Spearman's rank for geography
Spearman's rank (rs)
0.964
A strong positive correlation.
- Σd²
- 6
- Critical value
- 0.648
- Significant?
- Yes
| Pair | Rank 1 | Rank 2 | d | d² |
|---|---|---|---|---|
| 1 | 10 | 10 | 0 | 0 |
| 2 | 9 | 8 | 1 | 1 |
| 3 | 8 | 9 | −1 | 1 |
| 4 | 7 | 7 | 0 | 0 |
| 5 | 6 | 5 | 1 | 1 |
| 6 | 5 | 6 | −1 | 1 |
| 7 | 4 | 3 | 1 | 1 |
| 8 | 3 | 4 | −1 | 1 |
| 9 | 2 | 2 | 0 | 0 |
| 10 | 1 | 1 | 0 | 0 |
| Σd² | 6 | |||
Working
- Rank each variable separately, 1 for the largest value; equal values share the average of the ranks they would take.
- Find d, the difference between the two ranks for each site, square it and add up: Σd² = 6.
- rs = 1 − 6Σd² ÷ (n³ − n) = 1 − (6 × 6) ÷ (10³ − 10) = 1 − 36 ÷ 990 = 0.964.
- Compare |rs| with the critical value for 10 pairs: 0.648. It reaches it, so the correlation is significant.
Your result
0.964. A strong positive correlation. It is significant at the 95% level (p = 0.05, two-tailed): 0.964 reaches the critical value of 0.648 for 10 pairs, so the pattern is unlikely to be chance.
Plan and evaluate your fieldwork
Your mock plan, in three taps
Spearman's rank gives rs = 1 − 6Σd² ÷ (n³ − n): ten river sites whose width grows with distance downstream give rs = 0.964, a strong positive correlation.
Questions people ask
What is Spearman's rank used for in geography?
It tests whether two things measured at the same sites change together, such as river width and distance downstream, or pedestrian counts and distance from the town centre. It works on ranks, so it copes with data that is not evenly spread.
How do you rank tied values?
Give them the average of the ranks they would have taken. If two sites share the 3rd and 4th highest values, both get 3.5 and the next site is ranked 5.
What does the rs value mean?
rs runs from −1 to +1. Close to +1 means both variables rise together; close to −1 means one rises as the other falls; near 0 means no clear link. The critical value table tells you whether the result is strong enough, for that many pairs, to be unlikely to be chance.
How many pairs do I need?
At least 5 for the calculation and the table, but 10 or more gives a much more trustworthy result. With only a few sites, one unusual reading can swing rs a long way.
Do I need Spearman's rank for GCSE Geography?
It is not one of the statistics GCSE Geography papers list for you to calculate, but it is a strong way to analyse fieldwork data and you will use it again at A-level.
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How we work this out
What it does
Enter two sets of fieldwork measurements, site by site, to get Spearman's rank with the ranks, d² table and a significance check.
Spearman's rank correlation for 5 to 30 pairs of fieldwork measurements, with a significance check against a published table of critical values.
Method
- Each variable is ranked separately, 1 for the largest value; tied values share the average rank.
- d is the difference between a site's two ranks; Σd² adds up the squared differences.
- rs = 1 − 6Σd² ÷ (n³ − n). With tied ranks, rs is worked as the correlation of the ranks, which the shortcut only approximates.
- |rs| is compared with the critical value for that number of pairs at the chosen level.