Effects of Coarse Grouping and Skewed Marginal Distributions on the Pearson Product Moment Correlation Coefficient

Twelve non-normal bivariate distributions were constructed to investigate (a) the effects which coarsely grouped, skewed marginal distributions have on the correlation coefficient and (b) the accuracy of current methods of correction for grouping. The investigation revealed that the correlation coefficient is severely limited in the values it can assume when the underlying marginals are highly, oppositely skewed and one or both of the marginals has only two class intervals. The study further revealed that the correction formula (which is based on the assumption of underlying, normal marginals) is extremely accurate, regardless of the degree of marginal skewness, except where one or both of the marginals has only two class intervals. The major conclusions of the study were that the use of asymmetrical, dichotomous variables should be avoided in correlation analysis, and that the correction for coarse grouping should be applied, on an experimental basis, to correlations computed for joint distributions of coarsely categorized variables.