Appropriateness of interpreting significant factor effects in a non-significant GLM

Question

I realize similar questions have been asked several times, but I think this is different enough to warrant a seperate question.

I have poisson distributed catch data with independent variables of Tool (the thing used to catch the fish), Species, and Habitat. I am most interested in testing whether different tools catch fish at different rates (the tool*species interaction). All of these predictors are fixed, discrete factors. I know that none of these factors are the best predictor for catch (that would be a bunch of environmental variables that I don't have and am not particularly interested in). In order to test this, I ran a Poisson distributed GLM with the above listed Model Effects.

Given this situation, is it appropriate to interpret the significance (or lack thereof ) of the factor effects even when the model is highly non-signifant? If not, is there another way than a GLM that I can test whether the factor levels have any significant impact on the response variable?

Answer 1

"Significant" is a bad concept that is gradually being phased out. But you can interpret individual effects no matter what the overall model says. It's best to do that with compatibility intervals (aka confidence intervals) and not using null hypothesis "significance" testing. Whatever you do don't interpret a large P-value as indicating evidence of no effect. And on that note, with respect to the overall model, something akin to adjusted $R^2$ will put that into perspective.