Using Rank-Order Measures to Represent Continuous Variables

The correlations between rank-order measures and their underlying scores, sampled from continuous distributions, are obtained for various numbers of categories in eight different distributions. The purpose is to assess the amount of distortion which results when researchers have only rank-order measures of underlying continuous level variables. Both the number of rankorder categories and the nature of the underlying distribution are found to be important determinants of the degree of distortion. Further, the relationship between the number of rank-order categories and the degree of distortion depends on the nature of the underlying distribution. The results of this analysis are then compared with those based on Stuart's work (a) and Abelson and Tukey (a, b) (which are found to overestimate the degree of distortion) and Labovitz (which are found to underestimate the degree of distortion). The results of this analysis are then generalized and their implications for the use of rank-order measures of underlying continuous level variables are explored. Several studies have examined the correlation between samples of scores from continuous distributions and their rank-order scores. These studies are important for social scientists because of the insights they provide about loss of information, or degree of distortion, resulting from the use of rank-order measures to represent continuous underlying variables. The issue is crucial, since many of the variables used in the social sciences may be assumed to have a continuous underlying distribution, even though our measures of them are only ordinal. For example, although political stability and democratization may each be conceived of as having continuous underlying distributions, ranging from low to high, we may have only rank-order measures of these variables. However, if these ordinal measures could substitute for the underlying continuous variable without greatly distorting zero-order correlations, they would provide for the multivariate analysis of ordinal data through the parametric strategy (Kim).'