# Non-parametric methods for the study of the correlation: Spearman’s rank correlation coefficient and Kendall tau rank correlation coefficient

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We saw in the previous post, how to study the correlation between variables that follow a Gaussian distribution with the Pearson product-moment correlation coefficient. If it is not possible to assume that the values follow gaussian distributions, we have two non-parametric methods: the **Spearman’s rho test** and **Kendall’s tau test**.

For example, you want to study the productivity of various types of machinery and the satisfaction of operators in their use (as with a number from 1 to 10). These are the values:

Satisfaction: 6, 7, 4, 4, 8, 7, 3, 9, 5, 8

Begin to use first the ** Spearman’s rank correlation coefficient**:

a b cor.test(a, b, method="spearman") Spearman's rank correlation rho data: a and b S = 145.9805, p-value = 0.7512 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.1152698

The statistical test gives us as a result *rho = 0.115*, which indicates a low correlation (not parametric) between the two sets of values.

The *p-value > 0.05* makes us not accept the value of rho calculated as being statistically significant.

Now we check the same data with the ** Kendall tau rank correlation coefficient**:

a b cor.test(a, b, method="kendall") Kendall's rank correlation tau data: a and b z = 0.5555, p-value = 0.5786 alternative hypothesis: true tau is not equal to 0 sample estimates: tau 0.146385

Also with the Kendall test, the correlation is very low (*tau = 0.146*), and not-significant (*p-value > 0.05*).

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