The following data represent the results from an independent-measures experiment comparing three treatment conditions with n=4 in each sample. Conduct an analysis of variance with α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. Treatment A Treatment B Treatment C 4 6 9 4 6 5 5 8 6 7 4 8
The following data represent the results from an independent-measures experiment comparing three treatment conditions with n=4 in each sample. Conduct an analysis of variance with α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments.
| Treatment A | Treatment B | Treatment C |
|---|---|---|
| 4 | 6 | 9 |
| 4 | 6 | 5 |
| 5 | 8 | 6 |
| 7 | 4 | 8 |
F-ratio =
p-value =
Conclusion:
- There is a significant difference between treatments
- These data do not provide evidence of a difference between the treatments
η2=η2=
To calculate η2η2 you can find the directions in the Learning Activities for Module 16. The directions are within the paragraph that starts with "Another value that sometimes gets calculated..."
The results above were obtained because the sample means are close together. To construct the data set below, the same scores from above were used, then the size of the mean differences were increased. In particular, the first treatment scores were lowered by 2 points, and the third treatment scores were raised by 2 points. As a result, the three sample means are now much more spread out.
Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above?
| Treatment A | Treatment B | Treatment C |
|---|---|---|
| 2 | 6 | 11 |
| 2 | 6 | 7 |
| 3 | 8 | 8 |
| 5 | 4 | 10 |
F-ratio =
p-value =
Conclusion:
- There is a significant difference between treatments
- These data do not provide evidence of a difference between the treatments
η2=
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