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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:

90% accommodation envelope

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:

enter image description here

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!

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