Spearman's Rank Correlation Coefficient (DP IB Applications & Interpretation (AI)): Revision Note

Spearman’s rank

What is Spearman’s rank correlation coefficient?

• Spearman's rank correlation coefficient is a measure of how well the relationship between two variables can be described using a monotonic function

  • A function is monotonic if it is either always increasing or always decreasing

    • i.e. if the values are always increasing or always decreasing as the values increase

  • This can be used as a way to measure correlation in linear models

  • Though Spearman's Rank correlation coefficient can also be used to assess a non-linear relationship

• Each data is ranked, from biggest to smallest or from smallest to biggest

  • For n data values, they are ranked from 1 to n

  • It doesn't matter whether variables are ranked from biggest to smallest or smallest to biggest, but they must be ranked in the same order for both variables

• Spearman’s rank of a sample is denoted by 

  • r_s can take any value in the interval 

  • A positive value of r_s describes a degree of agreement between the rankings

  • A negative value of r_s describes a degree of disagreement between the rankings

  • r_s = 0 means the data shows no monotonic behaviour

  • r_s = 1 means the rankings are in complete agreement: the data is strictly increasing

    • An increase in one variable always means an increase in the other

  • r_s = -1 means the rankings are in complete disagreement: the data is strictly decreasing

    • An increase in one variable always means a decrease in the other

  • The closer to 1 or -1 the stronger the correlation of the rankings

How do I calculate Spearman’s rank correlation coefficient (PMCC)?

• Rank each set of data independently

  • 1 to n for the x-values

  • 1 to n for the y-values

• If some values are equal then give each the average of the ranks they would occupy

  • For example: if the 3^rd, 4^th and 5^th highest values are equal then give each the ranking of 4

    • 

• Calculate the PMCC of the rankings using your GDC

  • This value is Spearman's rank correlation coefficient