random assignment 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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Randomization of the Treatment Assignment for Conducting Experiments

Description.

This function can be used to randomize the treatment assignment for randomized experiments. In addition to the complete randomization, it implements randomized-block and matched-pair designs.

Randomized-block designs refer to the complete randomization of the treatment within the pre-specified blocks which contain multiple observations. Matched-pair designs refer to the randomization of the binary treatment variable within the pre-specified pair of observations.

A list of class randomize which contains the following items:

Kosuke Imai, Department of Government and Department of Statistics, Harvard University [email protected] , https://imai.fas.harvard.edu ;

block_ra: Block Random Assignment

Description.

block_ra implements a random assignment procedure in which units that are grouped into blocks defined by pre-treatment covariates are assigned using complete random assignment within block. For example, imagine that 50 of 100 men are assigned to treatment and 75 of 200 women are assigned to treatment.

A vector of length N that indicates the treatment condition of each unit. Is numeric in a two-arm trial and a factor variable (ordered by conditions) in a multi-arm trial.

A vector of length N that indicates which block each unit belongs to. Can be a character, factor, or numeric vector. (required)

Use for a two-arm design in which either floor(N_block*prob) or ceiling(N_block*prob) units are assigned to treatment within each block. The probability of assignment to treatment is exactly prob because with probability 1-prob, floor(N_block*prob) units will be assigned to treatment and with probability prob, ceiling(N_block*prob) units 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. tapply(prob_unit, blocks, unique) will be passed to block_prob .

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 the scalar m describes the fixed number of units to assign in each block. This number does not vary across blocks.

Use for a two-arm design. Must be of length N. tapply(m_unit, blocks, unique) will be passed to block_m .

Use for a two-arm design in which the vector block_m describes the number of units to assign to treatment within each block. block_m must be a numeric vector that is as long as the number of blocks and is in the same order as sort(unique(blocks)).

Use for a multi-arm design in which the values of block_m_each determine the number of units 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 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. Must be in the same order as sort(unique(blocks)). 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 TRUE.

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Browse Course Material

Course info, instructors.

• Dr. Jeremy Orloff
• Dr. Jennifer French Kamrin

Departments

• Mathematics

As Taught In

• Discrete Mathematics
• Probability and Statistics

Learning Resource Types

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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Design and Analysis of Experiments with randomizr (Stata)

Alexander coppock.

randomizr is a small package for Stata that simplifies the design and analysis of randomized experiments. In particular, it makes the random assignment procedure transparent, flexible, and most importantly reproduceable. By the time that many experiments are written up and made public, the process by which some units received treatments is lost or imprecisely described. The randomizr package makes it easy for even the most forgetful of researchers to generate error-free, reproduceable random assignments.

A hazy understanding of the random assignment procedure leads to two main problems at the analysis stage. First, units may have different probabilities of assignment to treatment. Analyzing the data as though they have the same probabilities of assignment leads to biased estimates of the treatment effect. Second, units are sometimes assigned to treatment as a cluster. For example, all the students in a single classroom may be assigned to the same intervention together. If the analysis ignores the clustering in the assignments, estimates of average causal effects and the uncertainty attending to them may be incorrect.

A Hypothetical Experiment

Throughout this vignette, we’ll pretend we’re conducting an experiment among the 592 individuals in R’s HairEyeColor dataset. As we’ll see, there are many ways to randomly assign subjects to treatments. We’ll step through five common designs, each associated with one of the five randomizr functions: simple_ra , complete_ra , block_ra , cluster_ra , and block_and_cluster_ra .

Typically, researchers know some basic information about their subjects before deploying treatment. For example, they usually know how many subjects there are in the experimental sample (N), and they usually know some basic demographic information about each subject.

Our new dataset has 592 subjects. We have three pretreatment covariates, Hair, Eye, and Sex, which describe the hair color, eye color, and gender of each subject. We also have potential outcomes. We call the untreated outcome Y0 and we call the treated outcome Y1.

Imagine that in the absence of any intervention, the outcome (Y0) is correlated with out pretreatment covariates. Imagine further that the effectiveness of the program varies according to these covariates, i.e., the difference between Y1 and Y0 is correlated with the pretreatment covariates.

If we were really running an experiment, we would only observe either Y0 or Y1 for each subject, but since we are simulating, we have both. Our inferential target is the average treatment effect (ATE), which is defined as the average difference between Y0 and Y1.

Simple Random Assignment

Simple random assignment assigns all subjects to treatment with an equal probability by flipping a (weighted) coin for each subject. The main trouble with simple random assignment is that the number of subjects assigned to treatment is itself a random number - depending on the random assignment, a different number of subjects might be assigned to each group.

The simple_ra function has no required arguments. If no other arguments are specified, simple_ra assumes a two-group design and a 0.50 probability of assignment.

To change the probability of assignment, specify the prob argument:

If you specify num_arms without changing prob_each, simple_ra will assume equal probabilities across all arms.

You can also just specify the probabilities of your multiple arms. The probabilities must sum to 1.

You can also name your treatment arms.

