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Rank Correlation

4. RANK CORRELATION

 

Let us suppose that a group of n individuals is given grades or ranks with respect to two characteristics. Then the correlation obtained between these ranks assigned on two characteristics is called rank correlation.

Let (x, y;), i = 1, 2, ........ ,n be the ranks of the i-th individual in two characteristics. Then -Spearman's Rank correlation coefficient is given as

where di=Xi- Yi .

It is also to be noted that -1≤ r ≤ 1 and the above formula is used when ranks are not repeated.

 

For repeated ranks, a correction factor is required in the formula. If m is the number of times an item is repeated then the factor

m(m2 – 1) is to be added to Σd2

For each repeated value, this correction factor is to be added.

 

Example 6. The ranks of some I 0 students in two subjects A and B are given below :

Calculate the rank correlation coefficient.

Solution. Here n = 10.

Rank correlation coefficient is given by

 

Example 7. Obtain the rank correlation coefficient for the following data :

Solution. Here n = 10

In the X series 85 has repeated twice and given ranks 2.5 instead of 2 and 3. For this the

Correction factor is

 Also, 74 has repeated thrice in X series and given ranks 6 instead of 5, 6, 7. For this the correction factor is

In the Y series 78 has repeated twice and given ranks 3.5 instead of 3 and 4. For this the correction factor is

 

So the total correction factors =

 Then the rank correlation coefficient is given by