Question

Twenty classrooms are randomly assigned to treatment A and twenty classrooms are randomly assigned to treatment B. Suppose there are 25 students in each class. Which is the most appropriate way to compare the effectiveness of the two treatments?

1) z-test
2) one-sample t-test
3) independent samples t-test on class means
4) independent samples t-test on individual scores

Answer 1

The most suitable method to compare the effectiveness of two treatments in classrooms is (4) the independent samples t-test on individual scores, given that individual student scores are used and comparisons are needed across all students.

Step-by-step explanation:

To compare the effectiveness of two treatments across classrooms, the most appropriate method would be to conduct an independent samples t-test on individual scores. This is because the data consists of scores from individual students in each classroom, which allows the comparison of the mean effects of Treatment A vs. Treatment B across all students.

If, instead, we were interested in the classroom as a unit of analysis (e.g., if classrooms were teaching different curricula), an independent samples t-test on class means might be more appropriate. The z-test is generally used when the sample size is large and the population variance is known. A one-sample t-test is not suitable because we have two samples (classrooms) and need to compare their means.