Page 268 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes Where, (n – 2) is degrees of freedom, r is coefficient of correlation between x and y. The
yx
computed value of t is compared with its table value. If the computed value is less than the table
value the null hypothesis is accepted or rejected otherwise at a given level of significance.

Example: A study of weight of 18 pairs of male and female employees in a company shows
that coefficient of correlation is 0.52. Test the significance of correlation.
Solution:
Applying t test:

n - 2
t = r
-
1 r 2
r = 0.52, n = 18

-
18 2
t = 0.52
-
1 (0.52) 2
0.52 ´ 4
= = 2.44
0.854
 = (n – 2) = (18 – 2) = 16
 = 16, t = 2.12
0.05
The calculated value of t is greater than the table value. The given value of r is significant.

12.3.2 Two Sample Test

Two sample test if known as F test

F-Test

Let there be two independent random samples of sizes n and n from two normal populations
1 2
1
with variances s and s respectively. Further, let s = å (X - X ) and
2
2
2
2
1 2 1 - 1i 1
n 1 1
1
s = å (X - X ) be the variances of the first sample and the second samples respectively.
2
2
2
n 2 - 1 2i 2
Then F - statistic is defined as the ratio of two  - variates. Thus, we can write
2
 2 n 1 1- (n - 1)s 1 2 /(n - 1) s 1 2
1
n - 1 s 2 1 s 2
F = = 1 = 1
 2 n 2 1- (n - 1)s 2 2 /(n - s 2 2
2
n - 1 s 2 2 1) s 2
2 2 2
Features of F- distribution
1. This distribution has two parameters v (= n – 1) and v (= n – 1).
1 1 2 2
v
2. The mean of F - variate with v and v degrees of freedom is 2 and standard error is
v - 2
1 2
2
æ v 2 ö 2(v + v – 2)
2
ç è v 2 – 2ø ÷ v 1 1 (v 2 – 4)
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