Monday, 5 September 2011

The lesser used coefficient- Kendall’s Tau

All of our knowledge of correlation coefficients so far has been limited to the Pearson’s correlation coefficient- the much used and analyzed and commented upon ‘R’. However, when going through the output of one of the exercises done in class, I came across a never before read about co-efficient- the Kendall’s Tau. So my ‘googling’ skills in tow, I have set out to figure out what this new animal is.

The Kendall’s Tau is a measure of rank correlation: that is, the similarity of the orderings of the data when ranked by each of the quantities. A non- parametric coefficient, it is an alternative to Spearman’s correlation coefficient and is much easier to interpret.

Although the actual calculation is a bit arduous and needs more than just googling abilities to figure out, the interpretation of this coefficient is done as below:

The Kendall tau correlation represents the difference between two probabilities – say that Sonia and Manmohan are raters, who are rating some object on some characteristic. Sonia says that A has a higher score than B. The tau-a correlation is the probability that Manmohan will say that they are in the same order minus the probability that he will say that they are in the opposite order. If the two are in complete agreement, this will be 1 – 0 = 1. If they are in complete disagreement, this will be 0 – 1 = -1, and if both Sonia and Manmohan are random, this will be 0.5 – 0.5 = 0.

The main advantages of using Kendall's tau are that the distribution of this statistic has slightly better statistical properties. However, the difficulty in its computation makes t a lesser used correlation coefficient.

Posted by
Jyoti Maheshwari

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