Question

The head of the Department of Mathematics would like to determine whether student performance in an introductory math course differs depending on the professor of the course and the time of day the course is offered. Two math professors, Dr. Smith and Dr. Johnson, are each teaching two sections of the same introductory math course this semester. Dr. Smith teaches sections A01 (at 9:30 a.m.) and A03 (at 1:30 p.m.) and Dr. Johnson teaches sections A02 (at 9:30 a.m.) and A04 (at 1:30 p.m.). At the end of the semester, the department head will compare the average grades of the students in the four sections.
This is an example of:
(A) a completely randomized design with four treatments.
(B) a randomized block design with two blocks and two treatments.

(C) a randomized block design with four blocks and four treatments.

(D) a matched pairs design with two treatments.
(E) an observational study.

Answer 1

Her, the variation in the result can be due to the following 2 sources

1) Professor

2) Course taught

These two maybe thought of as blocks and treatment respectively, but for it to be a Randomised block design, both the blocks should have all the treatments i.e. both the professors should teach all the 4 courses. Which is not the case here.

It can also not be a matched pair design with 2 treatments as here we have 4 treatments.

Therefore, we can consider each of pair of Professor and course studied which are

1) P1 A01

2) P1 A03

3) P2 A02

4) P2 A04

as 4 different treatments and conclude its a completely randomised design with 4 treatments.

Option A