## Design and analysis of experiments with randomizr

Random assignment of experimental units to treatments is carried out separately within each block. Similarities b/w Blocks and Strata Completely randomized . To create a random assignment for a completely randomized design with two factors, you can just modify the IF statement in the previous example. The following program generates a random assignment of treatments to 30 subjects, in which Factor A has 2 levels and Factor B has 3 levels (and hence 6 treatments). Aug 12,  · Study participants are randomly assigned to different groups, such as the experimental group, or treatment group. Random assignment might involve such tactics as flipping a coin, drawing names out of a hat, rolling dice, or assigning random numbers to participants.

## - Creating Random Assignments | STAT

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 random assignment of treatments 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 random assignment of treatments 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 random assignment of treatments effects and the uncertainty attending to them may be incorrect. We first need to transform the dataset, random assignment of treatments, which has each row describe a type of subject, to a new dataset in which each row describes an individual subject.

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 Nand they usually know some basic demographic information about each subject.

Our new dataset has subjects. We have three pretreatment covariates, HairEyeand Sexwhich describe the hair color, eye color, and gender of each subject.

We now need to create simulated potential outcomes. 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.

If we were really running an experiment, we would only observe either Y0 or Y1 for each subject, but since we are simulating, we generate both. Our inferential target is the average treatment effect ATEwhich is defined as the average difference between Y0 and Y1. We are now ready to allocate treatment assignments to subjects.

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.

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

You can also specify exactly how many units should be assigned to each arm. Researchers can plan exactly how many treatments will be deployed.

The standard errors associated with complete random assignment are generally smaller, increasing experimental power. See this guide on EGAP for more on experimental power. For example, when deploying a survey random assignment of treatments on a platform like Qualtrics, simple random assignment is the only possibility due to the inflexibility of the built-in random assignment tools.

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. In this simulation complete random assignment led to random assignment of treatments This decrease was obtained with a small design tweak that costs the researcher essentially nothing.

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 random assignment of treatments their pre-treatment covariates, and then complete random assignment is conducted within each block.

For example, a researcher might random assignment of treatments 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. 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. In the example above, random assignment of treatments, the different blocks have different probabilities of assignment to treatment. Left unaddressed, this discrepancy could bias treatment effects. A note for scrupulous readers: the estimands of these two approaches are subtly different from one another, random assignment of treatments.

The LSDV approach estimates the average block-level treatment effect. The IPW approach estimates the average individual-level treatment effect. They can be different. Since the average block-level treatment effect is not what most people have in mind when thinking about causal effects, analysts using this approach should present both.

How to create blocks? In the HairEyeColor dataset, we could make blocks for each unique combination of hair color, eye color, and sex, random assignment of treatments. An alternative is to use the blockTools package, which constructs matched pairs, trios, quartets, etc. A note for blockTools users: that package also has an assignment function. 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:. Clustered assignment decreases the effective sample size of an experiment. In the extreme case when outcomes are random assignment of treatments 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, random assignment of treatments.

Almost all cluster-assigned experiments fall somewhere in the middle of these two extremes. 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 randomizryou can specify multiple treatment arms random assignment of treatments a variety of ways:. 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, random assignment of treatments, or classrooms nested within discrete schools. All five random assignment functions in randomizr assign units to treatment with known if sometimes complicated probabilities.

The declaration object contains a matrix of probabilities of assignment:. In order to use inverse-probability weights, random assignment of treatments, we need to know the probability of each unit being in the condition that it is in. For each unit, random assignment of treatments, we need to pick the appropriate probability.

Random assignment procedures are often described as a series of steps that are manually carried out be the researcher. In order to make this procedure reproducible, these steps need to be translated into a function that returns a different random assignment each time it is called.

This assignment procedure is complicated by the sibling rule, which has two random assignment of treatments first, students are cluster-assigned by family, random assignment of treatments, and second, the probability of assignment varies student to student.

With this function, the random assignment procedure can be reproduced exactly, the complicated probabilities of assignment can be calculated, and the analysis is greatly simplified. For many designs, the probability of assignment to treatment random assignment of treatments be calculated analytically. For example, in a completely randomized design with units, 60 of which are assigned to treatment, the probability is exactly 0.

However, in more complicated designs such as the schools example described aboveanalytic probabilities are difficult to calculate. In such a situation, an easy way to obtain the probabilities of assignment is through simulation. This plot shows that the students who have a sibling in the lottery have a higher probability of assignment.

The more simulations, the more precise the estimate of the probability of assignment. Whenever you conduct a random assignment for use in an experiment, save it! At a minimum, the random assignment should be saved with an id variable in a csv, random assignment of treatments. Set a seed for reproducability set. Simple random assignment Simple random assignment assigns all subjects to treatment with an equal probability by flipping a weighted coin for each subject.

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. Block random assignment Block random assignment sometimes known as stratified random assignment is a powerful tool when used well. Clustered assignment Clustered assignment is unfortunate. 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 random assignment of treatments or control Clustered assignment decreases the effective sample size of an experiment.

Blocked and clustered assignment The power of clustered experiments can sometimes be improved through blocking. Calculating probabilities of assignment All five random assignment functions in randomizr assign units to treatment with known if sometimes complicated probabilities. For example, random assignment of treatments, consider the following procedure for randomly allocating school vouchers. If one sibling in a family wins, all other siblings automatically win too, random assignment of treatments.

Check probabilities of assignment directly For many designs, the probability of assignment to treatment can be calculated analytically. Call your random assignment function an approximately infinite number of times about 10, for most purposes. Count how often each unit is assigned to each treatment arm. Save your random assignment Whenever you conduct a random assignment for use in an experiment, save it!

### Randomly assign subjects to treatment groups To create a random assignment for a completely randomized design with two factors, you can just modify the IF statement in the previous example. The following program generates a random assignment of treatments to 30 subjects, in which Factor A has 2 levels and Factor B has 3 levels (and hence 6 treatments). Random assignment of experimental units to treatments is carried out separately within each block. Similarities b/w Blocks and Strata Completely randomized . Aug 12,  · Study participants are randomly assigned to different groups, such as the experimental group, or treatment group. Random assignment might involve such tactics as flipping a coin, drawing names out of a hat, rolling dice, or assigning random numbers to participants.