Kendall correlation coefficient

This is seen much less in our field than the Spearman correlation coefficient but is, like the Spearman coefficient, a non-parametric correlation coefficient. It uses ranks of values of the two variables but with a different computation from the Spearman correlation.

Kendall coefficients are often given the Greek letter tau, where Spearman coefficients are denoted by rho and Pearson coefficients by R.

Details #

What I originally said was: “Kendall actually proposed more than one rank correlation coefficient but this is getting way beyond our remit and we don’t think you’ll meet either of the main ones very often. Feel free to ask someone presenting data using Kendall correlations which is being used!”

Actually, with help from a typically good Wikipedia statistics section I can and probably should do better.

Tau a: I don’t think I’ve ever seen this used explicitly. It is a very simple function of the numbers of “concordant” and “discordant” pairs of values in your data as you sweep through from the smallest x value to the largest. See that Wikipedia section for a definition of concordant and discordant pairs. It makes no adjustments for ties in the data, i.e. for imperfect ranking in one or both variables.

Tau b: This adjusts the formula of Kendall’s tau a to take into account the number of ties in the data on each of the variables. This makes it a better indicator of correlation if their are ties but works best if their are similar numbers of possible scores on both the x and y variables.

Tau c: This uses a different adjustment for ties taking into account that the numbers of ties on the x variable may be rather different from the number of ties on the y variable if, for example, one is a very short rating scale of say only three levels and the other is much longer, say a correlation between an observer’s three level ratings of risk for early opting out from a planned twenty session therapy for say 57 clients against the numbers of sessions attended from 1 to 20

Try also … #

Correlation
Pearson correlation coefficient
Spearman correlation coefficient
Ranking
Ties

Chapters #

Nothing here yet!

Online applications #

At some point: online form into which you can upload data and get the scattergram for the data and correlation coefficients with the confidence interval around that observed value.

Dates #

Created before 19.xi.21, latest update 30.xii.23.