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

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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 (http://www.r-project.org/)
• 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.
cor.test(x,y,method="spearman")
cor.test(x,y,method="kendall")

• 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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