Should P-values of continuous variables be corrected?

Question

Usually, when doing multiple tests to compare means of categorical variables, it is advised to do some correction of the P-values to control the probability or proportion of false positives (Bonferroni, False Discovery Rate).

However, the definitions of these correction methods are so general that they seem to apply to any statistical test that yields a P-value.

Would it be make sense to correct P-values of tests that are comparing the value of continuous predictors to zero? In multiple regression models in ecology (generalized linear models, mixed effects models), we often test many predictors but never correct P-values explicitly. Is it relevant at all?

Answer 1

It makes just as much (or as little) sense to do this with this sort of statistic as with others. The issue is that you have done more than one test and, therefore, your chance of making a type I error is higher (over the multiple tests).

These issues don't depend on the nature of the test.

However, it is not at all clear whether to correct these p values nor how to correct them, if one chooses to correct. There are a lot of issues involved and, as was noted in a book I used in one of the first statistics courses I took "this is an area where reasonable people can differ".(Cohen Applied multiple correlation/regression for the behavioral sciences).