Spearman's Rank Correlation (Cambridge (CIE) A Level Biology)

Spearman's Rank Correlation

• Spearman’s rank correlation test can be used to determine whether there is correlation between variables when:

  • Data is not quantitative, e.g. an abundance scale has been used rather than a count of individuals

  • A visual inspection of data suggests a non-linear correlation

  • Data may not be normally distributed

• 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

Because 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 C and species D.

• n = 10 because 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

Step 4: Add up the values of D² to give ∑D² (= 6)

Step 5: 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

• Because 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 C and D