RM | Unit 260 - Non-parametric tests: Spearman’s rho and Kendall’s tau
Chapter 8: 8.1, 8.2, 8.3, 8.4, 8.5
Chapter 8.1: Introduction
Additivity requires that one unit change in variable X leads to the same amount of change in Y , no matter
what value X has.
Chapter 8.2: Spearman’s ρ (rho)
We could compute an average difference: the average difference is the sum of these differences, divided
by 10, so we get 0. This is because we have both plus and minus values. It would be better to take the
square of the differences so that we would get positive values
This is called the Spearman rank-order correlation coefficient rs, or
Spearman’s rho (the Greek letter ρ). It can be used for any two variables of
which at least one is ordinal. The trick is to convert the scale values into
ranks, and then apply the formula →
Chapter 8.4: Kendall’s rank-order correlation coefficient τ
If you want to study the relationship between two variables, of which at least one is ordinal, you can
either use Spearman’s rs or Kendall’s τ (tau, pronounced ’taw’ as in ’law’). However, if you have three
variables, and you want to know whether there is a relationship between variables A and B, over and
above the effect of variable C, you can use an extension of Kendall’s τ.
We can then fill in the formula to compute Kendall’s τ :
→ τ = agreements − disagreements / totalnumberof pairs = 37 45 = 0.8
This τ -statistic varies between -1 and 1 and can therefore be seen as a nonparametric analogue of
a Pearson correlation
Chapter 8: 8.1, 8.2, 8.3, 8.4, 8.5
Chapter 8.1: Introduction
Additivity requires that one unit change in variable X leads to the same amount of change in Y , no matter
what value X has.
Chapter 8.2: Spearman’s ρ (rho)
We could compute an average difference: the average difference is the sum of these differences, divided
by 10, so we get 0. This is because we have both plus and minus values. It would be better to take the
square of the differences so that we would get positive values
This is called the Spearman rank-order correlation coefficient rs, or
Spearman’s rho (the Greek letter ρ). It can be used for any two variables of
which at least one is ordinal. The trick is to convert the scale values into
ranks, and then apply the formula →
Chapter 8.4: Kendall’s rank-order correlation coefficient τ
If you want to study the relationship between two variables, of which at least one is ordinal, you can
either use Spearman’s rs or Kendall’s τ (tau, pronounced ’taw’ as in ’law’). However, if you have three
variables, and you want to know whether there is a relationship between variables A and B, over and
above the effect of variable C, you can use an extension of Kendall’s τ.
We can then fill in the formula to compute Kendall’s τ :
→ τ = agreements − disagreements / totalnumberof pairs = 37 45 = 0.8
This τ -statistic varies between -1 and 1 and can therefore be seen as a nonparametric analogue of
a Pearson correlation
