I used MANOVA in one of my papers to look at differences (in trust and efficacy) between three groups. Data came from a survey and I measured each construct using at least three items. The groups in the sample were not equal and the smallest group included 11 individuals (distribution of groups: 11, 37, 50, and 32 individuals). Both reviewers mentioned that differences in group size was problematic, and I should find another way to handle this. I wonder if there's a better statistic that MANOVA that can allow group differences.
Thank you,
Chamil
Dear Chamil,
Some researchers found that when the groups do not differ in size, the effect of heterogeneous covariance matrices is very small. However, when the samples are not equal in size, a heterogeneous covariance matrix can cause the type I error rate to be inflated and power to be diminished. When violations of the normality and homogeneous covariance matrix assumptions occur, statisticians often turn to a set of analytic approaches, collectively known as nonparametric statistics, which do not rely on such stringent assumptions to work properly.
The purpose of the attached paper is to compare the performance of the parametric MANOVA test statistics with a nonparametric alternative.
I hope you will find it useful for your research.
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