Completely Randomized Designs

Last updated on 2025-02-11 | Edit this page

Overview

Questions

  • What is a completely randomized design (CRD)?
  • What are the limitations of CRD?

Objectives

  • CRD is the simplest experimental design.
  • In CRD, treatments are assigned randomly to experimental units.
  • CRD assumes that the experimental units are relatively homogeneous or similar.
  • CRD doesn’t remove or account for systematic differences among experimental units.

A completely randomized design (CRD) is the simplest experimental design. In CRD, experimental units are randomly assigned to treatments with equal probability. Any systematic differences between experimental units (e.g.  differences in measurement protocols, equipment calibration, personnel) are minimized, which minimizes confounding. CRD is simple, however it can result in larger experimental error compared to other designs if experimental units are not similar. This means that the variation among experimental units that receive the same treatment (i.e. variation within a treatment group) will be greater. In general though, CRD is a straightforward experimental design that effectively minimizes systematic errors through randomization.

A single qualitative factor

The Generation 100 study employed a single qualitative factor (exercise) at three treatment levels - high intensity, moderate intensity and a control group that followed national exercise recommendations. The experimental units were the individuals in the study who engaged in one of the treatment levels.

Challenge 1: Raw ingredients of a comparative experiment

Discuss the following questions with your partner, then share your answers to each question in the collaborative document.

  1. How would you randomize the 1,500+ individuals in the study to one of the treatment levels?
  2. Is blinding possible in this study? If not, what are the consequences of not blinding the participants or investigators to treatment assignments?
  3. Is CRD a good design for this study? Why or why not?
  1. How would you randomize the 1,500+ individuals in the study to one of the treatment levels?
    You can use a random number generator like we did previously to assign all individuals to one of three treatment levels.
  2. Is blinding possible in this study? If not, what are the consequences of not blinding the participants or investigators to treatment assignments?
    Blinding isn’t possible because people must know which treatment they have been assigned so that they can exercise at the appropriate level. There is a risk of response bias from participants knowing which treatment they have been assigned. The investigators don’t need to know which treatment group an individual is in, however, so they could be blinded to the treatments to prevent reporting bias from entering when following study protocols. In either case random assignment of participants to treatment levels will minimize bias.
  3. Is CRD a good design for this study? Why or why not?
    CRD is best when experimental units are homogeneous or similar. In this study, all individuals were between the ages of 70-77 years and all lived in Trondheim, Norway. They were not all of the same sex, however, and sex will certainly affect the study outcomes and lead to greater experimental error within each treatment group. Stratification, or grouping, by sex followed by random assignment to treatments within each stratum would alleviate this problem. So, randomly assigning all women to one of the three treatment groups, then randomly assigning all men to one of the three treatment groups would be the best way to handle this situation.
    In addition to stratification by sex, the Generation 100 investigators stratified by marital status because this would also influence study outcomes.

Analysis of variance (ANOVA)

Previously we tested the difference in means between two treatment groups, high intensity and control, using a t-test. We could continue using the t-test to determine whether there is a significant difference between high intensity and moderate intensity, and between moderate intensity and control groups. This would be tedious though because we would need to test each possible combination of two treatment groups separately.

Analysis of variance (ANOVA) addresses two sources of variation in the data: 1) the variation within each treatment group; and 2) the variation among the treatment groups. In the boxplots below, the variation within each treatment group shows in the vertical length of the each box and its whiskers. The variation among treatment groups is shown horizontally as upward or downward shift of the treatment groups relative to one another. ANOVA quantifies and compares these two sources of variation.

R 

heart_rate %>% ggplot(aes(exercise_group, heart_rate)) + geom_boxplot()

ERROR 

Error in heart_rate %>% ggplot(aes(exercise_group, heart_rate)): could not find function "%>%"

Equal variances and normality

Confidence intervals

Inference

Prediction intervals

Design issues

Key Points

  • CRD is a simple design that can be used when experimental units are homogeneous.