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Apologies if this is a really simple question but I cannot work it out.

I am trying to find out if year and/or location influence the amount of insects caught. Insects are measured in grams per 10km2. Year is a factor with 3 levels, location with 6.

The insect data is not normally distributed. According to the levene test, the assumption of homogeneity of variance is met for year, but not for location.

Is there a two-way ANOVA "equivalent" I can use for this? Or are there only one-way equivalent options?

I've searched around but can't find an example quite the same to use as a guide.

Thanks in advance,

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    $\begingroup$ Look into the proportional odds model which generalizes the Wilcoxon test . $\endgroup$ Commented Feb 22, 2022 at 17:56
  • $\begingroup$ @Ranon I'd probably think about a GLM, perhaps a gamma GLM with log link $\endgroup$
    – Glen_b
    Commented Feb 23, 2022 at 1:36

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Given the nature of the dependent variable, it can be assumed that it is severely right-skewed and that it is always non-zero. I recommend switching from normal regression (or ANOVA) to log-normal in this case.

If you are only interested in p-values, calculate ANOVA in the usual way, but use $\log(Y)$ as the dependent variable, where $Y$ is the original dependent variable. Interpret the resulting p-values as you are used to.

If you want to interpret the parameters, I recommend rewriting the ANOVA as a general linear model. Then exponentially transform the $\beta$ coefficients you found. The values of $\exp(\beta)$ then tell you how many times more insects you catch at that location compared to the reference location (note that how many times more, not how much more, as it is a multiplicative model, not an additive).

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