A teacher believes that whatever he says in class has no effect on his students.

ID: 3200058 • Letter: A

Question

A teacher believes that whatever he says in class has no effect on his students. Just as he's about to quit his profession, a statistician enters the room and suggests that the teacher design a study to test his assumption. The study will look at whether providing in-class feedback on homework assignments enhances classroom performance. The teacher wants to know whether providing feedback before or after returning the assignments is most useful. He's also interested in the most effective means of presenting the feedback: verbal presentation, written handout, or a summary on overheads. Ultimately, he'd like to identify the best approach for increasing test scores of the students. There are 12 classes available in the school for the experiment. Design an experiment that helps answer these questions. Be sure to identify the factors, the levels of the factors, the treatment groups, and the response variable. Comment on how the students will be assigned to the different treatment groups. Is it possible to use simple random assignment of all students? As much as possible, use diagrams instead of words to summarize your experimental design.

Explanation / Answer

Solution

In brief, a randomized block design with 2 responses per cell would be able to answer all the relevant questions on treatment effects.

In detail

Treatments (3)

T1: Give verbal presentation

T2: Give written hand-outs

T3: Provide summary

Levels (2) for each treatment

L1: Give feedback before returning the assignments

L2: Give feedback after returning the assignments

Number of responses (2 per cell)

For each of the treatments and each of the levels under each treatment, assign 2 classes at random. [6 treatment-level combinations and 2 class per combination, takes care of 12 classes fully]

Response

Average test score of each class

Let xij1 and xij2 be the average scores of two classes assigned to treatment i and level j.

Then, the data sheet would be as shown below:

Level 1

Level 2

Treatment 1

x111, x112

x121, x122

Treatment 2

x211, x212

x221, x222

Treatment 3

x311, x312

x321, x322

Analysis

A two-way ANOVA with equal number (2) of observations per cell would bring out

1. Treatment effect

2. Level effect

3. Treatment-level interaction.