Pearson's R and Coarsely Categorized Measures

Abstract

Errors can be introduced into scientific research when continuous concepts are measured on scales that rank the concepts into a few categories. This presents a potential problem because measures of association between two variables may differ depending on whether continuous or collapsed measures are used. We analyzed simulated data and examined differences in the correlation between two normally distributed continuous variables and the same two variables collapsed into a small number of categories. In general, the differences in correlation coefficients computed on continuous variables and the same variables collapsed into a few categories are small. The greatest differences in the correlations between the two types of variable occur when the continuous variables' correlation is high and only a few categories are used for the collapsed variables. When as few as five categories are used to approximate the continuous variables, the correlation coefficients and their standard deviations for the collapsed and continuous variables are very close. These findings suggest that under certain conditions it may be justifiable to analyze categorical data as if it were continuous.