# Hypothesis test comparing groups where each measurement is a proportion?

I have data where there are 2 groups, 100 measurements per group and each measurement is a proportion (or number out of 1000) and I want to test for a statistically significant difference between the two groups. Can I use a t-test on the means, or does the fact that the values are proportions cause problems (meaning I would need a z-test)? But is there a problem with doing a z-test on means of proportions rather than raw populations?

Is it correct to say that because each measurement is a sample proportion and therefore each group represents a sampling distribution of the sample proportion, the mean proportion from all the measurements should be a good estimate of the population proportion? If this is true, surely I can use the mean proportion and standard deviation of each group for my z-test, instead of calculating the standard error to estimate the standard deviation, since I have way more than just one measurement of the proportion?

Just a note as well, I am not comfortable with treating all my samples as one large sample per group, as the proportion actually represents the results of a classification algorithm, in which each trial had some level of inbuilt randomness and the proportion of correct classifications is on the same data set for each trial.

Edit: To be clear, here is roughly what my data looks like:

As stated, each number is a number of 'success' trials out of 1000 and there are 100 of these measurements per group (with a difference in the independent variable).

• If your denominators are all equal, your data points are just in a unit 1000 times larger than originally (more or less), something like kilometers instead of meters. If you want to compare 60/1000, 37/1000, etc, just compare 60, 37, etc. Since the numerators are counts, you may want to do your test with the assumption of a Poisson distribution instead of the normal distribution that’s assumed for a t-test.
– Dave
Commented Apr 18, 2020 at 0:52
• @Dave Do you mean comparing the mean counts of each group using a poisson distribution? Commented Apr 18, 2020 at 0:56
• What I really mean is a Poisson regression with the group variable as the predictor, at least as a start. (You may end up preferring negative binomial, for instance.) You’re the one who know how your data look, though, and if a normal approximation is reasonable.
– Dave
Commented Apr 18, 2020 at 1:33