Nonparametric Correlations

The Nonparametric Correlations menu offers three nonparametric measures. Each Nonparametric correlation report gives the significance probability for the measure of association and displays the association value on a bar chart.

Spearman’s Rho

is a correlation coefficient computed on the ranks of the data values instead of on the values themselves.

Kendall’s Tau

is 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 (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.