I have two groups of samples ($A$, $n=100$ and $B$, $n=30$). For each groups we measured whether a trait is present or absent in each sample (0 or 1), resulting in frequency of "ones" for each trait. This we have done for 17 traits. Each individual trait can be easily compared using Chi square and we found that 3 out of 17 traits are significantly different between $A$ and $B$. Now, is there a way to test all 17 frequencies together and to show that populations $A$ and $B$ are different as a population when considering all 17 traits, although individual samples from $A$ and $B$ will look very similar when considering 1,2,... or 17 traits.
Or is it enough to say that since 3 out of 17 traits are significantly different between $A$ and $B$, these populations ARE indeed significantly different?
