If we fail to reject the null hypothesis of MANOVA at an alpha level, does that mean that all the underlying univariate ANOVA tests will not be significant as well at the same alpha level?
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$\begingroup$ Did you really mean to include "not" in "not be significant"? $\endgroup$– whuber ♦Commented Jun 2, 2015 at 19:20
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$\begingroup$ Yeah, my apology $\endgroup$– Tommy YuCommented Jun 2, 2015 at 19:54
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2 Answers
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Not necessarily. But if you're planning to do each individual ANOVA anyway (presumably adjusting for multiple comparisons), why bother with the MANOVA?
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If you fail to reject the null hypothesis of MANOVA at some alpha level, then you can report your result as "There is no statistically significant difference ..." And you do not need any follow up tests.
answered Mar 18, 2016 at 8:09