# McNemar's test with combined cell values?

I have 313 males and 356 females. Males and females each took two (gender specific) surveys (an original and a modified version). The survey I'm investigating is a measure of unwanted sexual experiences with parallel versions for men and women (e.g. female version = have you ever been victimized? male version = have you ever perpetrated?). Female's reported rates of being victimized (on the original version) are generally around 15%, while male reports of perpetration are generally around 4%. This discrepancy between female reports of being victimized, and male reports of perpetration, is what I'm interested in. I've revised the original survey into a modified version, and my hypothesis is that the female[victim]/male[perpetrator] discrepancy will diminish by using my modified survey version. So, I'm looking at frequency count data of dichotomous choices (yes [I've had this experience], or no [I've never had this experience]).

I've done the McNemar test for each gender, comparing survey versions and they show that male responses change (significantly) and are increased on the modified version, compared to the original, while female rates are equivalent across survey versions. I've also done paired sample t-tests comparing male-original X male-modified & female-original X female-modified, and the results here also show significant increase in male responding on the modified version, but no significant difference in women's scores on survey versions. So, I know that modified significantly increases male response rates (and does not increase female rates) so that the discrepancy has diminished, but now I want a more direct and statistically potent way of saying directly that the male-female discrepancies are significantly different between measures.

I was wondering if I could do a McNemar's again by combining male and female scores (e.g.

                                       ORIGINAL SURVEY
YES               NO
__________________________________________________
YES  | (male YY + female YY)  |  (male YN + female YN) |
MODIFIED SURVEY         |________________________|________________________|
NO   | (male NY + female NY)  |  (male NN + Female NN) |
|________________________|________________________|


Would this configuration preserve the correct proportions to address my question about male-female discrepancy-rate change across survey versions? If I'm off track here, can somebody please suggest some other method for comparing discrepancy rates of two groups on two different measures?

• Sorry for not answering your question; but I would like to mention that your idea / hypothesis is ideally suited for the randomized response technique, maybe you want to have a look at that (for future studies)? – hplieninger Jul 23 '13 at 5:56

If you want to look at the difference of Male-Female discrepancies between tests, start with a table of Male-Female and discrepancies.

Except for NY, these counts are (presumably) near zero. The statistical Expectations, under the null hypothesis, are for equal Ns for the counts in each column.

• Male Female
• NY NY
• YN YN

McNemar's Test for Changes is, logically, a Sign test being approximated by chi-squared.

The sign-test for the first column (second column) is McNemar's test on Males (Females).

The four cells can be tested for exact probabilities where the expected Probs are in the ratio of (313:313:356:356) for (males:males:females:females).

Maybe you should look into the interaction effects between the type of test/question-format, gender, and responses. So your model may look something like this:

answer_possibilities ~ gender*survey_type*q1 + gender*survey_type*q2


And then whittle it down from there. I may have jumbled up the explanatory variables...

Also, the discrepancy could be from one male perpetrating many times and doing that to multiple women. So maybe you could also add in a question asking the number of times women and men have done/experienced this and see if the total number of times add up to the same.