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I want to test whether the distribution of age classes of population 1 = that of population 2. I have 3 age classes (juvenile, subadult, adult). I also would like to compare these age class distributions between males and females. What kind of test should I use for this? I don't want to compare the distributions to an expected value.

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If I were you, I would probably use a Chi square test. Anyway, in case you are not satisfied with the Chi square solution, here it is als a quite complete list of possible analyses of cathegorical data: https://en.wikipedia.org/wiki/List_of_analyses_of_categorical_data

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