**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*).

"The p-value > 0.05 allows us to accept the value of rho calculated, being statistically significant."

ReplyDeleteNooooo....

Since p > 0.05, the sample rho is NOT statistically significant. This means you do not have sufficiently strong evidence to reject the null hypothesis (so it seems that the true rho could be zero... or at least, you haven't found convincing evidence that it isn't)

I completely agree with the above point. Please change and the statement. you cannot reject null at such a high p-value.

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