Data were collected on the genus of flea beetle Chaetocnema, which contains three species: concinna(Con), heikertingeri (Hei), and heptapotamica (Hep). Measurements were made on the width and angle of the aedeagus of each beetle.
We would like to know if the measurements of width and angle of the aedeagus are different among the three species. To test this we use a multivariate analysis of variance (MANOVA) with the variables Width and Angle as the dependent (Y) variables and the variable Species as the predictor (X) variable. The variable Species is discrete and has three levels.
The MANOVA results show that there is a difference between the species when considering both Width and Angle simultaneously as well as when considering Width and Angle individually using univariate ANOVA analyses. Scheffe post-hoc tests show that for Width all three species are different; however, for Angle the species concinnaand heikertingeri are similar with heptapotamica being different from the other two species. These differences are confirmed in the boxplots below.
A scatterplot of the Width residual vs. the Angle residual from the MANOVA model above shows that the residuals appear to have a Multivariate Normal distribution, which satisfies an assumption of the MANOVA model.