The Nonparametric Correlations menu offers three nonparametric measures for pairwise correlations. Each Nonparametric correlation report gives the significance probability for the chosen measure of association and displays the association value on a bar chart. The three nonparametric correlation measures are defined as follows:
Spearman’s Rho
A correlation coefficient computed on the ranks of the data values instead of on the values themselves.
Kendall’s Tau
Based on the number of concordant and discordant pairs of observations. A pair is concordant if the observation with the larger value of X also has the larger value of Y. A pair is discordant if the observation with the larger value of X has the smaller value of Y. There is a correction for tied pairs, which are pairs of observations that have equal values of X or equal values of Y.
Hoeffding’s D
A statistical scale that ranges from –0.5 to 1. Large positive values indicate dependence. The statistic approximates a weighted sum over observations of chi-square statistics for two-by-two classification tables. The two-by-two tables are made by setting each data value as the threshold. This statistic detects more general departures from independence.
Note: The nonparametric correlations are calculated using the Pairwise method, even if you selected a different Estimation Method in the launch window.
Note: When a Weight variable is specified, missing and zero-valued weights are excluded from the nonparametric correlation calculations. All other weight values are treated as 1.
For statistical details about these three methods, see the Nonparametric Measures of Association.