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ANOVA, MANOVA, t-tests
Message posted by Choi on January 29, 2000 at 12:00 AM (ET)
Dear friends out there,
I have an instrument containing 70 items. To identify underlying dimensions, factor analysis revealed 10 meaningful factors. I wanted to see if these factors will be different across two groups (say, company size, large or small), I conducted a MANOVA on all 10 items together. A significant difference was found (p-value of Wilk's Lambda was 0.001). But MANOVA doesn't tell where does the difference lies. I then conducted 10 ANOVAs on each of the 10 factors. None showed significant Fs. I thus conducted t-tests on each of the 70 items in the instrument (of course controlling alpha at 0.05). I found two items showed significant difference (and they are meaningful differences) across the two groups.
Can anyone comment on the appropriateness of these steps? Do you feel that there is something wrong methodological wise?
Any comments will be highly appreciated. Thanks a lot.
Choi
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: ANOVA, MANOVA, t-tests
Message posted by Bill on January 31, 2000 at 12:00 AM (ET)
It is unusual to find a significant MANOVA and not find at least one sig. variable in the 10 although I guess it may be theoretically possible. To conduct 70 t-tests after failing to find any of the 10 variables significant is simply data-snooping. Why would you have done the factor analysis and ANOVA's if this was not the preferred method of analysis? To then perform 70 t-tests is saying, "I did not like the results of the original analysis so I'll analyze it another way." If you do that then I suggest that we play poker together. If I don't like the results of a hand (your 4 of a kind vs by pair) then can I change the rules after seeing you cards so that the new rules and outcome are more to my liking?? Just food for thought.
Re: ANOVA, MANOVA, t-tests
Message posted by Jack Tomsky on February 2, 2000 at 12:00 AM (ET)
You can invert the MANOVA test and do multiple comparisons (simultaneous confidence bounds) across all variables and factors. There is a one-to-one relationship between the MANOVA hypothesis test and the existence of a statistically significant comparison.
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