Rank Correlation - Correlation & Regression, Business Mathematics & Statistics - Business Mathematics and Statistics - B Com

Rank Correlation Rank method for the computation of the coefficient of correlation is based on the rank or the order & not the magnitude of the variable. Accordingly it is more suitable when the variables can be arranged for e.g. in case of intelligence or beauty or any other qualitative phenomenon. The ranks may range from 1 to n.
Edward spearman has provided the following formula —

Where N = Number of pairs of variable X & Y
D = Rank difference

Example 4 : From the data given belows calculate the rank correlation between x & Y

Solution :
 Table : Computation of Rank Correlation

Rank correlation

This shows there is very high positive correlation between X & Y.

Example 5 : Calculate Rank Correlation from the following data.

Solution : Table : Calculation of Rank correlation

Here m, m₂ ... denote the number of times ranks are tied in both the variables, the subscripts & denote the first tie, second tie,...., in both the variables

= 1 – 0.205
= 0.795

Example 6 : Find the coefficient of correlation between price and sales from the following data :

Solution : Let the value of assumed mean for X(A_X) be 90
Let the value of assumed mean for Y(A_y) be 700
Table : Calculation of correlation coefficient

Note : As r is a pure number, change of scale does not affect its value. Hence the values are divided by 10 in column 4 to make the calculations simple. The following formula can be applied to all the problems.

Steps.
(i) find out the direction of change of X variable, i.e., as compared with the first value, whether the second value is increasing or decreasing or is constant. If it is increasing put (+) sign; if it is decreasing put (-) sign (minus) and if it is constant put zero. Similarly, as compared to second  value find out whether the third value is increasing, decreasing or constant. Repeat the same process for other values. Denote this column by Dx.
(ii) In the same manner as discussed above find out the direction of change of Y variable and denote this column by Dy.
(iii) Multiply Dx with Dy, and determine the value of c, i.e., the number of positive signs.
(iv) Apply the above formula,  i.e.,
r_c = +√+ (2C-n)/n
Note. The significance of + signs, both (inside the under root  and outside the under root) is that we cannot take the under root of minus sign. Therefore, if 2C-n is negative, this negative n value of multiplied with the minus sign inside would make it positive and we can take the under root. But the ultimate result would be negative. If 2C-n  is positive then, of course, we get a positive n value of the coefficient of correlation.
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