# Difference between two proportions

How do you compute the difference between two proportions so those differences can be further analyzed? I have some repeated measures data with a first and second data point per subject, and I want to take the differences between the two, but the data is proportional data (successes out of a varying number of trials). Is it as simple as taking the difference of the logit of the two?

I want to use these differences in a linear model. I'd like the results to be at least about as interpretable as differences in log-odds would be.

Edit: For example if you have (random numbers here) 23 of 55 successes on the first measurement and 33 of 62 successes on the second, and you want to take a regression line through the change in success rates, would you normally use the difference in ratios (should the differing number of trials matter), the logit of that (but how do you deal with negative results), the difference in the logit, etc?

If I weren't taking the difference, I'd just use the logit (via the binomial family in R's glm function), but that doesn't work directly in this case.

Edit again: I found a paper (http://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/PASS/Tests_for_Two_Proportions.pdf) linked from another question, which gives an overview of some options (difference, risk ratio, odds ratio), but how does this apply if I want to use those values in a regression analysis?

• Your question seems muddled. You ask how to "take the difference of two proportions"; but that's literally $p_1-p_2$, not "the difference of the logit". Can you clarify what it is you need, and be more explicit about what the circumstances are, please? – Glen_b -Reinstate Monica Nov 13 '14 at 22:11
• Well, that's my question. Is that the right way to analyze repeated measures proportional data? (I know that R's glm function makes use of the total trails to weight different data points.) – Joshua Taylor Nov 14 '14 at 1:45