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I would like to compare two beta coefficients from two different Poisson models which have the same variables and applied to different samples. I would like to test their difference to check if the null hypothesis that their difference is zero can be rejected. Both models run on a sample of size N=120. A similar question has been posted here for linear models: Test a significant difference between two slope values

$$ Z = \frac{b_{1}-b_{2}}{\sqrt{(SEb_{1})^2+(SEb_{2})^2}} $$

I am wondering if the same approach (z-test) can be used also in this case. Also a bit confused because z-tests assume knowledge of the population variance which we don't have either in my case or in the example. I presume it is based on assuming an asymptotic standard normal distribution under null hypothesis? Would a t-test be a more appropriate choice or some other test?

I understand that making one common model and having an interaction term would also answer this but i would like to know the appropriate way to test this when having two different models.

Barrett
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  • If t is appropriate, so is z; a t distribution with df = 120 is pretty much indistinguishable from a z. And the assumption of normality is common to both. – Peter Flom Jul 17 '23 at 11:50
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    Thank you for your reply Peter. Yes that is definitely the case, doesn't one though assume that the population variance is known when performing a z-test as opposed to a t-test where the sample variance is used or is this a triviality? Would you use the above formula to test the mentioned hypothesis? – Barrett Jul 17 '23 at 14:31
  • That would depend on whether the parameters of a Poisson model are normally distributed. I don't know, and wasn't able to find out. But, if not, then I would use something else, that doesn't depend on normality. With the usual sort of data, I might use a test of medians. But I don't know how that would work here. – Peter Flom Jul 17 '23 at 14:46

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