The Use of Pearson's with Ordinal Data

Through the use of computer simulations, Labovitz's (1970) examination of the effects of randomly stretching measurement scales on the correlation between these stretched scales and an equal distance scoring system are reformulated and extended. Specifically, we examine the effects of the number of rank categories (C) for rank-order variables on the product moment correlation (r) between stretched scales and an equal distance scoring system. The stretched scales are drawn from three types of distributions: (1) the uniform distribution (i.e., the one used by Labovitz), (2) the normal distribution, and (3) a skewed distribution (log-normal distribution). We find that the average correlation (r) between the equal distance scoring system and the stretched scale is quite high for both the uniform and normal distributions, and that I increases with C only when C is greater than four or five. Thus, contrary to suggestions in the literature, I is not a monotonic function of C. More importantly, for the skewed distribution, is a monotonically decreasing function of C and is substantially smaller than r's based on uniform and normal distributions. The implications of these findings for the use of Pearson's r with rank-order values are discussed.