What Spearman rank correlation means
Big idea: Spearman rank correlation measures how strongly two rankings move together. It is used for ordinal data or non-linear monotonic patterns.
If higher rank in one variable usually matches higher rank in the other, correlation is positive.
How to calculate Spearman coefficient
Meaning of d: d is the difference between the two ranks for the same observation.
Worked example
For 5 students, rank differences d are: 1, -1, 0, 2, -2. Find rs.
Step by step
- Square each d: 1,1,0,4,4
- Sum d2 = 10
- Use formula: rs = 1 - 6(10)/(5(25-1))
- rs = 1 - 60/120 = 0.5
Final answer
rs = 0.5, showing moderate positive rank correlation.
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Tied ranks and interpretation
Ties: If two values tie, assign each the average of the tied rank positions.
Worked example
Values: 10, 12, 12, 15. What ranks are assigned?
Step by step
- 10 gets rank 1
- 12 and 12 would be ranks 2 and 3, so each gets (2+3)/2 = 2.5
- 15 gets rank 4
Final answer
Ranks are 1, 2.5, 2.5, 4.
Exam Tips:
- Always show tied-rank calculation.
- Interpret sign and strength of rs in words.
- Do not claim causation.
Past-paper style responses
Weak response
- Only gives calculator output
- No context interpretation
- No mention of ties
Strong response
- Shows formula and key steps
- Interprets sign + strength in context
- Handles ties correctly
Full-credit habit: Write one final sentence in context, for example: There is a moderate positive association between revision ranking and test ranking.