- Spearman's Rank Correlation is a technique used to test the direction and strength of the relationship between two variables. In other words, its a device to show whether any one set of numbers has an effect on another set of numbers.
- It uses the statistic Rs which falls between -1 and +1.
Procedure for using Spearman's Rank Correlation

- State the null hypothesis i.e. "There is no relationship between the two sets of data."
- Rank both sets of data from the highest to the lowest. Make sure to check for tied ranks.
- Subtract the two sets of ranks to get the difference d.
- Square the values of d.
- Add the squared values of d to get Sigma d
^{2}. - Use the formula Rs = 1-(6Sigma d
^{2}/n^{3}-n) where n is the number of ranks you have. - If the Rs value...

... is -1, there is a perfect negative correlation.

...falls between -1 and -0.5, there is a strong negative correlation.

...falls between -0.5 and 0, there is a weak negative correlation.

... is 0, there is no correlation

...falls between 0 and 0.5, there is a weak positive correlation.

...falls between 0.5 and 1, there is a strong positive correlation

...is 1, there is a perfect positive correlation

between the 2 sets of data. - If the Rs value is 0, state that null hypothesis is accepted. Otherwise, say it is rejected.
Practical Example of Spearman's Rank Correlation

*Red type indicates what you have been given. Black type indicates the working done.*

__Null Hypothesis__: There is no relationship between the two sets of data.

**Distance From School (in miles)****r****IB Geography Grades Attained****r****d****d^2**3 2 4 4 2 4 7 1 4 4 3 9 2 3 7 1 2 4 2 3 6 2 1 1 1 5 5 3 2 4 Sigma d ^{2}= 22- Rs = 1-(6 Sigma d
^{2}/ n^{3}-n).- Sigma d
^{2}= 22 therefore 6 Sigma d^{2}= 132 - n = 5 therefore n
^{3}-n = 120

- Sigma d
- Rs = 1-(132/120)
- Rs = 1- 0.91
- Rs = 0.09
- There is a weak positive correlation between the two sets of data. The null hypothesis is rejected.