Page 214 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 10: Correlation

Notes
fdx -16 0 14  f.dx = 42

f.dx 2 16 0 14  fdx = 84
2
f.dxdy -5 0 3  fdxdy = 0

The value in the bracket in each cell shows fdxdy


n fdxdy   fdx  fdy
 =
2 2  2 2 

 fdy
n fdx  

   fdx  n fdy   
   
(66   2)  (40  12)
 =
2
2


  66  114 (40)   66  70 (12)  
 
 9.27
 =
89.76  67.82 
 9.27
 = = - 0.119
9.47  8.24
This shows very low degree of negative correlation between advertising expenditure (X) and
sales revenue (Y)
Rank Correlation (Spearman’s Method)
It is not possible to express attributes such as character, conduct, honesty, beauty, morality,
intellectual integrity etc. in numerical terms. For example, it is easy to for a class teacher to
arrange the students in his class in an ascending or descending order of intelligence. This means
that he can rank them according to their intelligence. Hence in problems that involve attributes
of the type mentioned above, the coefficient of correlation is entirely based on the rank differences
between corresponding items.
We may have two types of numerical problems in rank correlation:
(a) When actual ranks are given

(b) When ranks are not given

Calculation of Rank Correlation

(i) In the first case, when actual ranks are given, the difference of the two ranks (R – R ) are
1 2
taken and these are denoted by ‘d’
2
(ii) The differences are squared and their total (d ) obtained
(iii) Then the following formula is applied to calculate the rank correlation coefficient

6  d 2
r = 1 
2
s N(N  1)
Where r denotes Spearman’s Rank Correlation and N denotes number of pairs of
s
observations.

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