Complete Random Assignment

Complete random assignment is very similar to simple random assignment, except that the researcher can specify exactly how many units are assigned to each condition.

The syntax for complete_ra is very similar to that of simple_ra . The argument m is the number of units assigned to treatment in two-arm designs; it is analogous to simple_ra ’s prob. Similarly, the argument m_each is analogous to prob_each.

If you specify no arguments in complete_ra , it assigns exactly half of the subjects to treatment.

To change the number of units assigned, specify the m argument:

If you specify multiple arms, complete_ra will assign an equal (within rounding) number of units to treatment.

You can also specify exactly how many units should be assigned to each arm. The total of m_each must equal N.

Simple and Complete Random Assignment Compared

When should you use simple_ra versus complete_ra ? Basically, if the number of units is known beforehand, complete_ra is always preferred, for two reasons: 1. Researchers can plan exactly how many treatments will be deployed. 2. The standard errors associated with complete random assignment are generally smaller, increasing experimental power. See this guide on EGAP for more on experimental power.

Since you need to know N beforehand in order to use simple_ra , it may seem like a useless function. Sometimes, however, the random assignment isn’t directly in the researcher’s control. For example, when deploying a survey experiment on a platform like Qualtrics, simple random assignment is the only possibility due to the inflexibility of the built-in random assignment tools. When reconstructing the random assignment for analysis after the experiment has been conducted, simple_ra provides a convenient way to do so.

To demonstrate how complete_ra is superior to simple_ra , let’s conduct a small simulation with our HairEyeColor dataset.

The standard error of an estimate is defined as the standard deviation of the sampling distribution of the estimator. When standard errors are estimated (i.e., by using the summary() command on a model fit), they are estimated using some approximation. This simulation allows us to measure the standard error directly, since the vectors simple_ests and complete_ests describe the sampling distribution of each design.

In this simulation complete random assignment led to a 6% decrease in sampling variability. This decrease was obtained with a small design tweak that costs the researcher essentially nothing.

Block Random Assignment

Block random assignment (sometimes known as stratified random assignment) is a powerful tool when used well. In this design, subjects are sorted into blocks (strata) according to their pre-treatment covariates, and then complete random assignment is conducted within each block. For example, a researcher might block on gender, assigning exactly half of the men and exactly half of the women to treatment.

Why block? The first reason is to signal to future readers that treatment effect heterogeneity may be of interest: is the treatment effect different for men versus women? Of course, such heterogeneity could be explored if complete random assignment had been used, but blocking on a covariate defends a researcher (somewhat) against claims of data dredging. The second reason is to increase precision. If the blocking variables are predictive of the outcome (i.e., they are correlated with the outcome), then blocking may help to decrease sampling variability. It’s important, however, not to overstate these advantages. The gains from a blocked design can often be realized through covariate adjustment alone.

Blocking can also produce complications for estimation. Blocking can produce different probabilities of assignment for different subjects. This complication is typically addressed in one of two ways: “controlling for blocks” in a regression context, or inverse probability weights (IPW), in which units are weighted by the inverse of the probability that the unit is in the condition that it is in.

The only required argument to block_ra is block_var, which is a variable that describes which block a unit belongs to. block_var can be a string or numeric variable. If no other arguments are specified, block_ra assigns an approximately equal proportion of each block to treatment.

For multiple treatment arms, use the num_arms argument, with or without the conditions argument

block_ra provides a number of ways to adjust the number of subjects assigned to each conditions. The prob_each argument describes what proportion of each block should be assigned to treatment arm. Note of course, that block_ra still uses complete random assignment within each block; the appropriate number of units to assign to treatment within each block is automatically determined.

For finer control, use the block_m_each argument, which takes a matrix with as many rows as there are blocks, and as many columns as there are treatment conditions. Remember that the rows are in the same order as seen in tab block_var, a command that is good to run before constructing a block_m_each matrix. The matrix can either be defined using the matrix define command or be inputted directly into the block_m_each option.

Clustered Assignment

Clustered assignment is unfortunate. If you can avoid assigning subjects to treatments by cluster, you should. Sometimes, clustered assignment is unavoidable. Some common situations include:

• Housemates in households: whole households are assigned to treatment or control
• Students in classrooms: whole classrooms are assigned to treatment or control
• Residents in towns or villages: whole communities are assigned to treatment or control

Clustered assignment decreases the effective sample size of an experiment. In the extreme case when outcomes are perfectly correlated with clusters, the experiment has an effective sample size equal to the number of clusters. When outcomes are perfectly uncorrelated with clusters, the effective sample size is equal to the number of subjects. Almost all cluster-assigned experiments fall somewhere in the middle of these two extremes.

The only required argument for the cluster_ra function is the clust_var argument, which indicates which cluster each subject belongs to. Let’s pretend that for some reason, we have to assign treatments according to the unique combinations of hair color, eye color, and gender.

This shows that each cluster is either assigned to treatment or control. No two units within the same cluster are assigned to different conditions.

As with all functions in randomizr, you can specify multiple treatment arms in a variety of ways:

…or using conditions.

… or using m_each, which describes how many clusters should be assigned to each condition. m_each must sum to the number of clusters.

