Research Methodology - Dr. Krishan K. Pandey

Testing of Hypotheses I 215
σ diff . = Standard deviation of differences
n = Number of matched pairs
This calculated value of t is compared with its table value at a given level of significance as usual for
testing purposes. We can also use Sandler’s A-test for this very purpose as stated earlier in
Chapter 8.
Illustration 11
Memory capacity of 9 students was tested before and after training. State at 5 per cent level of
significance whether the training was effective from the following scores:
Student 1 2 3 4 5 6 7 8 9
Before 10 15 9 3 7 12 16 17 4
After 12 17 8 5 6 11 18 20 3
Use paired t-test as well as A-test for your answer.
Solution: Take the score before training as X and the score after training as Y and then taking the null
hypothesis that the mean of difference is zero, we can write:
H : μ μ
0 1= 2 which is equivalent to test H : D = 0
0
H : μ μ
a 1 < 2 (as we want to conclude that training has been effective)
As we are having matched pairs, we use paired t-test and work out the test statistic t as under:
D − 0
t =
σ . / n
diff
To find the value of t, we shall first have to work out the mean and standard deviation of differences
as shown below:
Table 9.8
Student Score before Score after Difference Difference
training training Squared
2
X Y (D = X – Y ) i i i i i Di 1 10 12 – 2 4
2 15 17 – 2 4
3 9 8 1 1
4 3 5 – 2 4
5 7 6 1 1
6 12 11 1 1
7 16 18 – 2 4
8 17 20 – 3 9
9 4 3 1 1
2
n = 9 ∑ Di = −7
∑ Di = 29