%0 Journal Article
%T On the Unlikely Case of an Error
%A George A. Marcoulides
%A Tenglong Li
%A Tenko Raykov
%J Educational and Psychological Measurement
%@ 1552-3888
%D 2018
%R 10.1177/0013164416686147
%X This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component¡ªand in particular for the first principal component¡ªto be error-free. In conjunction with the findings in Raykov et al., it is concluded that in practice no principal component can be perfectly reliable for a set of observed variables that are not all free of measurement error, whether or not their error terms correlate, and hence no principal component can practically be error-free
%K error variance
%K measurement error
%K observed variable
%K principal component
%K principal component analysis
%K reliability
%K variance
%U https://journals.sagepub.com/doi/full/10.1177/0013164416686147