EXAMPLE OF A GROUP’S ONE-TAILED T-TEST
Hypothesis: Teachers who offer their high school math students a group incentive for the completion of their assignments (which encompasses both in-class assignments and homework) will see an increase in assignment completion as compared to the number of completed assignments prior to offering a group incentive.
Null Hypothesis: Teachers who offer their high school math students a group incentive for the completion of their assignments (which encompasses both in-class assignments and homework) will see no change or a decrease in assignment completion as compared to the number of completed assignments prior to offering a group incentive.
Design
A quasi-experimental pre-test post-test design was used in this research study to determine the effect of a group contingency of student performance on classwork and homework assignments in an already existing high school math classroom. The independent variable was the incentive of a pizza party (group contingency) if performance improved by 20% over the term 2 pre-test average. The dependent variable was students’ performance on assignments based on the group contingency. Performance was defined as the grade which the student received for the assignment based on problems completed and problems solved correctly.
Results
The term 2 pre-test average for homework and classwork assignments combined was calculated by separately taking the average homework grade and the average classwork grade of the students who participated in the study. The homework and classwork averages were then averaged together to come up with the term 2 pre-test average. Both homework and classwork were weighted equally. This average represented the baseline of which the class had to increase their scores by 20% of the baseline average. The baseline average was 41.1%, so the class had to increase their average during the study by 8.2 percentage points to a 49.3% in order to meet the goal for the study.
The homework and classwork scores from the study were averaged together to come up with an average of 60.4%, 19.3 percentage points higher than the baseline term 2 pre-test average and 11.1 percentage points higher than the study’s post-test goal. The class exceeded the goal and received the pizza party reward. The pre-test and post-test averages were also calculated during the paired t-test (see Table 1).
Table 1: Paired t-test Results
| Group | Pre-test | Post-test |
| Mean | 41.139 | 60.396 |
| SD | 28.962 | 31.158 |
| SEM | 6.039 | 6.497 |
| N | 23 | 23 |
In order to further analyze the data, a paired t-test (see Table 1) was used to compare the pre-test term 2 data with the post-test term 3 data. In both the pre-test and post-test groups, each student’s homework and classwork average was taken. A one-tailed p value was calculated because we used a hypothesis which predicted that the post-test group would perform better on assignments than the pre-test group. Our degrees of freedom were 22, one less than the total number of students in the class. The one-tailed p value was 0.0058, which was considered statistically significant, with a t-value of 2.7551 and a standard error of difference of 6.989. This means that there was a high chance that the result of the study was not a product of random chance and that there was a significant correlation between offering a group contingency and improved academic performance on classwork and homework assignments. Because the p value was smaller than 0.05, we rejected the null hypothesis.
Although the post-test combined average for classwork and homework was higher than the pre-test combined average, we decided to individually compare classwork averages and homework averages as well. The pre-test average for classwork was a 53.8% while the post-test average for classwork was a 50.3%. These pre-test and post-test averages were very similar, with a slight decrease in the post-test group of 3.5 percentage points. On the contrary, the pre-test homework average was a 28.4% while the post-test homework average was a 70.4%. This is quite a large jump from the pre-test to the post-test group of 42 percentage points. The large increase in the post-test homework average greatly contributed to the increase in overall performance from the pre-test to the post-test groups (see Tables 3 and 4 in the Appendix).