I need to compare proportions of difference scores between 2 (unequal n) samples (males vs. females) on 2 different measures. I want to enter the difference scores into contingency table for chi-square type analysis.

I subtract male-female scores for each of the 2 measures

`R1C1 = Male"Yes"MeasureA - Female"Yes"MeasureA R1C2 = Male"Yes"MeasureB - Female"Yes"MeasureB R2C1 = Male"No"MeasureA - Female"No"MeasureA R2C2 = Male"No"MeasureB - Female"No"MeasureB `

When I use this method for getting difference scores, not surprisingly, some values are negative, which prevents me from doing chi-square. Is there a way to transform the data to do away with the negative values but preserve the proportions? For example, I was wondering if it would be acceptable to just square all difference scores, and then do chi-square?

So here's a bit more detail. I am investigating a measure of sexual experiences. The original measure asks respondents to indicate whether or not they've experienced a variety of sexual encounters. The survey has 2 parallel versions — one for females (asking about sexual victimization) and one for males (asking about perpetration). research has shown that, when given the original measure, females indicate ~2/3s increased rates of victimization, than males reported rate of perpetration. I have created a modified version of the survey (for both male and female versions) and I have hypothesized that this modified version will decrease the discrepancy rate between female/victims and male/perpetrators rates of responding.

I have an unequal number of males and females. each participant was given both versions of the survey (original and modified), the original was given first. I have collapsed the response data to be dichotimous — so either "yes" ([female]i have been raped/[male]i have raped someone) or "no" ([female]i have never been raped/[male]i have never raped anyone).

So, what i need is a way to determine if the male-female discrepancy ratio on the original measure is significantly different from the male-female discrepancy ratio of the modifed version.

further additional info. I have already run paired sample t-tests and determined that male report rates on the modified versin are significantly higher than on the original — female report rates are not significantly different across versions. So i know that the discrepancy is reduced (because male reports increased and females did not) but I'm looking for a direct way to compare the difference scores/proportions between measures.

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#### Best Answer

You say you did paired t-tests on the original data, before dichotomizing it, and that males increased significantly from the old form to the new but the female change was not significant. Unfortunately, that can *not* be taken as showing that the male change was bigger than the female change. You need to do an independent-groups t-test on the two sets of change scores. (Better yet, you could replace all the t-tests by confidence intervals for the corresponding means and mean differences, which would give you more information.)

For the dichotomized data, the situation is similar.

You have two contingency table, one for males and one for females.

`Males Yes No Total Yes Myy Myn My. No Mny Mnn Mn. Total M.y M.n M.. = M = total number of Males Females Yes No Total Yes Fyy Fyn Fy. No Fny Fnn Fn. Total F.y F.n F.. = F = total number of Females `

For each table, the analog of the paired t-test is the McNemar test,

http://en.wikipedia.org/wiki/McNemar%27s_test

I know of no simple standard test of the difference between the changes in endorsement rates, but if all of Myn, Mny, Myy+Mnn, Fyn, Fny, Fyy+Fnn are "large" then an asymptotic test might be justified.

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