Spearman's Rank Correlation Coefficient (Edexcel GCSE Statistics): Revision Note

Spearman's Rank Correlation Coefficient

What is Spearman’s rank correlation coefficient?

• Spearman's rank correlation coefficient measures the strength of the correlation between two data sets

  • i.e., to what extent does one always go up when the other one goes up (or always go down when the other one goes up)

  • It is not always easy to see this clearly on a scatter diagram

• The notation for the Spearman’s rank correlation coefficient of a sample is  

• Spearman's rank correlation coefficient is always a number between -1 and 1

  • i.e.   

• The value of tells you about the type and strength of any correlation

  • A positive value () means there is positive correlation between the data sets

    • An value close to 1 means strong positive correlation

  • If is zero (), then there is no correlation

  • A negative value () means there is negative correlation between the data sets

    • An value close to -1 means strong negative correlation

  • In general, the closer to 1 or -1 that is, the stronger the correlation between the data sets

• For example, if is calculated for the rankings of competitors given by two judges in a competition, then

  • would mean there was perfect agreement between the two judges' rankings

  • would mean the rankings were in completely opposite orders

  • would mean there was no agreement in the ranks given (but also not consistent disagreement)

• Spearman's rank correlation coefficient does not tell you anything about whether or not the data points lie along a straight line

  • It only tells you how true it is that one always tends to go up (or down) when the other one goes up