Loss of significance when changing baseline category in regression Let's say I am using age group as a factor in a linear regression model with some response variable, fitting the model with under-20s as the baseline category. If there are any significant effects for older age categories when compared with under-20s, I can see this easily through a coefficient whose 95% confidence interval excludes zero.
Let's say now that I set the 20-24 age category as the baseline, but otherwise enter all the same variables into the model. Unlike before, I now have the opportunity to test whether the 25-29 age category differs significantly from the 20-24 category in terms of its effect on the response variable.
My question is: are all my tests - across the two baselines - still being performed individually at the 95% significance level?  
 A: *

*Yes, all your tests would typically be performed (you haven't actually said what software platform you're using, so I can't be 100% sure ...) at the 95% significance level. 

*If you re-fit the model several times with different baselines, you might want to consider a multiple comparisons correction.

*If you're going to make pairwise comparisons at all you should probably consider using the Tukey all-pairwise-comparisons correction (e.g. see the multcomp package in R); this will be less severe/cost you less than the generic correction for $n(n-1)/2$ tests.

*if you want to test for significant differences between successive levels you could use ?contr.sdif from the MASS package.

*in general I think people are over-eager to do significance tests for specific patterns among levels of categorical predictors.  For example, suppose I have a situation where the response increases gradually among the groups "<20", "20-40", ">40", and that the change is gradual and noisy enough that among all pairwise comparisons I can only detect a significant difference between "<20" and ">40". It is true, but probably not very helpful, to say "young and old people are significantly different from each other but neither young nor old people are significantly different from middle-aged people" ... better just to say "there is a significant effect of age - overall, it appears that the response increases with age"

