Lesson 4B.3.1-4B.3.2

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

20 questions

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Lesson 4B.3.1-4B.3.2, Spearman's rank correlation coefficient: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 20: Non-parametric tests, written with Revision Ninja.

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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 r_s = +1 indicate about two sets of ranked data?

    • The rankings agree perfectly, so the higher-ranked item on one variable is always higher-ranked on the other
    • There is no association between the two variables
    • The two variables are statistically independent of each other
    • The two sets of raw data have identical means

  3. What does r_s = -1 indicate about two sets of ranked data?

    • The two sets of ranks are identical
    • The rankings are in exactly reversed order
    • There is no linear relationship between the variables
    • The two variables have equal variances

  4. What does Spearman's rank correlation coefficient use in its calculation?

    • The deviations of each value from the mean
    • The raw values after standardising them with z-scores
    • The ranks of the data values rather than the raw values
    • Only the largest value in each sample

  5. How should tied values be ranked when calculating Spearman's coefficient?

    • Each tied value is given the lowest rank among them
    • Each tied value is given the highest rank among them
    • Each tied value is given the mean of the ranks they would otherwise occupy
    • Tied values are removed from the data before ranking

  6. When is Spearman's rank correlation a suitable measure of association?

    • Only when both variables are normally distributed before any calculation
    • When the data are ordinal, or the relationship is monotonic but not linear, and normality is not assumed
    • Only when the relationship is linear and the sample is very large
    • Only when both variables use equally spaced interval data

  7. In the formula for r_s, what does d represent?

    • The difference between the two ranks of each pair
    • The product of the two ranks of each pair
    • The difference between the two raw values of each pair
    • The sum of the two ranks of each pair

  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. Seven students are ranked on maths and physics, and r_s = -0.6. Which interpretation is correct?

    • Students tend to be ranked in opposite order on the two subjects, showing a moderately strong negative association
    • The mean maths and physics scores are equal
    • Students with higher maths ranks tend to have higher physics ranks
    • Maths and physics performance are unrelated

  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. A researcher finds r_s = 0.9 between two variables. Which statement is correct?

    • The result shows that the regression slope is exactly 1
    • The result shows a strong monotonic association but does not establish causation
    • The result proves that one variable causes the other
    • The result shows that both variables are normally distributed

  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 the product moment correlation?

    • Ranking compresses extreme values, so an outlier's size does not affect its rank beyond its position
    • Ranking doubles the sample size, which dilutes the outlier
    • Ranking removes the outlier from the data before the calculation starts
    • Ranking forces all values to have the same variance

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