If we think about each situation on its own, we can use a paired t-test (also called a dependent t-test) to see if there’s a big difference between the scores before and after. This test works well when the same people are tested twice in different situations (like before and after a test). With a significance level of 0.05, the t-test will show us if the average difference is really different from zero.
Paired-Samples T-test
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Posttest_Score
82.0000
5
5.70088
2.54951
Pretest_Score
73.6000
5
8.35464
3.73631
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
Posttest_Score & Pretest_Score
5
.887
.045
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Posttest_Score – Pretest_Score
8.40000
4.21900
1.88680
3.16141
13.63859
4.452
4
.011
Item
Response
Comment
1. What’s the mean?
The mean difference between the pretest scores and post-test scores is 8.4.
On average, the scores increased by 8.4 points between the pretest and post-test for all the cases. This means that overall, there was an improvement in scores from before to after the test.
2. What’s the t-test results
The t-test resulted in a t-value of 4.452 with 4 degrees of freedom.
The t-value of 4.452 shows there’s a big difference between the scores before and after the test. At a significance level of 0.05, this t-value tells us it’s unlikely the score difference happened just by luck.
3. What’s the standard deviation
The standard deviation of the differences between the pretest scores and post-test scores is approximately 4.219.
The standard deviation of 4.219 shows how much the scores before and after the test vary. A small standard deviation means the differences are pretty consistent or close to the average difference of 8.4.
