Research Methodology - Dr. Krishan K. Pandey

216 Research Methodology
Di
∴ Mean of Differences or D =
n
∑
and Standard deviation of differences or
= − 7
=−0.
778
9
DiD n
σdiff .
n
= ∑ − ⋅
− 1
=
2
di
29 − − . 778 × 9
9 − 1
2
b g
= 2. 944 = 1715 .
− −
Hence, t = = −
0. 778 0 . 778
=−1361
.
1715 . / 9 0. 572
Degrees of freedom = n – 1 = 9 – 1 = 8.
As H is one-sided, we shall apply a one-tailed test (in the left tail because H is of less than type)
a a
for determining the rejection region at 5 per cent level which comes to as under, using the table of
t-distribution for 8 degrees of freedom:
R : t < – 1.860
The observed value of t is –1.361 which is in the acceptance region and thus, we accept H and 0
conclude that the difference in score before and after training is insignificant i.e., it is only due to
sampling fluctuations. Hence we can infer that the training was not effective.
Solution using A-test: Using A-test, we workout the test statistic for the given problem thus:
Di
A =
Di
∑
2
29
= = 0. 592
2 2 b∑g b−7g Since H in the given problem is one-sided, we shall apply one-tailed test. Accordingly, at 5% level of
a
significance the table value of A-statistic for (n – 1) or (9 – 1) = 8 d.f. in the given case is 0.368 (as
per table of A-statistic given in appendix). The computed value of A i.e., 0.592 is higher than this table
value and as such A-statistic is insignificant and accordingly H should be accepted. In other words,
0
we should conclude that the training was not effective. (This inference is just the same as drawn
earlier using paired t-test.)
Illustration 12
The sales data of an item in six shops before and after a special promotional campaign are:
Shops A B C D E F
Before the promotional campaign 53 28 31 48 50 42
After the campaign 58 29 30 55 56 45
Can the campaign be judged to be a success? Test at 5 per cent level of significance. Use paired
t-test as well as A-test.
2