. Including all measured mediators also produces a model which more closely matches reality, where all potential mediators are present. An additional benefit of multiple mediator models is the identification of mediation pathways that lead to beneficial relations on the outcome measures and mediating pathways that are actually counterproductive. These inconsistent mediation models, defined as mediation models where at least one mediated effect has a different sign than the direct effect, are more clearly identified in multiple mediator models ( MacKinnon et al. 2000 ).

Moderator Effects in Mediation Models

As previously described, moderation is an effect involving a third variable that changes the direction or magnitude of the relationship between two other variables. For example, the relationship between stress and health is moderated by social contacts; individuals with many friends show little relationship between stress and health while individuals with few friends have a strong positive relationship between stress and health ( Cohen and Wills 1985 ).

Moderator relationships can occur with mediation relationships. The combination of moderation and mediation can take on several forms. We briefly discuss these situations involving both mediation and moderation because they occur frequently within psychological research and can be confusing to understand. Moderation of a mediated effect occurs when a moderator variable ( Z ) affects the direction or strength of any or all the mediation regression coefficients. There are a number of ways to incorporate moderator effects into a mediation model. If the moderator is binary, such as gender, moderator effects can be evaluated by conducting analyses by group. Individual regression coefficients or estimates of the mediated effect can be compared across groups using t tests (see MacKinnon 2008 , p. 292). This method is straightforward and makes interpretation simpler, but it can only be used for binary moderators. More complex approaches are needed for continuous moderators and moderators with several categories.

In order to include continuous moderators in a mediation model, the moderators are incorporated into Eqs. 1 – 3 as interaction terms. For example, if a continuous variable, Z, is hypothesized to moderate the effect of X on M , Eq. 2 becomes:

where coefficient f represents the main or conditional effect of the moderator Z on the mediator M and coefficient g represents the interaction or moderator effect of X and Z . Tein et al. (2004) present a framework for testing moderation of all four mediation paths. This framework also allows for the inclusion of baseline covariates. For example, in evaluating a program to improve management and supervisor skills, a researcher may wish to control for pre-program level of skill by including this variable as a covariate.

Timing and Longitudinal Effects

The mediation model is a longitudinal model in that X precedes M and M precedes Y. However, in practice, tests of mediation may be conducted using cross-sectional data. There are a number of problems and limitations with using cross-sectional data to investigate longitudinal mediational processes, as outlined by several researchers ( Cheong et al. 2003 ; Cole and Maxwell 2003 ; MacKinnon 2008 ; Maxwell and Cole 2007 ). Conceptually, a problem arises because mediation is inherently a process that unfolds over time and cross-sectional data do not measure this unfolding over time. Statistically, several studies have shown that estimates of the cross-sectional-mediated effect are severely biased when compared to the estimates of the longitudinal mediated effect ( Maxwell and Cole 2007 ). The bias may be either positive or negative, further complicating the use of cross-sectional data.

The best-designed studies employ repeated measures because power to detect mediated effects is greatly enhanced. In addition, longitudinal studies allow for the measure of change in response to a manipulation ( Cohen 1988 ; Singer and Willet 2003 ). The methodological literature has emphasized the importance of temporal precedence in the investigation of mediation ( Gollob and Reichardt 1991 ; Judd and Kenny 1981 ; Kraemer et al. 2002 ; MacKinnon 1994 ) and has described methods for assessing longitudinal mediation ( Cheong et al. 2003 ; Cole and Maxwell 2003 ; MacKinnon 2008 ; Maxwell and Cole 2007 ). The evaluation of longitudinal mediation models is an important step in advancing mediation methods. Although there are several choices of longitudinal models described in the literature such as autoregressive models and latent change score models, latent growth curve models are a common choice for longitudinal mediation models ( Cheong 2002 ; Cheong et al. 2003 ). More detailed information on longitudinal mediation models can be found in Mitchell and James (2001) and MacKinnon (2008) .

