random assignments in r

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How to randomly assign participants to groups in R?

To randomly assign participants to groups, we can use sample function.

For example, if we have a data frame called df that contains a column say Employee_ID and we want to create five groups that are stored in a vector say Grp then random assignment of participants to values in Grp can be done by using the command given below −

Consider the below data frame and vector group −

The following dataframe is created −

Add the following code to the above snippet −

In order to randomly assign student ID’s to groups in Group vector, add the following code to the above snippet −

If you execute all the above given snippets as a single program, it generates the following Output −

In order to randomly assign employee ID’s to groups in Category vector, add the following code to the above snippet −

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Introduction to probability and statistics, r tutorial b: random numbers.

In order to run simulations of experiments with random outcomes we make use of R’s ability to generate random numbers. More precisely it generates a ‘pseudo-random’ number, which behaves in many ways like a truly random number.

The Function Sample(x, k, replace = TRUE)

Allowing repeated elements         # Sometimes you want to allow repeats. For example when  we roll a die repeatedly we expect to see numbers repeating. We can think of this as picking a random element from a set and then putting it back, i.e. replacing it, so it can be drawn again.

# In R we do this by setting the optional argument replace=TRUE

# Now there is no problem asking for more than 5 things from a set of 5 elements.  

# To generate an m x n array of random values we can use the function sample function followed by the matrix function.

# Let’s simulate rolling a die.          # We use 1:6 to make vector (1,2,3,4,5,6).

Simulation  

# First let’s simulate rolling 1 die 3 times and checking if one of the rolls was a 6.

# First we use sample to generate 3 samples from 1:6  

# To check if any of the 3 rolls are 6 we use the following command. It returns a vector of TRUE or FALSE depending on whether that entry of x is 6 or not. Note the use of the double equal sign. We can’t use a single equal sign because that would mean ‘set the value of x to 6’. Compare the result with the value of x above.  

#  We can also see which elements of x are less than 6  

#  Now let’s roll the die 1000 times and see what fraction of the rolls give 6. We expect that about 1/6 of them will be.

# Simulate 1000 rolls  

# x == 6 gives a vector of TRUE or FALSE. R is clever, when we sum the vector: each TRUE counts as 1 and each FALSE counts as 0. So the sum is the number of TRUE’s. In this case that means the number of 6’s, which happens to be 168.   

# Divide by 1000 to get the fraction of 6’s.  

# Compare that with the theoretical value of 1/6.  

# Now let’s estimate the probability of getting at least one 6 in 4 rolls.

# Goal: estimate the probability of getting at least one 6 in 4 rolls.         # Experiment: roll 1 die 4 times and check for a 6.          # Repeat the experiment 10 times and see what fraction of times this happens.

# So you can see all the commands at once, we’ll show them all and then explain them later. For commenting, we’ll put a command number before each ‘>’   

# Command 1: Generate a 4 by 10 random array. Each column represents one experimental trial of 4 rolls. The 10 columns represent the 10 trials.      # Command 2: Display x      # Command 3: See which of the rolls are 6’s. Note the double equals to check which rolls were 6. The result y is an array of TRUE or FALSE. You can check that it picks out the 6’s.      # Command 4: Display y      # Command 5: Sum each of the columns. The result is then number of 6’s in each trial (column).      # Command 6: Display z      # Command 7: If the column sum is greater than 0 there was at least one TRUE in the column, that is at least one 6. This command prints a vector of TRUE or FALSE representing  whether or not the experiment yielded a 6.      # command 8: sum the vector in command 7 to get the number of trials that yielded a 6. We see that 5 out of 10 trials did. (This is random. Your answer may be different.)      # Command 9: Display s      # command 10: The mean function is just the sum divided by the number of trials. This is just 5/10 = .5. Half the trials yielded a 10.      # command 11: Disply the mean

# Let’s repeat this but with 1000 trials instead of 10. Without all the comments it’s pretty short.  

Our estimate of the probability of at least one 6 in 4 rolls is .525. This is pretty close to the theoretical value of .518.

The dim() function          # We can always check that x has 4 rows and 1000 columns using the dim() function.  

One More Simulation  

# Goal: estimate the probability of getting a sum of 7 when rolling two dice.  

# Command 1: We assign the number of trials to the variable ntrials. Writing code like this makes it easier to modify later. If we want to change the number of trials to 7 we just have to change this one line of code.         # Command 2: we create 10000 columns with 2 rows. That is, we run 10000 experiments of rolling 2 dice.         # Command 3: we sum each of the columns, i.e., we sum the two dice.         # Command 4: we find the fraction of sums that are 7.

