Concurrent Deviation Method

The method of studying correlation is the simplest of all the methods. The only thing that is required under this method is to find out the direction of change of X variable and Y variable.

A very simple and casual method of finding correlation when we are not serious about the magnitude of the two variables is the application of concurrent deviations.

This method involves in attaching a positive sign for a x-value (except the first) if this value is more than the previous value and assigning a negative value if this value is less than the previous value.

This is done for the y-series as well. The deviation in the x-value and the corresponding y-value is known to be concurrent if both the deviations have the same sign.

Denoting the number of concurrent deviations by c and total number of deviations as m (which must be one less than the number of pairs of x and y values), the coefficient of concurrent-deviations is given by 

rc = +√+ (2C-n)/n

Where rc stands for coefficient of correlation by the concurrent deviation method; C stands for

the number of concurrent deviations or the number of positive signs obtained after multiplying

Dx with Dy

n = Number of pairs of observations compared.

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.,

rc = +√+ (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  

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 value of the coefficient of correlation.