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Confused over S2 Spearman rank ordering question

I got the sign of this incorrect (well, according to my stats book) and I am confused as to why. Would be good if someone could explain.

Question is:

At the end of a word-processing course the trainees are given a document to type. They are assessed on the time taken and on the quality of their work. For a random sample if 12 trainees the following results were obtained.

Unparseable latex formula:

(i) Calculate Spearman's coefficient of rank correlation for the data. Explain what the sign of your coefficient indicates about the data.

The reason my result has the opposite sign of the book answer is because I assumed that the lowest time would be rank 1.

Anyway, here is my working.

Unparseable latex formula:

[br]\begin{array} {lrrrrrrrrrrrr}[br] Trainee & A & B & C & D & E & F & G & H & I & J & K & L \\[br] Quality (\%) & 97 & 96 & 94 & 91 & 90 & 87 & 86 & 83 & 82 & 80 & 77 & 71 \\[br] Time (s) & 210 & 230 & 198 & 204 & 213 & 206 & 200 & 186 & 192 & 202 & 191 & 199 \\[br] Q rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\[br] T rank & 10 & 12 & 4 & 8 & 11 & 9 & 6 & 1 & 3 & 7 & 2 & 5 \\[br] diff & -9 & - 10 & -1 & -4 & -6 & -3 & 1 & 7 & 6 & 3 & 9 & 7 \\[br] diff^2 & 81 & 100 & 1 & 16 & 36 & 9 & 1 & 49 & 36 & 9 & 81 & 49 [br]\end{array}[br]

Total = 468

[br]r_{s} = 1 - \frac{6 * 468}{12 * 143} = -0.636[br]

The book answer was + 0.636. And the text of answer was: Positive sign indicates possible positive correlation.

It just seems more logical to me that longer time is worse. ie you don't win the 100 metres race by being slowest!!!

Is this just a confusing question or am I wrong? And why?

This was a past MEI paper apparently - marked as such.

(edited 9 years ago)

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