measuring interaction effects

cww

New Member
#1
I've spent months studying statistics texts, and I just cannot figure out how to do the following:

I've got categories distinguished by some characteristic, say M vs. F, and then each of those categories has been assigned to one of two groups, say the treatment and the control group in an educational study. I then want to use completion rates, or success rates (which is a binary categorical outcome variable, or a percentage for the group as a whole) as the dependent variable. None of the group Ns are the same.

Say I have the following results, for example:
Retention rates for each group:
M control: 60%
M treatment: 50%
F control: 70%
F treatment: 65%

I want to be able to test the following hypothesis:
The decrease in retention for males when moving from the control to the treatment group is greater than the decrease in retention for females.

I cannot figure out how to do this. I can compute z-scores showing that the decreases in M and in F from the control to treatment are statistically significant. I can compute z-scores showing that the higher F scores are statistically significant in both the control and the treatment groups. But there is no way to use this technique to compare the significance of the differences in proportions from one group to another.

I can run a BLR to try to determine if there is a second order interaction, but after much banging my head against the wall these past several months, I cannot figure out how to interpret the results. From the books I've read, it seems to me that the second order interaction is testing something different from what I want to test. Someone please tell me if I am wrong, but it is my understanding that the second order interaction will show up as significant if any of the pairwise comparison tests of combinations of two factors show up as statistically different - but this isn't what I want to test! I don't care, for example, if F control group retention is higher than M treatment group retention, and I already know how to test for pairwise differences of this kind.

Can anyone tell me if:
  1. I am correctly interpreting the results of BLR interaction terms, and/or;
  2. How I can actually test for significance for the differences between two sample proportions?

Or, if you can recommend a good book that would help, I would also be grateful! (I've looked at a bunch of books on interactions, and I cannot find one that really answers my question!

Thanks in advance for reading my post!
 
#2
I think you can test your hypothesis "The decrease in retention for males when moving from the control to the treatment group is greater than the decrease in retention for females" by fitting the logistic regression as follows:

Logit(P) = sex treatment sex*treatment

and noting if the interaction term sex*treatment is significant.
 

cww

New Member
#3
Thanks, d21e7x11, for your response. This is what I originally thought, too, but then I seemed to get results from the stat software that didn't make sense, and when reading through some texts about interactions, it seemed to me that the interaction term would come up as significant if any of the pairwise comparisons from the fully crossed design were statistically significant, which isn't the same thing. I'm just not totally clear on this.