Question

Two faculty members ranked 12 candidates for scholarships. Calculate the Spearman rank-correlation coefficient and test it for significance. Use a .02 level of significance. Candidate 1 2 3 4 5 6 7 8 9 10 11 12

Rank by Professor A 6 10 2 1 5 11 4 3 7 12 9 8

Rank by Professor B 5 11 6 3 4 12 2 1 7 10 8 9

The P-value for testing the significance of rank-correlation is

The Spearman Rank Correlation Coefficient is

Answer 1

We construct the following table:

Rank by professor A	Rank by professor B	d2 = (difference)2
6	5	1
10	11	1
2	6	16
1	3	4
5	4	1
11	12	1
4	2	4
3	1	4
7	7	0
12	10	4
9	8	1
8	9	1
		d2 = 38

The Spearman Rank correlation coefficient is = 1 - [6.d2 / n(n2-1)]

= 1 - 0.1329

= 0.8671

We use Minitab for calculating the p-value for testing the significance of rank-correlation. Using Minitab :

p-value = 0.000

Therefore, the rank correlation coefficient is significant.(as it is less than level of significance 0.02)