Example: how to calculate Spearman Correlation?

## 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.

1. Step 1: rank each student
 History Rank Algebra Rank 35 3 30 5 23 5 33 3 47 1 45 2 17 6 23 6 10 7 8 8 43 2 49 1 9 8 12 7 6 9 4 9 28 4 31 4
1. step 2: calculate difference between the ranks (d) and square d
 History Rank Algebra Rank d d2 35 3 30 5 2 4 23 5 33 3 2 4 47 1 45 2 1 1 17 6 23 6 0 0 10 7 8 8 1 1 43 2 49 1 1 1 9 8 12 7 1 1 6 9 4 9 0 0 28 4 31 4 0 0
1. step 3: sum (add up) all the d2 scores
• Σ d2 = 4 + 4 + 1 + 0 + 1 + 1 + 1 + 0 + 0 = 12
1. 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.

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### Prif. Reza contributed on 11-01-2021 18:24

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