Although longitudinal mediation modeling is the preferred method for evaluation of the mediation process, there are situations where only cross-sectional data are available. For example, secondary mediation analysis of data from a previously collected study may require the use of cross-sectional data. In this case, estimates of the cross-sectional mediated effect may not reflect the longitudinal mediated effect and researchers must provide evidence for temporal relations from theory or empirical research.

Decisions During Mediation Analysis

Recall the path model in Fig. 1 , which shows the directional relations between X , M , and Y for the single-mediator model. For the mediation framework that is most commonly used in psychology ( Baron and Kenny 1986 ; MacKinnon 2008 ), three regression equations are used to describe the relations in this model. These regression equations describe the effect of X on Y ( Eq. 1 ), the effect of X on M ( Eq. 2 ), and the effect of X on Y , controlling for M ( Eq. 3 ). The c coefficient is the total effect of X on Y. The c ′ coefficient is the direct effect of X on Y , controlling for M . The a coefficient corresponds to the “action theory” for the model, whereas the b coefficient corresponds to the “conceptual theory” for the model ( Fig. 2 ).

Baron and Kenny (1986) proposed a causal steps approach to testing whether statistical mediation is present in such a model. The causal steps approach describes a series of tests of regression coefficients that, together, can show mediation is occurring. The first step in this approach is to test whether changes in X produce changes in Y , i.e., whether there is an effect to be mediated. This is determined by the significance of the c regression coefficient in Eq. 1 . If there is no relation between X and Y , the causal steps approach stops. If there is a relation between X and Y , the next step is to determine if there is a relation between X and M by testing the a regression coefficient in Eq. 2 . Given that the independent variable significantly affects the mediator, the next step is to test whether M is related to Y , after controlling for the effect of X on Y. This is shown by testing the significance of the b regression coefficient in Eq. 3 . Finally, it must be shown that the effect of X upon Y , after controlling for M , is not significantly different than zero. The test of the c ′ coefficient in Eq. 3 should not be significant.

The requirements of the causal steps approach that c ≠ 0 and that c ′ = 0 results in reduced statistical power to detect a mediated effect. The requirement that c ≠ 0 is problematic because statistical tests are not absolute; there is always the potential for a Type I or Type II error in this decision. Additionally, if subgroups of participants (e.g., men vs. women) have opposing effects, ignoring these subgroups could result in a non-significant c value. The causal steps mediation approach also requires that c ′ = 0, meaning all effects from X to Y must be transmitted through M ; this type of mediation model is called a complete mediation model . The complete mediation model is the most defensible mediation conclusion from a research study, but it suffers from low statistical power when the causal steps approach is used. The complete mediation model is discussed in more detail shortly.

Modern methods of mediation analysis use regression (as well as structural equation modeling, an expansion of the regression framework) to quantify the mediated effect as a single number for which confidence intervals and significance tests can be calculated. The theory of mediation states that there is a causal relation in a mediation model, such that X causes M and M causes Y. Therefore, the mediated effect of X to Y via M can be quantified as the product of the regression coefficient relating X to M and the regression coefficient relating M to Y , or ab (using Eq. 2 and above). The test of ab can be more powerful than the test of c because it is a more precise explanation of how X affects Y ; the requirement that c be significant is not necessary for mediation to exist. Although modern methods pose that the test of c may not be as important in determining the mediating effect, the test of c is clearly important in its own right. A lack of statistically significant c is important in assessing manipulation and conceptual theory for future studies.

