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.
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 .
- Square the values of .
- Add the squared values of to get
- Use the formula where is the number of ranks you have.
- If the 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.
Practical Example of Spearman's Rank Correlation
Question: Use the Spearman's Rank Correlation to establish whether there is any relationship between the distance away from school students live and the IB Geography grades they attain.
- 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)||IB Geography Grades Attained|
This is a very poor example. There are three mistakes. 1) Firstly, the sign for standard deviation (σ) is used, it should be the sum of sign: Σ. 2) Some figures in column d should be negative (the reason for squaring d is to remove the negatives). 3) The final figures do not add up.
Not exactly great for a revision guide.