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What is rank correlation?

by krishna

Overview(rank correlation)

A group of n individuals may be arranged in order to merit with respect to some characteristics. The same group would give different orders for different characteristics. Considering the orders corresponding to two characteristics A and B, the correction between these n pairs of rank is called the rank correlation in the characteristics A and B for that group of individuals.

formula

Let be the ranks of  individuals corresponding to two characteristics.

Assuming nor two individuals are equal in either classification, each individual takes the values 1, 2, 3,  and hence their arithmetic means are, each

Suppose that be the values of variable X  and those of Y.

Then

Here X and Y are deviations from the mean.

Which is called the rank correlation or Spearman’s rank correlation coefficient and we denote it by Rho

Solved examples

Example: Compute Spearman’s rank correlation coefficient r for the following data:

PersonABCDEFGHIJ
Rank Statistics91065724813
Rank in income12345678910

Solution:

PersonRank StatisticsRank in incomed= R1 – R2
A91864
B102864
C6339
D5411
E7524
F26-416
G47-39
H8800
I19-864
J310-749

Example. Three judges A,B,C give the following ranks. Find which pair of judges has common approach

A 1 6 5 10 3 2 4 9 7 8

B 3 5 8 4 7 10 2 1 6 9

C 6 4 9 8 1 2 3 10 5 7

Solution

Here n = ten, so that we get the following table,

A (=x)Ranks byB(=y)C (=z)d1 =   x-yd2 =  y – z  d3 = z-x
136-2-354925
65411-2114
589-3-149116
10486-4-236164
371-46-216364
2102-88064640
4232-1-1411
91108-9164811
76511-2114
897-12-1141
Total  00020021460

.

Since is maximum, so that the pair of judge A and C have the nearest common approach.

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