How to compare multiple groups with multiple covariates?

#1
Hello,
Suppose you have a data set comprising 10 cases of 3 classes and 15 features (no assumptions about the distribution of the 15 features).

# Class F1 F2 … F15
1 A -0.2 -1.0 … 0.7
2 A 0.7 1.0 … 1.2
3 A -0.6 -0.4 … -1.2
4 B 2.2 -1.4 … 0.0
5 B -0.1 0.3 … -0.2
6 B 0.1 1.6 … -1.6
7 C 1.1 0.7 … 0.3
8 C 0.1 2.0 … -1.1
9 C -0.1 0.5 … 1.4
10 C -0.8 1.9 … -0.8


Are the classes significantly different?

If the data set had only feature F1, then the comparison would be straightforward; a one-way ANOVA would do the trick (with Tukey's posthoc test to find out where the differences are.)

However, the problem here involves multiple features. Which is the 'right' approach for testing all 15 features *at once*? Is it appropriate to perform 15 individual ANOVAs and then to correct for multiple testing (for instance, using Bonferroni or Holm)? Or is this problem to be tackled by MANOVA? I tried MANOVA in Minitab, but it seems that the number of features must be smaller than the number of cases, which is not the case in this example.

Any comments are greatly appreciated!
Thanks!
g.
 

JohnM

TS Contributor
#2
MANOVA is used when the multiple dependent variables can be considered together in a linear combination, and yes, you do need more cases than variables.

I would either run an ANOVA on each feature, or if you're concerned about Type I errors, maybe you could combine some of the features into categories and develop indices...