In a logistic regression, I have a categorical variable (3 levels) which the type III analysis of effects shows as non-significant (p >.05). Yet in the model parameter estimates, one of the individual parameters is significant (p <.05).
I thought the type III analysis tests that at least one of the betas is not zero. So I was assuming that, if the overall effect is non-significant, then none of the individual betas (2 in my case) would be significant as well. Is my thinking wrong? Is this a multiple testing issue?