Also, I am not sure how much such comparison would depend on the specific test. Let’s imagine that we have one population with average IQ 100 and other population with average IQ 120. If we give them a test consisting of IQ-110-hard questions, the two populations will probably seem more different than if we give them a test consisting of a mix of IQ-80-hard and IQ-140-hard questions.
You can compare by looking at which percentile of population B, the median of population A corresponds to.
Edit: also once you’ve compared several populations this way, you can try to see if there is a way to normalize the test such that the distributions for all the populations have similar shapes.
You can compare by looking at which percentile of population B, the median of population A corresponds to.
Edit: also once you’ve compared several populations this way, you can try to see if there is a way to normalize the test such that the distributions for all the populations have similar shapes.