# Note, this is essentially the exact answer of 1/6.

Exercise: Try to estimate the probability of two sixes when rolling two dice.

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Generating random numbers

You want to generate random numbers.

For uniformly distributed (flat) random numbers, use runif() . By default, its range is from 0 to 1.

To generate numbers from a normal distribution, use rnorm() . By default the mean is 0 and the standard deviation is 1.

If you want to your sequences of random numbers to be repeatable, see ../Generating repeatable sequences of random numbers .

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Methodology

• Random Assignment in Experiments | Introduction & Examples

Random Assignment in Experiments | Introduction & Examples

Published on March 8, 2021 by Pritha Bhandari . Revised on June 22, 2023.

In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomization.

With simple random assignment, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. Studies that use simple random assignment are also called completely randomized designs .

Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors, not research biases like sampling bias or selection bias .

Table of contents

Why does random assignment matter, random sampling vs random assignment, how do you use random assignment, when is random assignment not used, other interesting articles, frequently asked questions about random assignment.

Random assignment is an important part of control in experimental research, because it helps strengthen the internal validity of an experiment and avoid biases.

In experiments, researchers manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. To do so, they often use different levels of an independent variable for different groups of participants.

This is called a between-groups or independent measures design.

You use three groups of participants that are each given a different level of the independent variable:

• a control group that’s given a placebo (no dosage, to control for a placebo effect ),
• an experimental group that’s given a low dosage,
• a second experimental group that’s given a high dosage.

Random assignment to helps you make sure that the treatment groups don’t differ in systematic ways at the start of the experiment, as this can seriously affect (and even invalidate) your work.

If you don’t use random assignment, you may not be able to rule out alternative explanations for your results.

• participants recruited from cafes are placed in the control group ,
• participants recruited from local community centers are placed in the low dosage experimental group,
• participants recruited from gyms are placed in the high dosage group.

With this type of assignment, it’s hard to tell whether the participant characteristics are the same across all groups at the start of the study. Gym-users may tend to engage in more healthy behaviors than people who frequent cafes or community centers, and this would introduce a healthy user bias in your study.

Although random assignment helps even out baseline differences between groups, it doesn’t always make them completely equivalent. There may still be extraneous variables that differ between groups, and there will always be some group differences that arise from chance.

Most of the time, the random variation between groups is low, and, therefore, it’s acceptable for further analysis. This is especially true when you have a large sample. In general, you should always use random assignment in experiments when it is ethically possible and makes sense for your study topic.

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Random sampling and random assignment are both important concepts in research, but it’s important to understand the difference between them.

Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups.

While random sampling is used in many types of studies, random assignment is only used in between-subjects experimental designs.

Some studies use both random sampling and random assignment, while others use only one or the other.

Random sampling enhances the external validity or generalizability of your results, because it helps ensure that your sample is unbiased and representative of the whole population. This allows you to make stronger statistical inferences .

You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.

Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable .

• a control group that receives no intervention.
• an experimental group that has a remote team-building intervention every week for a month.

You use random assignment to place participants into the control or experimental group. To do so, you take your list of participants and assign each participant a number. Again, you use a random number generator to place each participant in one of the two groups.

To use simple random assignment, you start by giving every member of the sample a unique number. Then, you can use computer programs or manual methods to randomly assign each participant to a group.

• Random number generator: Use a computer program to generate random numbers from the list for each group.
• Lottery method: Place all numbers individually in a hat or a bucket, and draw numbers at random for each group.
• Flip a coin: When you only have two groups, for each number on the list, flip a coin to decide if they’ll be in the control or the experimental group.
• Use a dice: When you have three groups, for each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1 or 2 lands them in a control group; 3 or 4 in an experimental group; and 5 or 6 in a second control or experimental group.

This type of random assignment is the most powerful method of placing participants in conditions, because each individual has an equal chance of being placed in any one of your treatment groups.

Random assignment in block designs

In more complicated experimental designs, random assignment is only used after participants are grouped into blocks based on some characteristic (e.g., test score or demographic variable). These groupings mean that you need a larger sample to achieve high statistical power .

For example, a randomized block design involves placing participants into blocks based on a shared characteristic (e.g., college students versus graduates), and then using random assignment within each block to assign participants to every treatment condition. This helps you assess whether the characteristic affects the outcomes of your treatment.

In an experimental matched design , you use blocking and then match up individual participants from each block based on specific characteristics. Within each matched pair or group, you randomly assign each participant to one of the conditions in the experiment and compare their outcomes.

Sometimes, it’s not relevant or ethical to use simple random assignment, so groups are assigned in a different way.