When both M and Y are observed and continuous (so that linear regression or structural equation modeling is used to estimate Eqs. 1 – 3 ) and there are no missing data, it can be shown that the difference between the total effect of X on Y and ( c ), and the direct effect of X on Y and ( c ′) is numerically equivalent to ab . As previously noted, this result holds only for linear models such as linear regression, but not for non-linear models such as logistic regression ( Pearl, in press ). The c – c ′ estimate of the mediated effect reflects that any difference between the total relation between X and Y (the c coefficient) and the direct effect of X on Y while controlling for M (the c ′ coefficient) must be due to the indirect or mediated effect. Some researchers have suggested that only c – c ′ should be used for making causal inferences. The reasoning behind this stance is that, typically, only X is randomly assigned, whereas M is observed or self-selected by the participant. Therefore, the c – c ′ estimate of the mediated effect involves using only regression coefficients that are based upon random assignment to experimental conditions. The point of contention is often irrelevant because the two quantities ab and only c – c ′ are identical in linear regression and structural equation modeling of continuous measures. For logistic regression or other nonlinear statistical methods, the two estimators of the mediated effect may not be equal and may have different meanings ( Imai et al. 2010 ; Pearl 2011).

Complete Versus Partial Mediation

Some researchers (e.g., James and Brett 1984 ) suggest a slightly different approach to quantifying the mediated effect than has been presented here. James and Brett suggest that the model described by Eqs. 1 – 3 implicitly assumes partial mediation , i.e., the mediated path via M accounts for only some of the effect of X on Y. In other words, this approach implies a non-zero direct path or c ′ coefficient. James et al. (2006) suggest an alternative approach that begins from an assumption of complete mediation (sometimes also called “full mediation”), where the c ′ path is assumed to be zero and all effects of X on Y are transmitted through the mediator M . In the complete mediation framework, two regression coefficients are estimated. First, the effect of X on M is estimated using the a coefficient in Eq. 2 above. Second, the effect of M on Y is estimated using the expression

where b ′ is a new regression coefficient representing the relation of M and Y , completely ignoring X . The mediated effect is calculated as ab ′ and reflects the use of this new coefficient.

The complete mediation approach has several attractive features. First, fixing the value of the c ′ path to zero means that, from a structural equation modeling perspective, the complete mediation model is identified and has degrees of freedom, allowing for goodness-of-fit tests. Goodness-of-fit tests allow a researcher to test how closely the model matches the observed data, in addition to testing whether individual paths and the mediated effect are significantly different from zero. Second, the complete mediation model is a more parsimonious explanation of the causal relation from X to M to Y. From a philosophy of science perspective, a simpler or more parsimonious model is preferred. However, complete mediation is uncommon in many areas of psychology so it is likely that there is a direct effect of X on Y , and testing for complete mediation as a first step may not be informative for psychological research; this is a weakness shared by the causal steps approach to mediation described in Judd and Kenny (1981) , which requires that the null hypothesis that the c ′ path is equal to zero is not rejected.

Tests of Mediation and Confidence Limit Estimation

There are many statistical tests to evaluate the mediated effect. Some tests of the mediated effect involve dividing the estimate of the mediated effect by an estimate of its standard error ( Wald 1943 ) and this ratio is then compared to an appropriate statistical distribution, such as the normal distribution. Other tests of the mediated effect are non-parametric, resampling tests such as bootstrapping which use the observed data to determine the distribution and standard error of the mediation estimate. MacKinnon et al. (2002) provide an evaluation of fourteen different methods of evaluating the mediated effect, including methods of calculating the standard errors for ab and c – c ′.

One of the most common tests of the ab mediated effect is based on the multivariate delta standard error ( Sobel 1982 ). The ratio of the mediated effect to its standard error is compared to a standard normal ( z ) distribution to test significance. This method has reduced power because the product of two normally distributed regression coefficients is not normally distributed and instead follows the distribution of the product. The distribution of the product is variable in shape depending on the magnitude of the coefficients and is often asymmetric and highly kurtotic ( Aroian 1947 ; Craig 1936 ).

As described in MacKinnon et al. (2002) , tests of the mediated effect that are based on the distribution of the product have more accurate Type I error rates and have more power than many other tests. Critical values for the distribution of the product produce more accurate confidence intervals for the mediated effect. PRODCLIN (distribution of the PRODuct Confidence Limits for INdirect effects) automates the selection of critical values for the distribution of the product ( MacKinnon et al. 2007 ). The user inputs values of a , b , their respective standard errors, and the desired Type I error rate (e.g., α = .05); the program returns the upper and lower asymmetric confidence limits for the mediated effect. A new version of this program (RMEdiation; Tofighi and MacKinnon 2011 ) now provides several additional capabilities including plots of the distribution of the product and several options for confidence limits. Mackinnon et al. (2004) found that tests of significance based on the distribution of the product outperformed other single-sample methods in terms of Type I error rates, power, and accuracy of confidence limits.

