🏅 13 · Spearman Rank Correlation
Research Question:
Is there a monotonic relationship between study hours rank and exam rank (n=8)? Use Spearman when data is ordinal or non-normal.
| Student | Hours | Rank X | Exam Score | Rank Y | d = Rₓ−Rᵧ | d² |
|---|
| A | 3 | 1 | 62 | 2 | −1 | 1 |
| B | 4 | 2 | 55 | 1 | 1 | 1 |
| C | 5 | 3 | 68 | 3 | 0 | 0 |
| D | 6 | 4 | 74 | 5 | −1 | 1 |
| E | 7 | 5 | 71 | 4 | 1 | 1 |
| F | 8 | 6 | 85 | 7 | −1 | 1 |
| G | 9 | 7 | 80 | 6 | 1 | 1 |
| H | 10 | 8 | 91 | 8 | 0 | 0 |
| Σ | | | | | 0 | 6 |
🔴 Strong positive rank correlation — students who study more tend to score higher, rₛ(6) = .929, p < .001.
APA-7
A Spearman rank correlation indicated a strong positive relationship between study hours and exam performance, rₛ(6) = .93, p < .001. Students with more study hours consistently achieved higher exam ranks.
💡
Use Spearman (rₛ) instead of Pearson (r) when: (1) data is ordinal, (2) normality assumption is violated, or (3) outliers are present. The formula 1 − 6Σd²/[n(n²−1)] is exact when there are no ties.