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I have 5 groups of very different sizes. I want to know if various attributes are the same for the groups when I have corrected for the differences in size, e.g.

> Nordjylland_CG #smallest group

     A     B     C     D     E     
     0     0     96    9     29

> Hovedstaden_CG #largest group

     A     B     C     D     E     
     0     7     457   93    158

My idea is to sum across the categories and divide by the sum so that I get normalised or scaled numbers in stead of raw counts.

The counts can be assumed to be poisson distributed, but what is the distribution of the scaled counts (I'm using R with glm to do anova analysis of them)?

Thanks!

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If you want to compare the proportions, you could do that with a GLM or a log-linear model (loglin in R) -- or, for that matter, a chi-squared test or Fisher test, but you shouldn't just scale the counts to proportions, since the variance of those proportions depends on the number you scaled by.

If you're using a GLM you probably want to leave the numbers unscaled but write the model in such a way that the comparisons of interest correspond to a simple test of equality over a set of parameters.

If the categories are ordered you might want to consider an analysis that takes some account of that, perhaps ordered logit models

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  • $\begingroup$ Can you elaborate a bit? Which family should I choose in the GLM? Choosing "poisson" or "quasipoisson" and doing anova with Chi-sq or F-test returns a significant difference between groups (no surprise, the largest is several times larger than the smallest), but doing the same with the scaled counts only returns a significant difference between categories A,B,C,D,E as expected. What should I do instead? $\endgroup$
    – SiKiHe
    Jul 1, 2015 at 6:37

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