In a bivariate distribution, Spearman's Coefficient of Correlation is -0.25. If the sum of the squares of various ranks is 150, find out the number of pairs of items:
A)10
B)8
C)9
D)7

Question

Quizplus · Accepted Answer

Spearman's Coefficient of Correlation (ρ) is given by the formula: $$ρ = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}$$ where $\sum d^2$ is the sum of the squares of the differences between the ranks of each observation in two variables, and $n$ is the number of pairs. Given that $\sum d^2 = 150$ and $ρ = -0.25$, we can rearrange the formula to solve for $n$: $$-0.25 = 1 - \frac{6 \times 150}{n(n^2 - 1)}$$ Solving this equation for $n$ gives us $n = 9$, indicating there are 9 pairs of items.

In a Bivariate Distribution, Spearman's Coefficient of Correlation Is -0