This problem is based on problems 12.2 & 12.3 from Lomax & Hahs-Vaughn, 3rd ed.
A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.
First, run a 1-way fixed-effects ANOVA with this data and fill in the summary table. (Report P-values accurate to 4 decimal places and all other values accurate to 3 decimal places.
To follow-up from the omnibus test, the professor decides to use the Tukey HSD method to test all possible pairwise contrasts. To do so, the following table of statistics needs to be completed. For this presentation, the groups will be ordered from smallest to largest means. (In other words, Group A should be the group with the smallest mean.) First, indicate the appropriate order for the groups (use the group number). Then fill in the table with values accurate to 3 decimal places. (Furthermore, even though the sign does not matter, report all comparison statistics as positive values.)
Note: SPSS does not report the correct Std. Error for the Tukey HSD test. It appears to use the Scheffé S.E. instead of the Tukey HSD S.E. The formula for the S.E. should be:
.
What is the critical value for the Tukey HSD test (`alpha=0.01)?
Which pairwise comparisons are statistically significant?
A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.
| Group-1 | Group-2 | Group-3 | Group-4 |
|---|---|---|---|
| 74.2 | 83.3 | 53.8 | 48.7 |
| 68.7 | 62.1 | 52.9 | 52.2 |
| 80.9 | 71.7 | 65.8 | 55.2 |
| 55.6 | 69.8 | 48 | 57.8 |
| 54.7 | 78.6 | 58.1 | 68.1 |
| 58.3 | 81.4 | 49.9 | 73.8 |
| 91 | 96.2 | 74.2 | 81.3 |
| 52 | 79.9 | 63.4 | 62.8 |
| 55.2 | 67.9 | 41.7 | 67.5 |
| 55.8 | 74.5 | 70.6 | 62.9 |
| 65.3 | 81.9 | 81.3 | 73.6 |
| 76.3 | 41.9 | 40.5 | 70.5 |
| 62.5 | 81.6 | 60.5 | 70.2 |
| 46.3 | 74.1 | 71.5 | 69.8 |
| 50.8 | 66.4 | 60.6 | 51.9 |
| 79.1 | 81 | 55.5 | 74.3 |
First, run a 1-way fixed-effects ANOVA with this data and fill in the summary table. (Report P-values accurate to 4 decimal places and all other values accurate to 3 decimal places.
| Source | SS | df | MS | F-ratio | P-value |
|---|---|---|---|---|---|
| Between | |||||
| Within |
To follow-up from the omnibus test, the professor decides to use the Tukey HSD method to test all possible pairwise contrasts. To do so, the following table of statistics needs to be completed. For this presentation, the groups will be ordered from smallest to largest means. (In other words, Group A should be the group with the smallest mean.) First, indicate the appropriate order for the groups (use the group number). Then fill in the table with values accurate to 3 decimal places. (Furthermore, even though the sign does not matter, report all comparison statistics as positive values.)
| Groups (ascending order) | Comparison Groups | |||
|---|---|---|---|---|
| Group A | Group B | Group C | Group D | |
| Group A = | — | |||
| Group B = | — | |||
| Group C = | — | |||
| Group D = | — | |||
What is the critical value for the Tukey HSD test (`alpha=0.01)?
Which pairwise comparisons are statistically significant?