Solved – How to test whether variance explained by first factor of PCA differs across repeated measures conditions

correlationpcarstatistical significance

Context:

I have a study where six numeric variables are measured in each of two repeated measures experimental conditions (n = 200). Lets call the conditions $A$ and $B$ and the variables $A_1, A_2,…, A_6$ and $B_1, B_2,…, B_6$. Theoretically, I expect that in condition $B$ more variance in the variables should be explained by the first factor of a principal components analysis (PCA).

Typical values would be:

  • First factor of PCA on $A_1, …, A_6$ accounts for 30% of variance
  • First factor of PCA on $B_1, …, B_6$ accounts for 40% of variance.

Questions:

  • How can I test whether this difference is statistically significant?
  • How could this be implemented in R?

Best Answer

Just one (maybe silly) idea. Save 1st principal component scores variable for condition A (PC1A) and 1st principal component scores variable for condition B (PC1B). The scores should be "raw", that is, their variances or sum-of-squares equal to their eigenvalues. Then use Pitman's test to compare the variances.

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