1. The sum of the differences or ranks between two variables shall be zero.
Symbolically, ∑d = 0
2. Spearman’s correlation coefficient is distribution- free or non-parametric because no strict assumptions are made about the form of population from which sample observations are drawn.
3. The Spearman’s correlation coefficient is nothing but Karl Pearson’s correlation coefficient between the ranks. Hence it can be interpreted in the same manner as Pearsonian correlation coefficient.

In rank correlation we may have three types of problems:
A. Where ranks are given.
B. Where ranks are not given.
C. When ranks are equal.

A. Where ranks are given.

Where actual ranks are given to us the steps required for computing rank correlation are:
(i) Take the difference of the ranks, i.e., (R₁ - R₂) and denote these differences by D.
(ii) Square these difference and obtain the total ∑ D2       
(iii) Apply the formula


R = 1 -    6 ∑ D^₂
                N³ - N

B. Where ranks are not given.

When we are given the actual data and not the ranks, it will be necessary to assign the ranks. Ranks can be assigned by taking either the highest value as 1 or the lowest value as 1. But whether we start with the lowest value or the highest value we must follow the same method in case of both the variables.

C. When Ranks are Equal

In some cases it may be found necessary to rank two or more individuals or entries as equal. In such a case it is customary to give each individual an average rank. Thus if two individuals are ranked equal at fifth place, they are given the rank   (5+6)/2  , that is 5.5, while if three are ranked equal at fifth place they are given the rank  (5+6+7)/3 . In other words, where two or more items are to be ranked equal, the rank assigned for purposes of calculating coefficient of correlation is the average of the ranks which these individuals would have got had they differed slightly from each other.

Where equal ranks are assigned to some entries an adjustment in the above formula for calculating the rank coefficient of correlation is made.

The adjustment consists of adding 1/12(m3 – m) to the value ∑ D2   , where m stands for the number of items with common rank, this value is added as many times the number of such groups.

The formula can thus be written:



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