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
