Sample question

The scores for nine students in history and algebra are as follows:

• History: 35, 23, 47, 17, 10, 43, 9, 6, 28
• Algebra: 30, 33, 45, 23, 8, 49, 12, 4, 31

Compute the Spearman rank correlation.

Answer

1. Step 1: rank each student

2. step 2: calculate difference between the ranks (d) and square d

3. step 3: sum (add up) all the d² scores

• Σ d² = 4 + 4 + 1 + 0 + 1 + 1 + 1 + 0 + 0 = 12

4. step 4: insert the values in the formula. These ranks are not tied, so use the first formula:

\[\rho = 1 - \frac{6\sum{d^2_i}}{n(n^2-1)}\]

= 1 – (6*12)/(9(81-1))
= 1 – 72/720
= 1-0.1
= 0.9

> The Spearman Rank Correlation for this set of data is 0.9.