(This article was first published on Statistic on aiR, and kindly contributed to R-bloggers)
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, 8
Satisfaction: 6, 7, 4, 4, 8, 7, 3, 9, 5, 8
Begin to use first the Spearman's rank correlation coefficient:
a <- c(5, 7, 9, 9, 8, 6, 4, 8, 7, 7)
b <- c(6, 7, 4, 4, 8, 7, 3, 9, 5, 8)
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 allows us to accept the value of rho calculated, being statistically significant.
Now we check the same data with the Kendall tau rank correlation coefficient:
a <- c(5, 7, 9, 9, 8, 6, 4, 8, 7, 7)
b <- c(6, 7, 4, 4, 8, 7, 3, 9, 5, 8)
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
Even with the Kendall test, the correlation is very low (tau = 0.146), and significant (p-value > 0.05).
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