How to Calculate Spearman Rho and Kendall Tau Coefficients in SPSS or R


The Spearman and Kendall rank correlation coefficients are well-known methods for quantifying correspondences between lists of ordinal data. How are they calculated, and what do they mean? That's what this article is all about. Read on for more...

Things You'll Need

  • SPSS (now also known as PASW Statistics 17), any version, OR
  • R (
  • In SPSS: Go to the Analyze menu, select "Correlate -> Bivariate...", and select the variables you wish to correlate in the box that appears on the left (click on thumbnail image for a larger view). Move them over to the box on the right by clicking the blue arrow. Finally, ensure that there is a checkmark in either the "Kendall's tau-b" or "Spearman" checkbox, and click OK.

  • In R, rank-order correlations can be calculated with the "cor" command. Given vectors x and y, Spearman and Kendall rank correlations between the two can be calculated with the following commands.

  • Interpreting your results: Kendall's tau and Spearman's rho each range from 1 to -1; 1 indicates perfect correlation, -1 indicates a perfect inverse correlation, and 0 indicates no correlation. Spearman's rho does not have a meaningful operational interpretation, although it is the more frequently cited statistic in many fields; it is essentially equivalent to converting scores to numerical rank-order scores and computing a standard Pearson correlation between them, although the mathematical details differ in the case of ties. Kendall's tau does not require first converting scores to rank-orders and has several advantages from a statistical point of view, such as a near-normal distribution of the score function for small n. However, your results may be harder to compare to those in published literature, which often favors Spearman's rho out of tradition.

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