Calculate Pearson coefficient of correlation for the following series.

Question: Ten competitors in a beauty contest are ranked by three judges in the following order:

1st Judge: 1 6 5 10 3 2 4 9 7 7
2nd Judge: 3 5 8 4 7 10 2 1 6 9
3rd Judge: 6 4 9 8 1 2 3 10 5 7

Use the rank correlation coefficient to determine which pair of judges has the nearest approach to common tastes in beauty.

Solution:

Let R1, R2 and R3 denote the ranks given by the first, second and third judges respectively and let Pij, be the rank correlation coefficient between the ranks given by 6th and 7th judges, i . j = 1, 2, 3.

Let dij = Ri – Rj, be the different of ranks of an individual given by the ith and jth judege.

Calculation of Rank Correlation Coefficient

homework

Since P13 is maximum, the pair of first and thrid judges has the nearest approach to common tastes in beauty.

Remark. Since P12 and P23 are negative, the pair of judges (1,2) and (2,3) have opposite (divergent) tastes for beauty.

Case (ii) When Ranks are Not Given.

Spearman’s rank correlation above formula can also be used even if we are dealing with variables which are measured quantitatively, i.e., when the actual data but not the rank relating to variables are given. In such a case we shall have to convert the data into ranks. The higher (smallest) observation is given rank 1 and so on. It is immaterial in which way (descending or ascending) the ranks are assigned. However, the same approach should be followed for all the variables under consideration.