Bartlett's Test of SphericitySource:
Bartlett's (1951) test of sphericity tests whether a matrix (of correlations) is significantly different from an identity matrix. The test provides probability that the correlation matrix has significant correlations among at least some of the variables in a dataset, a prerequisite for factor analysis to work. In other words, before starting with factor analysis, one needs to check whether Bartlett’s test of sphericity is significant.
This function is strongly inspired by the
function in the psych package (Revelle, 2016). All credit goes to its
Revelle, W. (2016). How To: Use the psych package for Factor Analysis and data reduction.
Bartlett, M. S. (1951). The effect of standardization on a Chi-square approximation in factor analysis. Biometrika, 38(3/4), 337-344.