I've conducted a PCA analysis of n-anthropometric measures on separate sets of male and female data. Before analysis, these data were normalized within each group such that mean = zero and SD = 1.
As this is a design project, I am interested in accommodating 90% of male and 90% of females. For each PCA result, I calculated a 90% accommodation envelope about the PC Score and defined 8 boundary points and one centroid according the the the method described by Meindl (1993). The male results look similar to this:
The plot for the females is very similar (distributed about the origin), the only difference is fewer PC Scores due to fewer female cases.
As I know some of these boundary cases are redundant (e.g. large females will be within the male data cloud, and small males will be within the female cloud), I was wondering if there was a logical way to determine how these two distributions overlap in normalized (or non-normalized space)?
I tried a simple test where I multiplied the z-scores of the female boundary cases (calculated using male mean) with the PC score coefficients of the male data and came up with the following:
As you can see, the female cases (red circles) are shown overlapping the male distribution (yellow circles) and vice versa. The blue points are male PC score.
Note: this test case was done with only two body dimensions, so it was easy to compare against the original, non-normalized dimensions. Everything checked out - same cases appear redundant in non-normalized space as normalized PC space.
Is this a legitimate technique (i.e. treating female data as if it were male) to identify where a case lies in the male data? Is there another technique that would be preferable?
Thanks in advance!