Page 180 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 8: Correlation Analysis

Notes
10 236 5 16
r 0.96
10 85 25 10 706 256

Example:
A computer while calculating the correlation coefficient between two variables, X and Y, obtained
the following results :
= 25, = 125, 2 = 650, = 100, 2 = 460, = 508.

It was, however, discovered later at the time of checking that it had copied down two pairs
X Y X Y
of observations as 6 14 in place of the correct pairs 8 12 . Obtain the correct value of r.
8 6 6 8
Solution:

2
First we have to correct the values of X, X ...... etc.
Corrected X = 125 – (6 + 8) + (8 + 6) = 125

2
Corrected X = 650 – (36 + 64) + (64 + 36) = 650
Corrected Y = 100 – (14 + 6) + (12 + 8) = 100

2
Corrected Y = 460 – (196 + 36) + (144 + 64) = 436
Corrected XY = 508 - (84 + 48) + (96 + 48) = 520

25 520 125 100
r 0.67
2 2
25 650 125 25 436 100
8.1.6 Merits and Limitations of Coefficient of Correlation
The only merit of Karl Pearson’s coefficient of correlation is that it is the most popular method
for expressing the degree and direction of linear association between the two variables in terms
of a pure number, independent of units of the variables. This measure, however, suffers from
certain limitations, given below:

1. Coefficient of correlation r does not give any idea about the existence of cause and effect
relationship between the variables. It is possible that a high value of r is obtained although
none of them seem to be directly affecting the other. Hence, any interpretation of r should
be done very carefully.
2. It is only a measure of the degree of linear relationship between two variables. If the
relationship is not linear, the calculation of r does not have any meaning.
3. Its value is unduly affected by extreme items.
4. As compared with other methods, the computations of r are cumbersome and time
consuming.

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