Spearman's rank correlation and comparison with Pearson's r Problem set B Answers

\(r_s = −0.762\)

\(r_s = 0.929\)

\(r_s = 0.667\)

\(r_s = −0.963\)

A: \(r = −0.81\), \(r_s = −1\)

1. (a) 2, 7, 4.5, 8, 4.5, 1, 6, 3
2. (b) \(r_s = −0.898\)
3. (c) \(r_s = −0.898\): a strong negative association. As time online increases, exam mark tends to decrease. This does not show that one causes the other.

1. (a) The points fall from left to right along a curve that flattens out.
2. (b) The value always falls as age increases but the points lie on a curve, not near a straight line.
3. (c) \(r_s = −1\), \(r = −0.971\)

1. (a) \(r = 0.968\), \(r_s = 0.976\)
2. (b) \(r_s = 0.976\): a strong positive association. As number of adverts increases, sales tends to increase. This does not show that one causes the other.

1. (a) \(r = −0.242\), \(r_s = −0.762\)
2. (b) \(r = −0.998\), \(r_s = −1\)
3. (c) Pearson's r changed more (by 0.756, against 0.238 for \(r_s\)). The outlier is one far-out value, which pulls r a long way. Its rank can only be 1 to 8, so it changes \(r_s\) less.