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:

- I am correctly interpreting the results of BLR interaction terms, and/or;
- 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!