Question

Below are two sets of gain scores of two different groups.

I know that there is a statistical significance between the two when running an independent t-test; I already have this data set.

I need to know whether one group has a statistical significance of benefiting more or is more beneficial than the other.

I know this would be a one tailed t-test. However, I’m unsure how to perform this or interpret the data.

Group 1	Group 2
Gain Score	Gain Score
19.685	7.62
22.86	-2.54
10.16	5.08
21.273	-5.08
8.255	7.62
3.81	2.54
11.43	17.78
-2.54	10.16
5.08	0
10.16	5.08
0	13.97
1.27	-1.27
9.208	7.62
0	-22.86
16.51	-12.7

Answer 1

Let us denote the difference

d : Gain score in Group 1 - Gain score in Group 2

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size n = 15

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that mean in Gain score for Group 1 is significantly greater than that of for Group 2.