Another Look at the Robustness of the Product-Moment Correlation Coefficient to Population Non-Normality
Year: 1982
Type: article
Abstract: PerspectiveStudies of the effects of population nonnormality on the sampling distribution of the product-moment correlation coefficient date from the 1920's.For example, E. S. Pearson (1929), after studying samples taken from two "considerably non-normal distributions" concluded that "the normal bivariate surface can be mutilated and distorted to a remarkable degree without affecting the frequency distribution of r." (Quotations taken from Kowalski, 1972).Other studies of the period resulted in essentially the same conclusion.(See Kowalski 1972 for a review of this literature.)Later researchers tend to agree with Pearson's (1929) conclusion provided that IE' Iis near zero.Norris and Hjelm (1961) state, "When there was essentially no correlation in the population, the shape of the sampling distributions for the product-moment correlation coefficients did not vary markedly as a function of nature or extent of nonnorrnality in the bivariate distribution.In general, these obtained sampling distributions conform very closely to their theoretical distributions."This point of view has become so popular that Kowalski (1972), after reviewing the literature, states "Everyone seems to agree that the distribution of r is quite robust to nonnormality when P = 0•••."
DOI: 10.62798/tzqq1969
Authors: R. Clifford Blair, Stephanie Bear Lawson
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W3005116162