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:
Productivity: 5, 7, 9, 9, 8, 6, 4, 8, 7, 7 Satisfaction: 6, 7, 4, 4, 8, 7, 3, 9, 5, 8Begin 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).