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.
Answer
- Step 1: rank each student
| Student # | History Score | History Rank | Algebra Score | Algebra Rank |
| 1 | 35 | 3 | 30 | 5 |
| 2 | 23 | 5 | 33 | 3 |
| 3 | 47 | 1 | 45 | 2 |
| 4 | 17 | 6 | 23 | 6 |
| 5 | 10 | 7 | 8 | 8 |
| 6 | 43 | 2 | 49 | 1 |
| 7 | 9 | 8 | 12 | 7 |
| 8 | 6 | 9 | 4 | 9 |
| 9 | 28 | 4 | 31 | 4 |
- step 2: calculate difference between the ranks (d) and square d
| Student # | History Score | History Rank | Algebra Score | Algebra Rank | d | d2 |
| 1 | 35 | 3 | 30 | 5 | 2 | 4 |
| 2 | 23 | 5 | 33 | 3 | 2 | 4 |
| 3 | 47 | 1 | 45 | 2 | 1 | 1 |
| 4 | 17 | 6 | 23 | 6 | 0 | 0 |
| 5 | 10 | 7 | 8 | 8 | 1 | 1 |
| 6 | 43 | 2 | 49 | 1 | 1 | 1 |
| 7 | 9 | 8 | 12 | 7 | 1 | 1 |
| 8 | 6 | 9 | 4 | 9 | 0 | 0 |
| 9 | 28 | 4 | 31 | 4 | 0 | 0 |
- step 3: sum (add up) all the d2 scores
- Σ d2 = 4 + 4 + 1 + 0 + 1 + 1 + 1 + 0 + 0 = 12
- 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
Azad university
Statistics Nwosu Chijioke Peter contributed on 04-06-2023 22:22
It added to my knowledge of statistics