Correlation and the Product-Moment Coefficient · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading r without being fooled

Mathematics · Data & Statistics · ages 17-18
Name ______________________   Date ____________

  1. A scatter plot shows points hugging a straight line that climbs uphill from left to right. Which value of r fits this plot best?

    • 0.95
    • 0.05
    • -0.95
    • 0.50

  2. A scatter plot shows points hugging a straight line that climbs uphill from left to right. Which value of r fits best?

    • 0.95
    • 0.05
    • -0.95

  3. A significant correlation between two quantities proves that one causes the other.

    Circle one:   True   False

  4. Which plot matches r equal to minus 0.88?

    • A shapeless cloud with no drift
    • Points climb tightly uphill
    • Points fall tightly downhill

  5. Data follow a strong U shaped curve and score r near zero. What should you have done first?

    • Computed r twice
    • Plotted the data and looked
    • Collected fewer pairs

  6. Priya says r equal to 0.40 from only 8 pairs counts as significant because any positive r is real. The critical value for 8 pairs is 0.707. Is Priya right?

    Circle one:   True   False

  7. Which description matches a scatter plot with r equal to -0.88?

    • Points fall tightly downhill
    • Points climb tightly uphill
    • A shapeless cloud with no drift
    • A U shaped curve

  8. Ten pairs give r equal to 0.82. The critical value for ten pairs at the 5 percent level is 0.632. What follows?

    • Significant, and it proves cause
    • Not significant, so no pattern
    • Significant linear link, but cause is still open

  9. Ten pairs give r equal to 0.50. The critical value is 0.632. Can you call it significant?

    • Yes, any positive r counts
    • No, 0.50 sits below the bar
    • Yes, ten pairs are plenty

  10. One wild point sits far from an otherwise shapeless cloud, yet r looks strong. What is the safe verdict?

    • Trust r, numbers beat plots
    • The outlier may be faking it, check the plot
    • Collect one more pair to confirm
LightMySky · lightmysky.comW1-mt_Rs_Z0P7ELJ-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading r without being fooled W1-mt_Rs_Z0P7ELJ-s1

  1. 0.95 · An uphill line means a positive r, and points hugging the line mean r is near 1, so 0.95 fits best.
  2. 0.95 · Uphill means positive, and hugging the line means near 1, so 0.95 fits best.
  3. False · It never proves cause. Both may share an outside cause instead.
  4. Points fall tightly downhill · The sign is negative so the drift runs downhill, and 0.88 is near 1 in size so the points sit near a line.
  5. Plotted the data and looked · r only tracks straight drift, so the plot warns you when a curve makes the number lie.
  6. False · 0.40 is below the critical value 0.707, so with only 8 pairs this r could easily be luck.
  7. Points fall tightly downhill · The negative sign means downhill drift and 0.88 is near 1 in size, so the points fall tightly downhill.
  8. Significant linear link, but cause is still open · 0.82 beats 0.632, so the pattern is real, but cause needs more than r.
  9. No, 0.50 sits below the bar · Significance means beating the bar for your sample size, and 0.50 does not.
  10. The outlier may be faking it, check the plot · A single outlier can fake a strong r, so describe the plot before trusting the number.
Worksheet · LightMySky