Question

Comparing cancer treatments The progress of a type of cancer differs in women and men. Researchers want to design an experiment to compare three therapies for this cancer. They recruit $500$male and $300$female patients who are willing to serve as subjects.

a. Which are the blocks in this experiment: the three cancer therapies or the two sexes? Why?

b. What are the advantages of a randomized block design over a completely randomized design using these $800$subjects?

c. Suppose the researchers had $800$male and no female subjects available for the study. What advantage would this offer? What disadvantage?

Short answer

(a) The blocks in this experiment are the two sexes i.e. gender.

(b) The advantage of randomized block design is that it only considers the changes of predictor variables.

(c) The advantage is that the researchers can fix on whether drug will work on males or not and disadvantage is that drug will work or all mankind or not.

Step-by-step solution

Part (a) Step 1: Given information

We need to find whether the blocks in the experiment are tree cancer therapies or two sexes.

Part (a) Step 2: Explanation

We know that

The patients were either male or female (gender), and they were allocated to a therapy at random (treatment).

Because therapies are not features of patients, they cannot be used as barriers for patients (they were randomly assigned to the treatments).

The blocks must represent features of the patients, not therapies, and hence the gender must be one of the different blocks, as the gender of a subject is a characteristic of the subject.

Part (b) Step 1: Given information

We need to find the advantages of randomized block design over a completely randomized design.

Part (b) Step 2: Explanation

A randomized block design can organize people into blocks with a common characteristic, allowing us to account for the change of one or more additional variables.

Only the changes in the predictor variables can be taken into consideration in a completely randomized design.

Part (c) Step 1: Given information

We need to find the advantages and disadvantages.

Part (c) Step 2: Explanation

The study's use of $800$ males and $0$ females has the advantage of allowing researchers to focus on whether the medication works in males or not. One disadvantage is that it is now hard to assess whether the medicine works for all humans or just males because it is no longer a block trial.