Kendall correlation

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Description | Example | Discussion | See also

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)