Spearman’s rank-order correlation (often called Spearman’s *ρ* or *rho*) is a non-parametric test which measures the monotonic relationship between two ranked variables. This test is often used when Pearson product-moment correlation cannot be used because (one of) the assumptions for the test are challenged. Most of the time, the assumptions of normality and linearity will be a reason for not using Pearson’s product-moment correlation.

Spearman’s rho comes with one main assumption: the monotonicity of the relationship between variables. To better understand what monotonic relationship implies, check the following picture taken from Lærd statistics’ webpage:

As you may understand, as the first variable increases, the second variable must either increase or decrease in a monotonic manner, but not necessarily in a proportional manner.

Let’s check this with an example. Here we consider weather records for the last 12 months in Bergen. The variables are `rain`

and `temperature`

, and we’ll try to see whether there is a form of relationship between these variables.

Normality and equal variance are not to be check here, so let’s draw directly a scatter plot:

Hard to see any obvious relationship…

Let’s check Spearman’s *ρ*. The function is `cor.test()`

. Note that the function is the same as for Pearson’s *r* and Kendall’s *tau*. The extra parameter `method=" "`

defines which correlation coefficient is to be considered in the test (choose between `"pearson"`

, `"spearman"`

and `"kendall"`

; if the parameter method is omitted, the default test will be Pearson’s *r*)

`cor.test(rain, temperature, method="spearman")`

```
##
## Spearman's rank correlation rho
##
## data: rain and temperature
## S = 358, p-value = 0.4301
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.2517483
```

In this test, the null hypothesis `H0`

states that there is no relationship between the variables. Here, the p-value is largely greater than 0.05, this null hypothesis cannot be rejected.