Question

Student Q.T. M.A

Ranking Ranking

A 2 3

B 7 6

C 6 4

D 1 2

E 4 5

F 3 1

G 5 8

H 8 7

Work out the spearman rank correlation .

Answer 1

Answer on Question #66355 – Math – Statistics and Probability

Question

Work out the Spearman’s rank correlation.

Solution

Since all the data in columns consists of distinct integers, we can compute Spearman’s rank correlation coefficient using the following formula:

$$\rho = 1 - \frac {6 \sum_ {i = 1} ^ {n} d _ {i} ^ {2}}{n (n ^ {2} - 1)},$$

where $d_{i} = rg(x_{i}) - rg(y_{i})$ is the difference between two ranks (measure of order) of each observation, $n$ is number of observations. In our case ranks coincide with observations, so we’ll just sort data by Q.T. for clarity. Then we compute $d$ and $d^{2}$.

Finally, we substitute obtained values into the formula:

$$\rho = 1 - \frac {6 (1 + 1 + 4 + 1 + 9 + 4 + 1 + 1)}{8 (8 ^ {2} - 1)} = \frac {31}{42} \approx 0.7381$$

**Answer**: $\rho = \frac{31}{42} \approx 0.7381$.

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