# Spearman's Rank Correlation Coefficient

#### katlego

##### New Member
Since Spearman’s rho is a measure of general dependence between two variables, does this mean a correlation of zero means zero relationship between variables?

#### Dason

Spearman's tests for a monotone relationship. So we could have a perfect relationship between two variables and still have spearmans give us a correlation of 0.

Here's some R code to illustrate an example (even if you don't know R hopefully this should be relatively simple to follow along with):
Code:
> x <- seq(-10, 10)
> y <- x^2
> cbind(x, y)
x   y
[1,] -10 100
[2,]  -9  81
[3,]  -8  64
[4,]  -7  49
[5,]  -6  36
[6,]  -5  25
[7,]  -4  16
[8,]  -3   9
[9,]  -2   4
[10,]  -1   1
[11,]   0   0
[12,]   1   1
[13,]   2   4
[14,]   3   9
[15,]   4  16
[16,]   5  25
[17,]   6  36
[18,]   7  49
[19,]   8  64
[20,]   9  81
[21,]  10 100
> cor(x, y, method = "spearman")
[1] 0

#### katlego

##### New Member
How could this be true, because the reason a correlation of zero does not mean zero dependence between variables for a Pearson product moment correlation coefficient is that Pearson correlation coefficient measures linear relationship. Now Spearman’s rho measures general dependence at ordinal scale. Why can’t it be zero dependence when we have zero correlation?