A reanalysis of Shaycroft's matrix of intercorrelations of 10 test variables plus 4 random variables is discussed. Three different procedures were used in the reanalysis: (1) Image Component Analysis, (2) Uniqueness Rescaling Factor Analysis, and (3) Alpha Factor Analysis. The results of these analyses are presented in tables. It is concluded from the results that factor analysis or image component analysis offers protection from interpreting random relationships as being meaningful. (Author/DB)