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

  1. Step 1: rank each student
Student #History ScoreHistory RankAlgebra ScoreAlgebra Rank
1353305
2235333
3471452
4176236
510788
6432491
798127
86949
9284314
  1. step 2: calculate difference between the ranks (d) and square d
Student #History ScoreHistory RankAlgebra ScoreAlgebra Rankdd2
135330524
223533324
347145211
417623600
51078811
643249111
79812711
8694900
928431400
  1. step 3: sum (add up) all the d2 scores
  • Σ d2 = 4 + 4 + 1 + 0 + 1 + 1 + 1 + 0 + 0 = 12
  1. 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 

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