I have two groups, one participated in a special program and one did not. I want to examine if the program affected the students who participated in it differently according to gender. Usually we do such a test with repeated measures, but the scores do not follow normal distribution.
I used Mann Whitney test to examine the influence of the program, but did not know what test to use to examine the interaction between the intervention (the program) and gender.
I don't believe that you need a non-parametric test for doing this. The assumptions of ANOVA are generally phrased wrong. You can use a two-way ANOVA to test this unless your residuals are not bad. The residuals must be normal not the data. There are problems about interactions when using a nonparametric test. Attached an informative link
https://www.researchgate.net/post/Can_I_do_a_two-way_ANOVA_on_a_rank-transformed_data
Dear Mehmet,
Many thanks for the answer. I did the test for the normality of residuals and indeed they were normal, but another problem still exists: the variances are not equal. Of course I did the variances test for the original scores and not the residuals. So, what should I do? Can I for example compute the difference between the scores of the post and pre tests and then do Mann Whitney test of the difference over gender?
You should check homogeneity of variances in residuals too.
ANOVA has some protection against non-normality and non-homogeneity of variances. If you have equal sample sizes in your cells, protection against the latter strengthens.
You could do t-test as well as MW to pre-post differences. But you could not find out interaction that way.
Dear Mehmet, thanks for answering. what does the MW to pre-post differences over gender measure?
Another issue, I wonder what references I can depend on that mention the residuals as those that should be taken in consideration when looking for normality and equal variances, rather than the original data.
Good question. I think it is better to use t-test with differences otherwise the interpretation might be harder. There is a long discussion about the differences between t-test and MW that you could find on internet or RG.
I have found an article reference (I guess not the very original one but anyway)
The Assumptions of the Linear Regression Model
Author(s): Michael A. Poole and Patrick N. O'Farrell
Source:
Transactions of the Institute of British Geographers
, No. 52 (Mar., 1971), pp. 145-
158
There are many textbook references including Design and Analysis of Experiments by Douglas C. Montgomery too.
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