The rank correlation coefficient (r), Mathematics

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The Rank Correlation Coefficient (R)

Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among two variables where the variables arranged in a ranked form.

R = 1 – {(6Σd²)/(n(n² -1))}

Whereas d = difference among the pairs of ranked values.

n = numbers of pairs of rankings

Illustration

A group of 8 accountancy students are tested in Quantitative Techniques and Law II. Their rankings in the two tests were as:

Student	Q. T. ranking	Law II ranking	d	d²
A	2	3	-1	1
B	7	6	1	1
C	6	4	2	4
D	1	2	-1	1
E	4	5	-1	1
F	3	1	2	4
G	5	8	-3	9
H	8	7	1	1

Σd² = 22

d = Q. T. ranking - Law II ranking

R = 1 - {(6Σd²)/(n(n² -1))}

1 -{(6(22))/(8(8² -1))} = 0.74

Hence we conclude that there is a reasonable agreement among student's performances in the two types of tests.

NOTE: in this illustration, if we are given the actual marks then we find r. R varies between -1 and +1.

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