**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 *d _{i}=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(m^{2} – 1) is to be added to Σd^{2}

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 :*

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