A program to compute nonparametric partial correlation coefficients

Abstract

Measures of correlation and partial correlation provide crucial information about the interrelations among research variables and underlying factors. The techniques of causal modeling and causal path analysis, in which measures of partial association carry the critical information, provide a powerful quantitative framework within which to develop and test scientific theories (Asher, 1983; Cohen & Cohen, 1983; Kim & Mueller, 1978; Morris, 1990a, 1990b; Reynolds, 1974). The paper by Reynolds (1974) is provocative in that it demonstrates the efficacy of nonparametric (ordinal) partial correlation coefficients in t~st­ ing spurious correlation models. To support population inferences, parametric measures of association or partial association, such as the (partial) Pearson product moment correlation or the partial regression coefficient, require stringent structural assumptions (general linear model), distributional assumptions (bivariate normal distribution), and according to some (Nelson, 1984), scaling assumptions (interval or ratio scale). Measurement in the social sciences often fails to satisfy some or all of these assumptions, which renders parametric measures of association questionable (Nelson, 1984; Reynolds, 1974). To be sure, the debate about measurement scales and scale-dependent permissible transformations continues (Gaito, 1980; Townsend & Ashby, 1984), and sophisticated qualifications of earlier conclusions have recently emerged (Davison & Sharma, 1988; Michell, 1986). Nevertheless, nonparametric measures obviate paramet~c assumptio~s, yet nonparametric measures of correlatton and partIal correlation are almost completely absent from the experimentalliterature. The present scarcity of nonparametric measures of partial correlation in the literature may be due to their unfamiliarity and inaccessibility relative to the more popular parametric measures. . My goal in the present paper is to make nonparametnc measures of correlation and partial correlation more accessible to researchers by describing the statistical basis of three related nonparametric measures and presenting a computer program that computes all three. First, following Wilson (1974), I d~scribe a class of,three no~­ parametric bivariate correlations. Next, I de~nbe Quade s (1974) generalization of this class of corr~latlOns.to partial correlations and his formula for calculating their asymptotic standard error and thereby testing their statistical significance. Finally, I present a flexible PC-eompatible computer program (Turbo Pascal version 3.0) that computes