Population Proportion of Explained Variance in Principal Component Analysis: A Note on Its Evaluation Via a Large-Sample Approach

A large-sample procedure for examining explained population variance in principal component analysis is discussed. The method yields interval estimates for the proportions of variance accounted for by the considered for retention principal components. The obtained confidence intervals can be used to make decisions about the number of selected components, based on their performance in studied populations. The approach can also be employed for ascertaining group similarity or differences in percentage explained variance by the considered principal components. The procedure is illustrated with 2 examples.