Page 182 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes 4. If the data are not uniformly spread in the relevant quadrants the value of r may give a
misleading interpretation of the degree of relationship between the two variables. For
example, if there are some values having concentration around a point in first quadrant
and there is similar type of concentration in third quadrant, the value of r will be very
high although there may be no linear relation between the variables.
5. As compared with other methods, to be discussed later in this unit, the computations of r
are cumbersome and time consuming.

9.1.5 Probable Error of r

It is an old measure to test the significance of a particular value of r without the knowledge of
test of hypothesis. Probable error of r, denoted by P.E.(r) is 0.6745 times its standard error. The

value 0.6745 is obtained from the fact that in a normal distribution r  0.6745 S.E. covers 50%
of the total distribution.
According to Horace Secrist “The probable error 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.”
-
-
Since standard error of r, i.e., S.E. = 1 r 2 , \ P.E. ( ) r = 0.6745  1 r 2
r
n n
Uses of P.E.(r)

1. It can be used to specify the limits of population correlation coefficient r (rho) which are
defined as r – P.E.(r)  r  r + P.E.(r), where r denotes correlation coefficient in population
and r denotes correlation coefficient in sample.
2. It can be used to test the significance of an observed value of r without the knowledge of
test of hypothesis. By convention, the rules are:
(a) If |r| < 6 P.E.(r), then correlation is not significant and this may be treated as a
situation of no correlation between the two variables.
(b) If |r|> 6 P.E.(r), then correlation is significant and this implies presence of a strong
correlation between the two variables.

(c) If correlation coefficient is greater than 0.3 and probable error is relatively small,
the correlation coefficient should be considered as significant.

Example: Find out correlation between age and playing habit from the following information
and also its probable error.

Age 15 16 17 18 19 20
No. of Students 250 200 150 120 100 80
Regular Players 200 150 90 48 30 12

Solution:
Let X denote age, p the number of regular players and q the number of students. Playing habit,
denoted by Y, is measured as a percentage of regular players in an age group, i.e., Y = (p/q) × 100.

176 LOVELY PROFESSIONAL UNIVERSITY