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Interpret correlation coefficients and avoid the causation trap

12th grade (Year 13 in England) · 16 questions · Common Core: HSS.ID.C.8, HSS.ID.C.9 · England: GCSE Higher Statistics, A-level Statistics

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  1. Question 1

    Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other?

    • A. Not necessarily: a third factor, hot, sunny weather, could explain both
    • B. Yes, but only if r is above 0.9
    • C. No: the correlation must be a calculation error
    • D. Yes: strong correlation proves causation

  2. Question 2

    A data set has correlation coefficient r = −0.45. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  3. Question 3

    Towns with more libraries have more crime. Does this show that one causes the other?

    • A. Yes: strong correlation proves causation
    • B. Yes, but only if r is above 0.9
    • C. Not necessarily: a third factor, population size, could explain both
    • D. No: the correlation must be a calculation error

  4. Question 4

    A data set has correlation coefficient r = 0.38. How would you describe the correlation?

    • A. Strong positive
    • B. Moderate positive
    • C. Little or no linear correlation

  5. Question 5

    Children with bigger shoe sizes have better reading scores. Does this show that one causes the other?

    • A. Not necessarily: a third factor, age, could explain both
    • B. Yes, but only if r is above 0.9
    • C. No: the correlation must be a calculation error
    • D. Yes: strong correlation proves causation

  6. Question 6

    A data set has correlation coefficient r = −0.95. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  7. Question 7

    Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other?

    • A. No: the correlation must be a calculation error
    • B. Yes: strong correlation proves causation
    • C. Yes, but only if r is above 0.9
    • D. Not necessarily: a third factor, hot, sunny weather, could explain both

  8. Question 8

    A data set has correlation coefficient r = −0.45. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  9. Question 9

    Children with bigger shoe sizes have better reading scores. Does this show that one causes the other?

    • A. Yes: strong correlation proves causation
    • B. Yes, but only if r is above 0.9
    • C. No: the correlation must be a calculation error
    • D. Not necessarily: a third factor, age, could explain both

  10. Question 10

    A data set has correlation coefficient r = 0.71. How would you describe the correlation?

    • A. Strong positive
    • B. Moderate positive
    • C. Little or no linear correlation

  11. Question 11

    Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other?

    • A. Yes: strong correlation proves causation
    • B. No: the correlation must be a calculation error
    • C. Not necessarily: a third factor, hot, sunny weather, could explain both
    • D. Yes, but only if r is above 0.9

  12. Question 12

    A data set has correlation coefficient r = −0.82. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  13. Question 13

    Towns with more libraries have more crime. Does this show that one causes the other?

    • A. Yes, but only if r is above 0.9
    • B. Not necessarily: a third factor, population size, could explain both
    • C. No: the correlation must be a calculation error
    • D. Yes: strong correlation proves causation

  14. Question 14

    A data set has correlation coefficient r = −0.1. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  15. Question 15

    Children with bigger shoe sizes have better reading scores. Does this show that one causes the other?

    • A. No: the correlation must be a calculation error
    • B. Not necessarily: a third factor, age, could explain both
    • C. Yes, but only if r is above 0.9
    • D. Yes: strong correlation proves causation

  16. Question 16

    A data set has correlation coefficient r = 0.38. How would you describe the correlation?

    • A. Strong positive
    • B. Moderate positive
    • C. Little or no linear correlation

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  1. Not necessarily: a third factor, hot, sunny weather, could explain both
  2. Moderate negative
  3. Not necessarily: a third factor, population size, could explain both
  4. Moderate positive
  5. Not necessarily: a third factor, age, could explain both
  6. Strong negative
  7. Not necessarily: a third factor, hot, sunny weather, could explain both
  8. Moderate negative
  9. Not necessarily: a third factor, age, could explain both
  10. Strong positive
  11. Not necessarily: a third factor, hot, sunny weather, could explain both
  12. Strong negative
  13. Not necessarily: a third factor, population size, could explain both
  14. Little or no linear correlation
  15. Not necessarily: a third factor, age, could explain both
  16. Moderate positive