Since there is a significant difference in mean vectors between the groups for Example 1 of Manova Basic Concepts, we would like to better understand where this difference lies. The natural first step is to see whether there is a difference between the groups for any of the dependent variables using ANOVA.
While this is the natural first step, it isn’t usually the best option since the whole idea of using MANOVA is to capture the correlations between the dependent variables, something which is lost when performing ANOVA on each of the dependent variables.
For Example 1 of Manova Basic Concepts, we can perform the ANOVA tests using the standard Excel ANOVA: Single Factor data analysis, but it is much easier to use the Multiple Anova option in the Real Statistics MANOVA data analysis tool (see Figure 2 of Manova Real Statistics Support). You should normally keep the default alpha value of .05. A Bonferroni correction will automatically be applied, and so the alpha value for each ANOVA test will be α/k = .05/3 = 0.016667. You can always override this value by changing the value of Alpha in the output.
The output is shown in Figure 1 (slightly reformatted to fit in the figure).
Figure 1 – Multiple Single Factor Anova
Note that despite the fact that a significant difference was detected by the MANOVA test, none of the ANOVA tests shows a significant difference (p-value > .05/3 = 0.16667). In fact, none shows a significant difference even if α = .05.