Bootstrapping is a resampling technique that is often used to evaluate a test statistic (such as the mediated effect) when the true distribution of the statistic is either unknown or difficult to obtain. The bootstrapping method involves taking many (e.g., 1000) repeated “samples” from the observed sample, calculating the statistic of interest, and producing a distribution based on these values of the statistic. Confidence intervals are obtained empirically, i.e., by observing the value in the bootstrapped distribution beyond which a certain proportion of the test statistics lie. For example, for a two-tailed test with an alpha value of .05, order the 1000 bootstrap statistics from lowest to highest, and choose the value of the (1000 × 0.025) = 25th observation as the lower critical bound of the confidence interval and the value of the (1000 × 0.975) = 975th observation as the upper bound of the confidence interval. Bootstrap methods for determining the significance of the mediated effect generally perform well in terms of power and Type 1 error (see MacKinnon et al. 2004 ). Routines to perform bootstrap analyses are included in many common statistical software programs, including AMOS, M plus , and EQS and programs for conducting bootstrap analyses in SAS and SPSS are also available ( Lockwood and MacKinnon 1998 ; Preacher and Hayes 2004 ). Another advantage of bootstrap methods is that they can be easily expanded as the complexity of the model increases; for example, bootstrapping can easily be applied to a multiple mediator model in which X → M 1 → M 2 → Y , where the mediated effect is calculated as the product of three regression coefficients.

In summary, an ideal method includes an estimate of the mediated effect along with a confidence interval for the indirect effect. Confidence intervals may be made with a bootstrap method or the distribution of the product. The effect size for the paths in the mediation model such as the standardized coefficients or partial correlation measure should be reported. Note that it is important to report statistical tests of the relation of X to Y (i.e., the c coefficient from Eq. 1 in the single mediator model), but this relation is not necessary for mediation to exist. In fact, a test of mediation may be more important when there is not a statistically significant relation of X to Y because the path from X to M represents a test of action theory and the path from M to Y represents a test of conceptual theory. When reporting mediation analyses, it is important to provide detailed information regarding the models tested along with the coefficients from these models (e.g. a , b , c ′, and ab ) and the confidence intervals ( Mackinnon 2008 ).

Decisions Following Mediation Analysis

Several assumptions were made for the regression equations described earlier that can be addressed in the design phase of the study or by appropriate statistical analysis. However, several assumptions are untestable and cannot be completely addressed using design or statistical approaches. These assumptions are related to confounders of the mediated effect, higher order relations between X and M , the causal ordering of X , M , and Y , and measurement error. Many aspects of these assumptions can be addressed by sensitivity analysis, a method of assessing how much the results of an analysis may change due to violation of assumptions. Typically, sensitivity analysis involves systematically changing values of specific parameter values in the model (for example, the a path from X to M ) to determine how much the parameter must change in order to change the substantive interpretation (i.e., significance) or change the estimates by a specific, pre-determined amount (e.g., to change the estimate of the mediated effect by 25%). Sensitivity analysis is one of the most challenging aspects of mediation analysis, but there has been considerable development in these methods in recent years.

Confounders

For the ab estimator of the mediated effect and ordinary least squares regression, the errors in Eqs. 2 and 3 are assumed to be independent. The uncorrelated errors assumption may be violated if there are confounding variables that are omitted from the analysis. Confounders can have a substantial effect on the analysis of the mediated effect. Figure 3 shows how confounders can potentially influence multiple paths in a mediation model. Ideally, measures of the potential confounding variables are included in the statistical model, but if they are not, the confounders may result in biased estimates. As with any study, even when some potential confounders are included in the analysis, there is no guarantee that all possible confounders were included.