Block and Clustered Assignment

The power of clustered experiments can sometimes be improved through blocking. In this scenario, whole clusters are members of a particular block – imagine villages nested within discrete regions, or classrooms nested within discrete schools.

As an example, let’s group our clusters into blocks by size

• radiant.data
• radiant.design
• radiant.basics
• radiant.model
• radiant.multivariate

Design > Random assignment

Vincent r. nijs, rady school of management (ucsd).

Randomly assign respondents to experimental conditions

To use the random assignment tool, select a data set where each row in the data set is unique (i.e., no duplicates). A dataset that fits these requirements is bundled with Radiant and is available through the Data > Manage tab (i.e., choose Examples from the Load data of type drop-down and press Load ). Select rndnames from the Datasets dropdown.

Names is a unique identifier in this dataset. If we select this variable and specify two (or more) Conditions (e.g., “test” and “control”) a table will be shown with a columns .conditions that indicates to which condition each person was (randomly) assigned.

By default, the Random assignment tool will use equal probabilities for each condition. However, as can be seen in the screenshot below, it is also possible to specify the probabilities to use in assignment (e.g., 30% to “test” and 70% to the “control” condition).

If we expect that some variables are likely predictive of the outcome of our experiment then we can use blocking to decrease sampling variability. In block random assignment (or stratified random assignment) subjects are first sorted into blocks (or strata) based on one or more characteristics before being randomly assigned within each block. For example, if we select Gender as a Blocking variable the Random assignment tool will attempt to put exactly 30% of men and exactly 30% of women in the treatment condition based on the Probabilities we specified in advance. As we can see in the screenshot below, the assignment of men and women to the test and control condition turned out exactly as intended.

By default, the random seed is set to 1234 to ensure the sampling results are reproducible. If there is no input in Rnd. seed , the selected rows will change every time we generate a sample.

To download data with the assignments in the .conditions column in CSV format, click on the icon in the top-right of your screen. The same data can also be stored in Radiant by providing a name for the dataset and then clicking on the Store button.

Report > Rmd

Add code to Report > Rmd to (re)create the sample by clicking the icon on the bottom left of your screen or by pressing ALT-enter on your keyboard.

R-functions

For an overview of related R-functions used by Radiant for sampling and sample size calculations see Design > Sample

For more information see the vignette for the randomizr package that radiant uses for the Random assignment tool.

The key functions from the randomizr package used in the randomizer tool are complete_ra and block_ra .

randomizr Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

• Design and Analysis of Experiments with randomizr
• block_and_cluster_ra: Blocked and Clustered Random Assignment
• block_and_cluster_ra_probabilities: probabilities of assignment: Blocked and Clustered Random...
• block_ra: Block Random Assignment
• block_ra_probabilities: probabilities of assignment: Block Random Assignment
• cluster_ra: Cluster Random Assignment
• cluster_ra_probabilities: probabilities of assignment: Cluster Random Assignment
• cluster_rs: Cluster Random Sampling
• cluster_rs_probabilities: Inclusion Probabilities: Cluster Sampling
• complete_ra: Complete Random Assignment
• complete_ra_probabilities: probabilities of assignment: Complete Random Assignment
• complete_rs: Complete Random Sampling
• complete_rs_probabilities: Inclusion Probabilities: Complete Random Sampling
• conduct_ra: Conduct a random assignment
• custom_ra: Custom Random Assignment
• custom_ra_probabilities: probabilities of assignment: Custom Random Assignment
• declare_ra: Declare a random assignment procedure.
• declare_rs: Declare a random sampling procedure.
• draw_rs: Draw a random sample
• obtain_condition_probabilities: Obtain the probabilities of units being in the conditions...
• obtain_inclusion_probabilities: Obtain inclusion probabilities
• obtain_num_permutations: Obtain the Number of Possible Permutations from a Random...
• obtain_permutation_matrix: Obtain Permutation Matrix from a Random Assignment...
• obtain_permutation_probabilities: Obtain the probabilities of permutations
• randomizr: randomizr
• simple_ra: Simple Random Assignment
• simple_ra_probabilities: probabilities of assignment: Simple Random Assignment
• simple_rs: Simple Random Sampling
• simple_rs_probabilities: Inclusion Probabilities: Simple Random Sampling
• strata_and_cluster_rs: Stratified and Clustered Random Sampling
• strata_and_cluster_rs_probabilities: Inclusion Probabilities: Stratified and Clustered Random...
• strata_rs: Stratified Random Sampling
• strata_rs_probabilities: Inclusion Probabilities: Stratified Random Sampling
• Browse all...

block_ra : Block Random Assignment In randomizr: Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

View source: R/block_ra.R

Block Random Assignment

Description.

block_ra implements a random assignment procedure in which units that are grouped into blocks defined by pre-treatment covariates are assigned using complete random assignment within block. For example, imagine that 50 of 100 men are assigned to treatment and 75 of 200 women are assigned to treatment.

A vector of length N that indicates the treatment condition of each unit. Is numeric in a two-arm trial and a factor variable (ordered by conditions) in a multi-arm trial.

Related to block_ra in randomizr ...

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