Answer-first summary for fast verification
Answer: -0.2
The Spearman rank correlation coefficient is calculated using the formula: \[ r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \] where \( d_i \) is the difference in ranks for each observation, and \( n \) is the sample size. For the given data: - The sum of squared differences in ranks is \( \sum d_i^2 = (2-1)^2 + (3-2)^2 + (4-3)^2 + (1-4)^2 = 1 + 1 + 1 + 9 = 12 \). - Substituting into the formula: \( r_s = 1 - \frac{6 \times 12}{4(16 - 1)} = 1 - \frac{72}{60} = 1 - 1.2 = -0.2 \). Option A is correct because it accurately reflects this calculation. Option B is incorrect due to omitting the multiplier of 6, and Option C is incorrect for using unsquared differences.
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An analyst ranks four paired observations of random variables X and Y as follows: Observation 1 (X:1, Y:2), Observation 2 (X:2, Y:3), Observation 3 (X:3, Y:4), Observation 4 (X:4, Y:1). The Spearman rank correlation coefficient between X and Y is closest to:
A
-0.2
B
0.8
C
1.0
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