In article <[EMAIL PROTECTED]>,
Dr. John C. Caruso <[EMAIL PROTECTED]> wrote:
>What are the advantages of having orthogonal (independent) significance
>tests?  For example, if I have two dependent variables (like neurotocism
>scores and extraversion scores) for two seperate t-tests (with the IV being,
>say, gender; the research question would be "do neuroticism or extraversion
>scores differ for males and females?") what would be the advantage (if any)
>of having uncorrelated neuroticism and extraversion scores in terms of error
>(Type I and Type II) rates?

It is not even the case that orthogonal and independent are the
same; independence is much stronger.

The situation for Type II is quite complicated, as the effects of
the alternatives may not be independent, even if independence under
the null hypothesis exists.  The Type I error probabilities for the
individual tests are unaffected by the existence of the other tests,
but the joint probabilities are.

For example, if the two error probabilities are .05, if the tests
are independent, the probability that there will be a rejection by
the union test is .0975.  Without assuming independence, all that
can be stated is that it is between .05 and .10.

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED]         Phone: (765)494-6054   FAX: (765)494-0558

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