Bartlett's Test of Sphericity and the KMO Measure

Factor analysis and PCA are only useful when the observed variables share meaningful common variance — if your ten signals are all nearly uncorrelated with each other, there's no shared latent structure to extract, and any "factors" the algorithm produces will just be curve-fitted noise. Bartlett's test of sphericity formally checks this: its null hypothesis is that the correlation matrix is the identity matrix (all variables uncorrelated, "spherical" in the geometric sense), and a small p-value lets you reject that and proceed with factor analysis — a large p-value is a warning that extraction has nothing real to work with.

The Kaiser-Meyer-Olkin (KMO) measure goes further, checking not just whether any correlation exists but whether it's the right kind: it compares each variable's correlations with the others against its partial correlations (correlation left over after controlling for all the other variables), since factor analysis needs correlation that runs through a common factor, not correlation that's really just a direct pairwise relationship between two variables. KMO ranges from 0 to 1, and values above roughly 0.6–0.7 are usually taken as adequate for proceeding, with values near 1 indicating the correlation structure is well-suited to factor extraction.

A KMO of 0.85 alongside a Bartlett's test p-value under 0.001 together give reasonable confidence that ten valuation and quality ratios genuinely share common factor structure, rather than the analyst about to extract factors from what is essentially noise.