4B.3.1-4B.3.2 Spearman's rank correlation coefficient Quiz: Pearson Edexcel Further Maths, Unit 20

The 20 questions

1. Which formula gives Spearman's rank correlation coefficient r_s for n pairs of ranks with differences d?

   • r_s = 6 sum(d^2) / (n(n^2 - 1)) - 1
   • r_s = 1 - sum(d^2) / n^2
   • r_s = 1 - 6 sum(d^2) / (n(n^2 - 1))
   • r_s = 1 - 6 sum(d^2) / (n(n + 1))

2. What does a Spearman's rank correlation coefficient of +1 indicate?

   • Perfect agreement
   • No correlation
   • Perfect opposition
   • Non-linear association

3. What does a Spearman's rank correlation coefficient of -1 indicate?

   • Perfect agreement
   • Perfect opposition
   • Zero variance
   • No correlation

4. What does Spearman's rank correlation coefficient use in its calculation instead of raw data?

   • Means
   • Frequencies
   • Ranks
   • Variances

5. How are tied values handled when calculating Spearman's rank correlation coefficient?

   • Lower rank
   • Random assignment
   • Mean of ranks
   • Upper rank

6. What type of relationship is measured by Spearman's rank correlation coefficient?

   • Linear only
   • Monotonic
   • Quadratic
   • Exponential

7. In the formula for Spearman's rank correlation coefficient, what does d represent?

   • Rank difference
   • Sample size
   • Data mean
   • Standard deviation

8. Six pairs of ranks have sum(d^2) = 10. What is r_s?

   • 0.857
   • 0.5
   • 5/7, about 0.714
   • 2/7, about 0.286

9. Eight pairs of ranks have sum(d^2) = 42. What is r_s?

   • -0.5
   • 0.75
   • 0.25
   • 0.5

10. Five pairs of ranks have sum(d^2) = 4. What is r_s?

    • 0.8
    • 0.6
    • -0.8
    • 0.2

11. Ranks of x are 1, 2, 3, 4, 5 and ranks of y are 5, 4, 3, 2, 1. What is r_s?

    • -0.5
    • 0
    • 1
    • -1

12. Values of x are 2, 4, 4, 7, 9. What rank is given to each of the two values equal to 4?

    • 2
    • 2.5
    • 2.25
    • 3

13. What does a Spearman's rank correlation coefficient of -0.6 indicate?

    • Negative association
    • No association
    • Positive association
    • Perfect correlation

14. Four pairs of ranks: x ranks 1, 2, 3, 4 and y ranks 2, 1, 4, 3. What is r_s?

    • 0.8
    • 0.6
    • 0.2
    • 0.4

15. Twelve pairs of ranks have sum(d^2) = 100. What is r_s, to 3 decimal places?

    • 0.650
    • -0.650
    • 0.350
    • 0.500

16. Which property can a high Spearman's rank correlation coefficient establish between two variables?

    • Normality
    • Association
    • Causation
    • Linearity

17. Two variables satisfy Y = X^3 for all positive X. What is the Spearman rank correlation between their data?

    • about 0.5
    • -1
    • 0
    • 1

18. Five pairs of ranks give sum(d^2) = 34. What is r_s?

    • 0.7
    • 0.3
    • -0.7
    • -1.7

19. Four pairs of ranks have r_s = 0.4. What is the value of sum(d^2)?

    • 6
    • 3
    • 12
    • 24

20. Why is Spearman's rank correlation less affected by outliers than product moment correlation?

    • Uses ranks
    • Uses squared sums
    • Uses raw data
    • Removes extremes

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