I am quite new to statistical tests and not sure how to exactly describe my question. I searched but could not find similar questions. Please do let me know if this is a redundant question.
I recently tried to compare a distribution between male and female. Two-sample KS test seems to be a good fit and the result is somewhat strange to me. The distributions are shown in the following graph.
Dist for male and female:
It is quite obvious that there are two modes in female's distribution, whereas only one exists in male's. The two sample KS test gives me somewhat weird result:
Two-sample Kolmogorov-Smirnov test data: male and female D = 0.10714, p-value = 0.9834 alternative hypothesis: two-sided
The large p-value indicates insufficient evidence to reject the null hypothesis that they come from the same probability distribution, right? I think one of the reason is that my sample size is very low: (20+ for male and 50+ for female). But it is still too big -- whereas the empirical distributions are bimodal and unimodal.
Is there other more appropriate tests that I should use for these samples?