Question

A student commented in a discussion group: "Random permutations are used to assign treatments to experimental units with a randomized block design just as with a completely randomized design. Hence, there is no basic difference between these two designs." Comment?

Answer 1

What is Randomized block designs

Randomized block designs differ from the completely randomized designs in that the experimental units are grouped into blocks according to known or suspected variation which is isolated by the blocks. Variation such as fertility, sand, and wind gradients, or age and litter of animals can be isolated by appropriate blocking. Therefore, within each block, the conditions are as homogeneous as possible, but between blocks, large differences may exist. The treatments are assigned within the individual blocks at random with separate randomization for each block.

Let me explain a bit more clearly

Subject: This is the same for both CRD and RBD. It is the unit being measured such as a plant, a mouse, a person, etc.

Blocking Factor: This is something that is a natural grouping of subjects. Examples are a field, a town, a cage, a hospital, a classroom, etc.

Treatment: This is what you want to test the effect of. Examples of treatments a drug, a fertilizer, a new treatment, etc.

The factor of Interest (treatment): This is the level that captures the effect that you are interested in. This is also the level at which the treatment is applied. For instance, fertilizer to a field, drugs to a person, etc.

Nuisance Factors: These are sources of natural variation that you want to eliminate through randomization. For instance, by randomizing people you are hoping for similar distributions of height and weight to avoid the effect of confounding.

Now, for the two designs:

CRD: A completely randomized design randomizes at the level of the subject. Thus, each subject is randomized into treatment A, B, C, etc. Given subjects are randomized, they are also the factor of interest. Thus, you will compare the average of subjects in treatment A with those in treatment B, etc.

There are some key assumptions for this to work and be valid:

1. Subjects are independent: That means what happens to subject 1 will not impact subject 2 and so one.
2. There is no risk of cross-contamination: If you treat subject 1 with treatment A, it will not impact treatment B

RBD: This is a modification of the RB design. It is used when you either 1) you cannot randomize subjects without fear of cross-contamination, or 2) the treatment cannot be applied at the subject level.

An example would be helpful:

If you want to test the effect of a new medication upon people with diabetes. You could use a CRB that randomizes subjects into the new medication and a placebo. You can do this because each person takes their own medications and one person taking medication should impact another.

In contrast, if you were interested in field testing a new fertilizer, you would probably use a CRBD. In this design, you would apply different fertilizers to different fields ( randomize fields), because it would be too difficult to apply different fertilizers to different plants in a field without having cross-contamination

Advantages of randomized block designs

1. Complete flexibility. It can have any number of treatments and blocks.

2. It provides more accurate results than the completely randomized design due to grouping.

3. Relatively easy statistical analysis even with missing data.

4. Allows calculation of unbiased error for specific treatments.

Disadvantages of randomized block designs

1. Not suitable for large numbers of treatments because blocks become too large.

2. Not suitable when the complete block contains considerable variability.

3. Interactions between block and treatment effects increase error.

Thanks