When comparing different groups

Sometimes, differences between participants are the main focus of a study, for example, when comparing men and women or people with and without health conditions. Participants are not randomly assigned to different groups, but instead assigned based on their characteristics.

In this type of study, the characteristic of interest (e.g., gender) is an independent variable, and the groups differ based on the different levels (e.g., men, women, etc.). All participants are tested the same way, and then their group-level outcomes are compared.

When it’s not ethically permissible

When studying unhealthy or dangerous behaviors, it’s not possible to use random assignment. For example, if you’re studying heavy drinkers and social drinkers, it’s unethical to randomly assign participants to one of the two groups and ask them to drink large amounts of alcohol for your experiment.

When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers). These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Prospective cohort study

Research bias

• Implicit bias
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic
• Social desirability bias

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.

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.

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.

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Declare a random assignment procedure.

The number of units. N must be a positive integer. (required)

A vector of length N that indicates which block each unit belongs to.

A vector of length N that indicates which cluster each unit belongs to.

Use for a two-arm design in which m units (or clusters) are assigned to treatment and N-m units (or clusters) are assigned to control. In a blocked design, exactly m units in each block will be treated. (optional)

Use for a two-arm trial. Under complete random assignment, must be constant across units. Under blocked random assignment, must be constant within blocks.

Use for a multi-arm design in which the values of m_each determine the number of units (or clusters) assigned to each condition. m_each must be a numeric vector in which each entry is a nonnegative integer that describes how many units (or clusters) should be assigned to the 1st, 2nd, 3rd... treatment condition. m_each must sum to N. (optional)

Use for a two-arm design in which either floor(N*prob) or ceiling(N*prob) units (or clusters) are assigned to treatment. The probability of assignment to treatment is exactly prob because with probability 1-prob, floor(N*prob) units (or clusters) will be assigned to treatment and with probability prob, ceiling(N*prob) units (or clusters) will be assigned to treatment. prob must be a real number between 0 and 1 inclusive. (optional)

Use for a two arm design. Must of be of length N. Under simple random assignment, can be different for each unit or cluster. Under complete random assignment, must be constant across units. Under blocked random assignment, must be constant within blocks.

Use for a multi-arm design in which the values of prob_each determine the probabilities of assignment to each treatment condition. prob_each must be a numeric vector giving the probability of assignment to each condition. All entries must be nonnegative real numbers between 0 and 1 inclusive and the total must sum to 1. Because of integer issues, the exact number of units assigned to each condition may differ (slightly) from assignment to assignment, but the overall probability of assignment is exactly prob_each. (optional)

Use for a two-arm design in which block_m describes the number of units to assign to treatment within each block. Note that in previous versions of randomizr, block_m behaved like block_m_each.

Use for a multi-arm design in which the values of block_m_each determine the number of units (or clusters) assigned to each condition. block_m_each must be a matrix with the same number of rows as blocks and the same number of columns as treatment arms. Cell entries are the number of units (or clusters) to be assigned to each treatment arm within each block. The rows should respect the ordering of the blocks as determined by sort(unique(blocks)). The columns should be in the order of conditions, if specified.

Use for a two-arm design in which block_prob describes the probability of assignment to treatment within each block. Differs from prob in that the probability of assignment can vary across blocks.

Use for a multi-arm design in which the values of block_prob_each determine the probabilities of assignment to each treatment condition. block_prob_each must be a matrix with the same number of rows as blocks and the same number of columns as treatment arms. Cell entries are the probabilities of assignment to treatment within each block. The rows should respect the ordering of the blocks as determined by sort(unique(blocks)). Use only if the probabilities of assignment should vary by block, otherwise use prob_each. Each row of block_prob_each must sum to 1.

The number of treatment arms. If unspecified, num_arms will be determined from the other arguments. (optional)

A character vector giving the names of the treatment groups. If unspecified, the treatment groups will be named 0 (for control) and 1 (for treatment) in a two-arm trial and T1, T2, T3, in a multi-arm trial. An exception is a two-group design in which num_arms is set to 2, in which case the condition names are T1 and T2, as in a multi-arm trial with two arms. (optional)

logical, defaults to FALSE. If TRUE, simple random assignment is used. When simple = TRUE , please do not specify m, m_each, block_m, or block_m_each. If simple = TRUE , prob and prob_each may vary by unit.

for custom random assignment procedures.

logical. Defaults to TRUE.

A list of class "declaration". The list has five entries: $ra_function, a function that generates random assignments according to the declaration. $ra_type, a string indicating the type of random assignment used $probabilities_matrix, a matrix with N rows and num_arms columns, describing each unit's probabilities of assignment to conditions. $blocks, the blocking variable. $clusters, the clustering variable.