Confounders of mediation relations. The true model requires d 1 , d 2 , d 3 , and d 4 , otherwise the coefficients are confounded

Sensitivity analysis is one way to assess the influence of omitted variables on the observed mediation relations. Since randomization of X theoretically eliminates confounders in the X → M relationship, the goal of sensitivity analysis in mediation for experimental studies is typically to assess how large a confounder effect on the M → Y relation (i.e., sequential ignorability) must be in order to invalidate the conclusions of the analysis ( Frank 2000 ; Li et al. 2007 ; Lin et al. 1998 ; Rosenbaum 2002 ). The correlation between the errors in Eqs. 2 and 3 reflects the contribution of omitted variables to the observed relation of M to Y , or the degree to which the assumption of sequential ignorability is violated. Thus, by systematically increasing the correlation between the errors in Eqs. 2 and 3 , one can evaluate how much the b and c ′ coefficients change due to violation of this assumption ( Imai et al. 2010 ).

Promising approaches to improving causal inference by addressing the bias introduced by omitted variables have been proposed ( Frangakis and Rubin 2002 ; Holland 1988 ; Jo 2008 ; Murphy et al. 2001 ; Pearl 2009 , in press ; Robins and Greenland 1992 ; Robins et al. 1992 ; Rubin 2004 ; Shipley 2000 ; Sobel 1998 , 2008 ; Winship and Morgan 1999 ) but most have not been extensively evaluated in simulation studies and applied settings. Vander Weele (2008 , 2010 ) has formalized several useful methods to probe bias in mediation relations when one or both assumptions of Sequential Ignorability have been violated. Imai et al. (2010) describe another method and include a computer program to assess the sensitivity of the results to potential confounders. These methods allow the researcher to draw a conclusion about the direction of the bias by suggesting relations of unmeasured confounders on relations in the mediation model.

X – M Interaction

The standard single mediator model assumes that Eqs. 2 and 3 represent causal relations that are linear, additive, and recursive ( Holland 1988 ; James and Brett 1984 ; James et al. 2006 ; McDonald 1997 ). An additivity assumption implies that there is no interaction between X and M ( Collins et al. 1998 ; Judd and Kenny 1981 ), i.e., the effect of X on Y does not depend on the value of M and the effect of M on Y does not depend on the value of X . The additivity assumption can be directly tested by including the interaction of X and M; if the interaction term is significant, the assumption of additivity is violated. In this context, the mediated effect differs across levels of X and further analyses can explore the size and significance of the mediated effect at different values of X .

Causal Ordering

Since mediation is a causal model, it is important to clearly define the causal chain from X to M to Y. The mediation model makes the assumption that the correct causal order has been specified, such that X causes M and M causes Y. When X is randomly assigned, it is clear that X occurs before M and Y. However, the ordering of M and Y is less clear and theory and prior empirical research can help make the causal ordering more concrete.

Hill (1965) outlined nine considerations for clarifying the ordering of causal relations. These points were initially developed to investigate smoking as a cause of cancer but have applications to establishing causal ordering in mediation models. These are substantive considerations rather than statistical tests, so they require a substantive researcher to carefully evaluate the variables involved. The nine criteria are (1) strength, (2) consistency, (3) specificity, (4) temporality, (5) biological gradient, (6) plausibility, (7) coherence, (8) experiment, and (9) analogy. According to Hill, causality is implied by (1) a stronger relation rather than a weaker relation, (2) consistent findings by multiple people in multiple samples, (3) specific findings (e.g., about a specific disease rather than general unhealthiness), (4) the “cause” occurring prior to the “effect” in time, (5) a larger effect seen with larger exposure to the “cause,” (6) a plausible and sensible mechanism by which the causal relationship occurs, (7) agreement between laboratory and observational studies, (8) experimental evidence of the causal relationship, and (9) similar “causes” resulting in similar “effects.” These criteria can be applied to M and Y (or to X , M , and Y , if X is not randomized) to provide evidence that the presented causal ordering is the correct ordering.

