# Which test should I use for a proportion of a categorical variable in one sample?

I was wondering which test I should use to compare two proportions in one sample? My research is about white matter hyperintensities (WMH) in migraine compared to tension-type headache. There are three options: only deep WMH (63,6%), only periventricular WHM (6,1%) or both (30,3%). I want to know if there are more 'only deep'WMH compared to only periventricular WMH (only for migraine). I've a small sample (N=33). Can I use an one sample t-test?

Indeed pv+both and deep+both but how can I compare 33 patients with 12 pv and 31 deep to each other? Also with binominal?

• A one-sample t-test is used to compare a sample mean with a specified mean. Since your dealing with proportions the answer is no. I'm not sure what exactly you are trying to compare but it sounds like a job for a test of independence or Fisher exact test May 17, 2017 at 9:19
• Thank you. I want to compare deep WMH (63,6%) to periventricular WMH (6,1%) in the group with migraine. I came across this site statpac.com/statistics-calculator/percents.htm, so that's why I thought I could use an one-sample t-test May 17, 2017 at 9:32
• I stand (partly) corrected. Apparently people use t-test although not completely appropriate. Still given that there are three possibilities instead of two, I'm unsure whether a t-test is really appropriate. Perhaps this is more what you're looking for May 17, 2017 at 13:09
• Maybe a chi square goodness of fit is appropriate? May 17, 2017 at 13:42

You have 2 p-WMH and 21 d-WMH. Under assumption of equal probability of being p- or d-WMH, it should follow binomial distribution Bin(0.5, 23). Under this null hypothesis, the probability of getting 2 or less cases in p-WMH is 3.3 x $10^{-5}$. Same for 2 or less cases in d-WMH. So the p-value is 6.6 x $10^{-5}$.