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# Kendall correlation

Explanations > Social ResearchAnalysis > Kendall correlation

## Description

The Kendall Tau Rank Correlation Coefficient is used to measure the degree of correspondence between sets of rankings where the measures are not equidistant. It is used with non-parametric data

The Kendall coefficient is denoted with the Greek letter tau (τ).

τ = (4P / (n * (n - 1))) - 1

Where P is the number of concordant pairs and is calculated as the sum over all the items, of items ranked after the given item by both rankings.

## Example

A group of people, denoted as A to E, have their IQ and hat size measured, to determine if a bigger brain makes you brainier. The people are ranked by both IQ and hat size (1 - highest rank), and put in a table, as below.

 Person A B C D E Rank by IQ 1 2 3 4 5 Rank by hat size 3 5 2 1 4 Number of higher ranked hat sizes (lower numbers) to the right 2 3 1 0 0

Now P is the sum of the 'unexpected' rankings, measured as the sum of the number ranked hat sizes to the right (ie. in lower positions than the assessed position).

P = 2 + 3 + 1 + 0 + 0 = 6

And so:

τ = (4*6 / (5* (6 - 1))) - 1 = 0.04

Which, sadly, shows very little correlation between IQ and hat size.

## Discussion

Kendall is used with two ordinal variables or an ordinal and an interval.

Before computers were commonly available, Spearman correlation was often used as a substitute as it was easier to calculate. Kendall is now often viewed as being a superior metrics.

The measure is sometimes just referred to as 'Kendall's tau'.

SPSS: Analyze, Correlate, Bivariate, (check Kendall's tau)

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