SIGN CHANGES WHEN CORRECTING FOR RANGE RESTRICTION - A NOTE ON PEARSONS AND LAWLEYS SELECTION FORMULAS

K. Pearson (1903) recognized that the correlation coefficient was subj ect to distortion when a sample was censored or preselected in some wa y. He proposed 3 univariate correction formulas for better estimates i n these circumstances. These have become well known from the work of R . L. Thorndike (1949). D. N. Lawley (1943) proposed a general solution usually called the multivariate correction for range restriction. Bot h Pearson's and Lawley's corrections are discussed and examples are pr esented. Of particular interest are the opportunities for the correcte d correlations to change sign as a result of the correction. Numerical examples are presented that show that correlations can change signs i n the Pearson-Thorndike Case 3 and in Lawley's general solution.