Effect vs parameter significance

[mostater]

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?

Thanks for any help you can offer!

[lvm]

A significant individual parameter in your case could simply be due to a type I error.

[mostater]

Thanks lvm. I'm wondering the same thing but wanted to make sure that I wasn't overlooking something or not thinking through the problem correctly.