dennis roberts wrote:
>
> we have to first separate out 2 things:
>
> 1. some test statistics are naturally (the way they work anyway) ONE sided
> with respect to retain/reject decisions
>
> example: chi square test for independence ... we reject ONLY when chi
> square is LARGER than some CV ... to put a CV at the lower end of the
> relevant chi square distribution makes no sense
I don't know about that... In the "sterile" conditions assumed in intro
textbooks ("Doubt that the stars are fire...but never doubt the validity
of the assumed model") it makes no sense; however in practice it makes
plenty of sense to stop and reconsider the whole model - thus
effectively rejecting the null hypothesis, albeit in favor of the third
hypothesis
H_oz: Toto, we're not in Kansas anymore.
If you want to apply the hypothesis testing approach to this
consistently rather than Trusting the Force, you have to decide just how
low chi-squared can be before you decide that This Cannot Happen. Then
that's a critical value.
You could even modify your alpha, representing a probability under the
reinforced null hypothesis
H_oo: all the assumptions hold and moreover we have independence.
of rejecting at one end or the other.
Just a thought...
-Robert
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