[lal mohan kumar]

Thanks Clyde Schechter for your reply. I thought that increasing Type 2 will automatically reduce Type 1 error. If possible (and if you have time), can you connect the multicollinearity aspects with both errors in a lucid way. You mentioned in the same thread that "You shouldn't be doing significance tests as the nominal results have no discernible connection to actual Type I error rates in this setting". If you any thoughts on these please explain how errors can be affected my multicollinearity.

[Clyde Schechter]

I thought that increasing Type 2 will automatically reduce Type 1 error.

Not necessarily. It depends on how you make the changes. If you decide to use a different critical value for your test and change nothing else, then, yes, a critical value that increases Type 2 error will automatically also reduce Type 1 error. But that is almost never done. (I'm not saying it shouldn't be done, just that one seldom sees it in practice.)

Think about what happens when you decrease the sample size and then rerun the same analysis. The type I error doesn't change: it is still .05, or whatever critical value you select. But the type 2 error goes up with a smaller sample. Multicolinearity is just like that. In fact, multicolinearity is, as Goldberger points out, just a misleading term for "too small a sample size." The presence of multicolinearity decreases power (i.e. increases type 2 error) but has no effect at all on type 1 error.

You mentioned in the same thread that "You shouldn't be doing significance tests as the nominal results have no discernible connection to actual Type I error rates in this setting".

The setting I was referring to here was exploratory data analysis, with many different analytic approaches and hypotheses being tested. I think it is Statistics 101 level knowledge that when you do that, the nominal significance levels you get from that kind of data dredging have nothing to do with actual Type 1 error rates. Since "statistical significance" can't be directly interpreted in that context, it is pointless to even do statistical tests.

[lal mohan kumar]

Thanks a lot Clyde Schechter for the excellent (as usual) explanations. This thread is very informative.