# Completely Randomized Design

## Completely Randomized Design As the most basic type of study design, the completely randomized design (CRD) forms the basis for many other complex designs. CRD is one of the most popular study designs and can be applied in a wide range of research areas such as behavioral sciences and agriculture sciences. There are two primary reasons for its popularity of CRD. One is its simplicity and another is that participants are randomly assigned to treatment conditions according to CRD, which provides a strong basis for causal inference.

The CRD can be considered as any design in which each participant is assigned to one of 2 or more conditions at random. In other words, the probability of being grouped to any specific condition is the same for each participant. However, the probability for assignment of every condition doesn't have to be the same. One quick example, let's say there are 3 treatments in a clinical trial, and the probabilities of assignment are 0.3, 0.3 and 0.4 for treatment 1, 2 and 3 respectively (Figure 1). From a statistical perspective, keeping these probabilities equal may have benefits, but in some specific cases, application of unequal probabilities may be better. Figure 1. The completely randomized design.

The CRD is very flexible since the conditions can be either qualitatively or quantitatively different. In addition, these conditions can also differ along a dimension or multiple dimensions (in the latter case, this design is usually considered as a factorial design). That is to say, in a simplest case, each participant will be only measured one single response variable or dependent variable, but this design can also be applied to multiple dependent variables. Besides researchers usually use ANOVA (analysis of variance) to analyze data, and if there are more than one dependent variable, MANOVA (multivariate analysis of variance) will be applied.

In recent years, researchers pay more attention to calculating an appropriate sample size in the CRD. An adequate sample size is crucial to get acceptable statistical power that is used to reject the null hypothesis if it is false and to have sufficiently narrow confidence intervals to compare the mean differences. Obviously, there is a single biggest disadvantage of the CRD that it usually needs a quite large sample size to get adequate power and precision. For example, there are 2 treatments of equal size and α=0.05 (two-tailed), then a total sample size of 128 participants is basically needed to have an 80% probability of observing a medium effect size. All sources that make a specific participant’s score differ from the mean score in that participant’s group are considered as errors in the ANOVA model accompanying a CRD. It means that CRD totally counts on the randomization of all relevant influences on the dependent variable rather than making efforts on controlling of those influences. That's why a large error variance is acquired, lowering power and precision in the ANOVA associated with the CRD. In order to control extraneous influences and thus increase power and precision, people have developed some more complex designs and analyses, namely randomized block design, analysis of covariance, etc.

At CD BioSciences, we can help you not only the completely randomized design but also the appropriate choice of statistical strategy. If you have any questions, please feel free to contact us.