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I am trying to compare if the proportion of one bird subspecies in a roosting area is different now from over 20 years ago.

My dataset looks like following:

-In 1996 birds were counted at a roosting site and were identified as one of two possible subspecies. These counts were done during 3 two-week periods.

-In 2019 birds were again counted at the same roosting site and the same 3 two-week periods, and were also identified as one of two subspecies.

I want to know if:

a) Are the subspecies' proportions different for the different two time periods?

b) Are the subspecies' proportions different in 2019 from 1996?

c) Is there an interaction between a) and b)? I do not expect this but I don't know if this should be included in any potential model.

I have considered using a GLM, but I'm not very familiar with how they work so I thought I'd better double check first. I am trying to do the statistics using R.

Thank you very much for your answers!

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I think building a GLM (generalized linaer model?) is overcomplicating things. I am not sure about how many external features you would (if you have any) include to the model.

So, the straight-forward approach would be to perform a proportion comparison test. Let's say you want to compare two groups with estimated proportions $\hat{p}$ and $\hat{q}$ with sample sizes of $m$ and $n$ respectively. Let $r$ be the overall proportion (when considering both groups together). Then, under the null hypothesis of both groups being equal:

$$Z:= \frac{\hat{p} - \hat{q}}{\sqrt{r(1-r) (\frac{1}{m} + \frac{1}{n}) }}$$

Follows a standard normal distribution $N(0,1)$. Typically, values outside the $(-2, 2)$ interval are considered enough for rejecting the null hypothesis. There are plenty of charts/software that will enable you to transform the $Z$-score into a $p$-value.

FOR YOUR SPECIFIC CASE: You can apply this strategy to solve "a" and "b". For "c", you can consider all year-period combination and test every possible pair of groups. If you go for this, please remember to apply a correction like Bonferroni's in order to control the chance of false positives eventually appearing after multiple tests are done. You can even make your life easier by just comparing the highest and lowest proportions against each other. If no significance differences are found, then you are already done!

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  • $\begingroup$ Thanks for your answer! The problem I have is (if I understood you correctly) that this doesn't really tell me whether there are differences between the three counting periods or the two years in my dependent variable (the subspecies' proportion). Just if there are differences between the six combinations of year and counting period. How would you do that? Thanks a lot! $\endgroup$ – Nico Ordax Sommer Jul 17 '19 at 9:31

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