Spearman's Rank Correlation Coefficient (Edexcel GCSE Statistics)

Spearman's Rank Basics

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

Calculating Spearman's Rank Correlation Coefficients

How do I calculate a Spearman's rank correlation coefficient?

• A Spearman's rank correlation coefficient can be calculated for two sets of data

  • This will be bivariate data

    • i.e. the data will occur in pairs of values that 'go together'

    • One set can be thought of as the 'x values'

    • And the other set as the corresponding 'y values'

• STEP 1
  Rank the values in each set

  • Rank the highest x value as 1, the next highest as 2, etc.

    • Then do the same thing for the y values

  • It's helpful to add extra rows (or columns) to a table to write down the rankings in

    • along with additional rows (or columns) for the and values calculated in Steps 2 and 3

  • You can also start with the lowest value as 1 and rank from lowest to highest

    • But you must do the same thing for both sets!

• STEP 2
  Calculate the difference between the ranks for each pair of values

  • 

• STEP 3
  Calculate the squares of the differences between the ranks for each pair of values

  • i.e. square each value to find the corresponding value

• STEP 4
  Find the sum of all the values found in Step 3

  • This sum of values is denoted by

• STEP 5
  Calculate the Spearman's rank correlation coefficient by using the formula

  • 

    • is the sum of the differences squared

    • is the number of data values in each set

    • This formula is on the exam formula sheet, so you don't need to remember it