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 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?

Patients were males or females and they were randomly assigned to a therapy for treatment. The progress of a type of cancer differs in women and men. They recruit $500$males and $300$for this purpose.

As therapies are not the characteristics of patients, it cannot be blocks as they were randomly assigned to treatment. Blocks need to be the characteristics of patients. Therapy is also not the block. Gender will be the block as gender of subject is characteristic of subject.

Blocks are gender: male or female.

Random block design can group subject into blocks having common characteristics. It allow us to take into account more variables.

Completely randomized design, on the other hand take into account the changes of predictor variables only.

Advantages:

It can be fixated by researchers if drug is working on males or not.

Disadvantage:

It becomes non block study and it is not possible to find out if the drug works for males only or on all manking.