Measurement Error

Mediation analysis assumes that the measures are both reliable and valid ( Baron and Kenny 1986 ; Holland 1988 ; James and Brett 1984 ; MacKinnon 2008 ; McDonald 1997 ). As previously discussed, Hoyle and Kenny (1999) showed that unreliability of the mediator leads to underestimation of the b path and overestimation of c ′ which results in underestimation of the mediated effect and lower power to detect the mediated effect.

After the study is completed, a correction for unreliability in measured variable models can be applied to obtain estimates of coefficients if reliability is assumed to be a certain value (see MacKinnon 2008 , p. 189). This new model results in the estimation of coefficients that have been adjusted for more or less reliable measures. Limitations of this method are that the reliability estimate used may not always be accurate and the correction approach may not adequately address measures that are actually composed of more than one factor. In addition, if there are multiple factors for some measures, the relationship of these factors may have important relationships with other variables in the model that will be ignored ( Bagozzi and Heatherton 1994 ).

Planning for the Next Study

Every study can be thought of as a single piece of an overall body of research; each study builds upon previous studies, resulting in an accumulation of knowledge. Studies involving statistical mediation are no different. In this article, we have discussed a number of potential limitations to the interpretation of mediation analysis, particularly causal inference limitations. For example, we discussed potential confounders of the mediated effect, including experimental design methods that can help rule out the presence of potential confounders and newly developed sensitivity analysis methods that can determine the amount of bias caused by omitted confounders. The consideration of limitations of interpretability and generalizability of results may be especially important for mediation studies because of the number of omitted variables that may affect observed results. As an illustration, consider a study involving a non-randomly assigned X variable. There are several limitations of the interpretation of the mediated effects in this study. The relationship between X and M may be biased for several reasons; the true causal ordering of X and M is potentially unclear and there may be confounders that bias the estimate of the relationship between X and M . A follow-up study can address both of these limitations by incorporating a randomly assigned manipulation of the X variable. Random assignment of the X variable ensures the causal ordering of X and M because X is randomly assigned before M is measured; random assignment also ensures that there are no confounders of the relationship between X and M . If the follow-up study produced results that match the initial study, the researcher can be confident that causal inference based on the X → M relationship is sound. If the follow-up study produces conclusions that differ from the initial study, further research is needed; for example, confounders of the M → Y relationship may be affecting the results. In either situation, multiple studies are typically required to produce a clear picture of the true relationships.

Statistical mediation analysis is a powerful tool for testing the process by which an effect occurs in both experimental and observational studies. In this article, we discussed how design decisions made prior to conducting a study and statistical choices made during analysis influence the conclusions that can be drawn from a study that involves statistical mediation. We also discussed the limitations of interpretation of a mediation process for even well-designed and analyzed studies. The major point is that the investigation of mediation processes requires careful planning and is part of a cumulative program of research using evidence from a variety of sources including clinical observation, qualitative studies, and replication ( MacKinnon 2008 ). Mediation analysis is popular because it directly addresses important theoretical questions about processes by which effects occur. This importance of mediating variables for scientific understanding was identified many years ago ( Lazarsfeld 1955 ; Woodworth 1928 ) and there is now a body of statistical techniques to test and evaluate mediation theory. Business research is an ideal area for the application of these techniques to evaluate whether a variable is truly intermediate in a causal sequence.

Acknowledgments

This article was supported in part by Public Health Service Grant DA09757 from the National Institute on Drug Abuse.

Contributor Information

David P. MacKinnon, Department of Psychology, Arizona State University, Tempe, AZ 85287-1104, USA.

Stefany Coxe, Department of Psychology, Arizona State University, Tempe, AZ 85287-1104, USA.

Amanda N. Baraldi, Department of Psychology, Arizona State University, Tempe, AZ 85287-1104, USA.

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