Random Treatment Assignments for Randomized Block Designs

Description.

Randomly draws a specified number of assignment vectors or matrices according to a randomized block design.

Assignments are randomly permuted within each block.

If w is a matrix, the permutations occur by row.

A list of random assignment vectors or matrices.

Joseph J. Lee and Tirthankar Dasgupta

completeRand , latinRand

We're sorry, but some features of Research Randomizer require JavaScript. If you cannot enable JavaScript, we suggest you use an alternative random number generator such as the one available at Random.org .

RESEARCH RANDOMIZER

Random sampling and random assignment made easy.

Research Randomizer is a free resource for researchers and students in need of a quick way to generate random numbers or assign participants to experimental conditions. This site can be used for a variety of purposes, including psychology experiments, medical trials, and survey research.

GENERATE NUMBERS

In some cases, you may wish to generate more than one set of numbers at a time (e.g., when randomly assigning people to experimental conditions in a "blocked" research design). If you wish to generate multiple sets of random numbers, simply enter the number of sets you want, and Research Randomizer will display all sets in the results.

Specify how many numbers you want Research Randomizer to generate in each set. For example, a request for 5 numbers might yield the following set of random numbers: 2, 17, 23, 42, 50.

Specify the lowest and highest value of the numbers you want to generate. For example, a range of 1 up to 50 would only generate random numbers between 1 and 50 (e.g., 2, 17, 23, 42, 50). Enter the lowest number you want in the "From" field and the highest number you want in the "To" field.

Selecting "Yes" means that any particular number will appear only once in a given set (e.g., 2, 17, 23, 42, 50). Selecting "No" means that numbers may repeat within a given set (e.g., 2, 17, 17, 42, 50). Please note: Numbers will remain unique only within a single set, not across multiple sets. If you request multiple sets, any particular number in Set 1 may still show up again in Set 2.

Sorting your numbers can be helpful if you are performing random sampling, but it is not desirable if you are performing random assignment. To learn more about the difference between random sampling and random assignment, please see the Research Randomizer Quick Tutorial.

Place Markers let you know where in the sequence a particular random number falls (by marking it with a small number immediately to the left). Examples: With Place Markers Off, your results will look something like this: Set #1: 2, 17, 23, 42, 50 Set #2: 5, 3, 42, 18, 20 This is the default layout Research Randomizer uses. With Place Markers Within, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p1=5, p2=3, p3=42, p4=18, p5=20 This layout allows you to know instantly that the number 23 is the third number in Set #1, whereas the number 18 is the fourth number in Set #2. Notice that with this option, the Place Markers begin again at p1 in each set. With Place Markers Across, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p6=5, p7=3, p8=42, p9=18, p10=20 This layout allows you to know that 23 is the third number in the sequence, and 18 is the ninth number over both sets. As discussed in the Quick Tutorial, this option is especially helpful for doing random assignment by blocks.

Please note: By using this service, you agree to abide by the SPN User Policy and to hold Research Randomizer and its staff harmless in the event that you experience a problem with the program or its results. Although every effort has been made to develop a useful means of generating random numbers, Research Randomizer and its staff do not guarantee the quality or randomness of numbers generated. Any use to which these numbers are put remains the sole responsibility of the user who generated them.

Note: By using Research Randomizer, you agree to its Terms of Service .

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Generating Random Dates

How can I generate a set of 12 random dates within a specific date range?

I thought the following would work:

But the result looks like a random set of numbers?

5 Answers 5

seq has a method for class Date which works for this:

• How can I then change the format of the output to be in a format such as 01/01/1999? –  AAA Commented Feb 1, 2014 at 19:39
• 2 See ?format.Date . To produce this format, you want the format string '%m/%d/%Y' (or perhaps '%d/%m/%Y' -- for this reason I recommend against this format). –  Matthew Lundberg Commented Feb 1, 2014 at 20:12
• Specifically, this is seq.Date if you want to read the docs. –  qwr Commented Jul 26 at 18:52
• Also sample draws without replacement by default. –  qwr Commented Jul 26 at 18:57

Several ways:

Start with a single Date object, and just add result from sample()

Start with a sequence of Date objects, and sample() it.

To follow base R functions like rnorm , rnbinom , runif and others, I created the function rdate below to return random dates based on the accepted answer of Matthew Lundberg .

The default range is the first and last day of the current year.

As expected, it returns valid dates:

And the randomness check, generating a million dates from this year:

• What is the purpose of this function? To provide default values and a sorting option? Otherwise it is just slight shorthand for the sample function? –  qwr Commented Jul 22 at 20:45

Note the use of as.Date() and origin parameter. Not sure why the code wont run without them...

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