Page 190 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes
!
Caution This method is suitable only for the study of short term fluctuations because it
does not take into account the changes in magnitudes of the values.

Self Assessment

Fill in the blanks:

1. The coefficient of correlation obtained on the basis of ranks is called .......................
2. The only merit of Karl Pearson’s coefficient of correlation is that it is the most popular
method for expressing the ....................... and ....................... of linear association.
3. The ....................... of correlation coefficient is an amount which if added to and subtracted
from the mean correlation coefficient, gives limits within which the chances are even that
a coefficient of correlation from a series selected at random will fall.
4. The value of Karl Pearson’s coefficient is unduly affected by ....................... items.
5. ....................... correlation is used as a measure of the degree of association in situations
where the nature of population, from which data are collected, is not known.
6. A ....................... rank correlation implies that a high (low) rank of an individual according
to one characteristic is accompanied by its high (low) rank according to the other.
7. When two or more individuals have the same rank, each individual is assigned a rank
equal to the ....................... of the ranks that would have been assigned to them in the event
of there being slight differences in their values.
8. If correlation coefficient is greater than ....................... and probable error is relatively
......................., the correlation coefficient should be considered as significant.
9. Coefficient of correlation r does not give any idea about the existence of .......................
relationship between the variables.
10. If X and Y are independent they are .......................
11. The coefficient of correlation lies between .......................
12. The coefficient of correlation is independent of the change of ....................... and .......................
of measurements.
13. Even when the characteristics are measurable, it is desirable to ....................... such
measurements due to shortage of time, money, complexities of calculations due to large
data, etc.

9.2 Multiple Correlation

The coefficient of multiple correlation in case of regression of x on x and x , denoted by R , is
i j k i×jk
defined as a simple coefficient of correlation between x and x .
i ic
Cov ( ,x x ic ) å x x å x x - x . i jk )
( i
i
i ic
i
Thus R =  
i×jk ( ) å 2 2 2
( )Var x
Var x i ic x i å x ic å x i å ( i x . i jk )
x -
2
å x - å x x i jk å x - å x x i jk
2
2
×
×
i
i
i
i
= 
å x i å (x - x i jk )x i å x i å 2 i – å x i i jk )
2
2
( x
x
×
×
i
(Using property III)
184 LOVELY PROFESSIONAL UNIVERSITY