18.2.6 Spearman's Rank Correlation

How to calculate Spearman's rank correlation coefficient

• If there is an apparent relationship between two variables but the data does not show a normal distribution, Pearson’s linear correlation coefficient should not be used
• Spearman’s rank correlation determines whether there is correlation between variables that don’t show a normal distribution
• Method:
  • Step 1: Create a scatter graph and identify possible linear correlation
  • Step 2: State a null hypothesis
  • Step 3: Use the following equation to work out Spearman’s rank correlation coefficient r

• • • Where:
      • r_s = spearman’s rank coefficient
      • D = difference in rank
      • n = number of samples

  • Step 4: Refer to a table that relates critical values of r_s to levels of probability

• If the value calculated for Spearman’s rank is greater than the critical value for the number of samples in the data ( n ) at the 0.05 probability level (p),  then the null hypothesis can be rejected, meaning there is a correlation between two variables

As the data was not normally distributed they decided to use Spearman’s rank correlation coefficient.

Null hypothesis: there is no correlation between the abundance of species A and species B.

• • n = 10 as there are 10 quadrat samples

Step 1: Rank each set of data (rank 1 being the smallest data figure)

Step 2: Find the difference in rank between the two species, D

Step 3: Square the difference in rank, D² (= 6)

Step 4: Substitute the appropriate numbers into the equation (remember n = 10)

Step 5:  Refer to a table that relates values of r_s to probability. Look for the 0.05 probability level with n = 10

• • As R_s = 0.964, it is greater than the critical value of 0.65. The null hypothesis can be rejected, there is genuine positive correlation between the abundance of species A and B