# How to analyze the effects of two treatments on two groups as measured by pre, post, and delayed post tests?

I taught two different classes using two different teaching approaches. Each class was given pre-test, immediate post-test, and delayed post-tests to assess their understanding of the topic. The pre-test was used to analyze their existing knowledge. I would like to compare the immediate post-test score between the inductive teaching approach group with the deductive teaching approach group(to see which one is more effective after immediately teaching). Then, I want to compare the immediate post-test score with the delayed post-test score of both groups, to determine which teaching approach is more effective one week after teaching. So which statistical method should I use? My sample is 30 students. 14 students in the control group, 16 in the experimental group. I'm a novice, so please help me. Thank you.

• If I got it right, you have class A (14 students) attending inductive teaching approach and class B (16 students) attending deductive teaching approach. Each class will be tested with pre, post and delayed post tests. Is that correct? Commented Aug 27, 2021 at 12:22
• @Pitouille Yes, that's correct. Commented Aug 27, 2021 at 13:46

Below is an overview of the data that you have collected (or will be collecting):

Class Control: Inductive teaching approach (n=14)

Student Score Pre Score Post Score Delayed
Student 1 x y z
... ... ... ...
Student 14 a b c

Class Experimentation: Deductive teaching approach (n=16)

Student Score Pre Score Post Score Delayed
Student 1 x y z
... ... ... ...
Student 16 a b c

For your first assessment (post-test), one approach that I could suggest would be: for each group and each student, calculate the difference of score between Pre and Post. You will get 2 samples $$X_1$$ and $$X_2$$ of "differences" (i.e. increase or decrease in score within each class and by student) and then perform a Welch's t-test on the obtained samples to determine whether the means of both approaches are statistically significant:

• null hypothesis: means (variation of score in average) are equal
• alternative hypothesis: means (variation of score in average) are not equal

in R, t.test(X1, X2) will perform a Welch t-test by default with unequal variance. The output of the test will also provide you with the confidence interval. You can follow the same approach for the second test.

For this type of test, you can also consider Mann-Whitney. There is study from Winter and Dodou that you can find in the stats literature that could be relevant to your problem. Here is a link on a site that covers this issue: https://blog.minitab.com/en/adventures-in-statistics-2/best-way-to-analyze-likert-item-data-two-sample-t-test-versus-mann-whitney

You can also have a look at @Glen_b's answer which discuss the approach: Mann Whitney or two tailed t-test