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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression

For 10 items, Σd² was computed as 48. Later it was found that one item's ranks had been taken as 3 and 7 when they should have been 5 and 6 (all other ranks were correct). What is the corrected Spearman's rank correlation coefficient?

The corrected coefficient is 0.8. Remove the wrong contribution of 16 and add the right one of 1, so Σd² becomes 33. Then r = 1 − 6×33/990 = 1 − 0.2 = 0.8.

  1. A0.8Correct
  2. B0.71
  3. C0.61
  4. D-0.8

Explanation

The wrong pair contributed (3−7)² = 16. The correct pair contributes (5−6)² = 1. Corrected Σd² = 48 − 16 + 1 = 33. r = 1 − 6×33/(10×99) = 1 − 198/990 = 1 − 0.2 = 0.8. The value 0.71 is the uncorrected result, and 0.61 comes from adding both terms instead of replacing one with the other.

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