Question

Calculate the rank correlation coefficient from the following data specifying the ranks of 7 students in 2 subjects.

Subject 1 98 92 89 83 69 69 65

Subject 2 87 90 98 92 61 83 69

Answer 1

Find the ranks for each individual subject. Each tied data point assigned a mean rank.

Add a third column, d, to your data. The d is the difference between ranks. In a fourth column, square your d values.

Sum (add up) all of your d-squared values.

The Spearman Rank Correlation coefficient:

$ρ= 1 -\frac{6\sum d^2_i}{n(n^2-1)} \\ ρ = 1 -\frac{6 \times 16.5}{7(49-1)} \\ = 1 -0.2946 \\ = 0.7054$