# 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 **Statistic on aiR**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**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:

Productivity: 5, 7, 9, 9, 8, 6, 4, 8, 7, 7
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 0.1152698The 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 0.146385Also with the Kendall test, the correlation is very low (

*tau = 0.146*), and not-significant (

*p-value > 0.05*).

To

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