CIMA BA1 Syllabus C. Informational Context Of Business - Spearman's rank correlation coefficient - Notes 10 / 10
Spearman's rank correlation coefficient
If you are given ranking rather than actual values.
Use Spearman's rank correlation coefficient to evaluate correlation.
n = number of pairs of data
d = the difference between the rankings
The coefficient of rank correlation can be interpreted in exactly the same way as the ordinary correlation coefficient.
Its value can range from —1 to +1 .
Illustration
The following data relates to 5 students:
| Students | Ranking by how many hours studied | Ranking by exam result |
|---|---|---|
| A | 2 | 1 |
| B | 1 | 3 |
| C | 4 | 7 |
| D | 6 | 5 |
| E | 5 | 6 |
Required
Judge whether the performance of students correlates with their performance.
Solution
Correlation must be measured by Spearman's coefficient because we are given the data as rankings.
| Difference in rankings | Difference2 | |
|---|---|---|
| A | 1 | 1 |
| B | 2 | 4 |
| C | 3 | 9 |
| D | 1 | 1 |
| E | 1 | 1 |
| Total | ----- 8 ----- | ----- 16 ----- |
where d is the difference between the rank in hours studied and exam performance for each Student.
R = 1 - {(6 x 16) / [5 x (25 - 1)]}
R = 1 - (96 / 120)
R = 1 - 0.8
R = 0.2
The correlation is positive, 0.2, but the correlation is not strong.