This method is a development over the rank correlation method in the sense that its process of calculation is the simplest, and shortest of all the algebraic methods discussed above. Any number of observations can be easily solved under this method.
The special features of this method are as follows:
- For both the variables of X and Y, deviations of each of the succeeding values from its immediately proceeding value is noted in terms of the direction of changes (i.e., + , – , or 0) under columns styled dx and dy.
- Each of the pairs of deviation signs thus noted under dx and dy are multiplied in a separate column styled dxdy.
- Only the positive signs i.e. the products of the concurrent, or similar signs in the dxdy column are totaled, and shown as the value of the concurrent deviation, or C.
- The number of pairs of deviations rather than the number of pairs of observations is taken as the value of n, and for this, the number of pairs of observation is reduced by one in as much as the first pair of observations does not fall under the pairs of the deviations.
- The following formula is applied to find both the degree and direction of the correlation which always lies between ± 1.
r(c) = ± √(±2c-N/N
where, r(c) = co-efficient of concurrent deviation.
C = number of concurrent deviations and
n = number of pairs of deviation.
The purpose of putting ± signs inside the root is to convert to negative value of 2c-N/N, if any, into the positive value by multiplying the same with the minus sign in order that the root of 2c-N/N, can be found out algebraically.
Further, the purpose of putting ± signs outside the root is to show the ultimate result with its original sign by multiplying the derived result with the minus sign again. In case 2c-N/N, gives a positive value, all such multiplications cited above will not be necessary.