In this part you will be considering four different scenarios to which one-way ANOVA has been applied. Four StatTools one-Way ANOVA summary tables for these scenarios are supplied for you. One of the scenarios is not legitimate for using One-way ANOVA. Your task is to match the scenarios with the summary tables and to identify the result that is not reliable. You must explain why the particular ANOVA summary table belongs with the scenario you chose, and why the one result is not reliable.
Each scenario involves randomly selecting ni observations from four, independent, Normal populations as described.
|
Scenario
|
|
1
|
2
|
3
|
4
|
|
Population
|
ni
|
Population
|
ni
|
Population
|
ni
|
Population
|
ni
|
|
N(50, 4)
|
10
|
N(50, 4)
|
10
|
N(50, 7)
|
10
|
N(50, 4)
|
10
|
|
N(50, 4)
|
10
|
N(60, 4)
|
8
|
N(50, 7)
|
10
|
N(60, 7)
|
10
|
|
N(50, 4)
|
10
|
N(50, 4)
|
12
|
N(50, 7)
|
10
|
N(50, 4)
|
10
|
|
N(50, 4)
|
10
|
N(40, 4)
|
10
|
N(50, 7)
|
10
|
N(40, 7)
|
10
|
|
One-way ANOVA
|
Sum of Squares
|
Degrees of Freedom
|
Mean Squares
|
F-Ratio
|
p-Value
|
|
Between Variation
|
275.642
|
3
|
91.881
|
1.703
|
0.1836
|
|
Within Variation
|
1941.911
|
36
|
53.942
|
|
|
|
Total Variation
|
2217.553
|
39
|
|
|
|
|
OneWay ANOVA
|
Sum of Squares
|
Degrees of Freedom
|
Mean Squares
|
F-Ratio
|
p-Value
|
|
Between Variation
|
1806.075
|
3
|
602.025
|
25.368
|
< 0.0001
|
|
Within Variation
|
854.330
|
36
|
23.731
|
|
|
|
Total Variation
|
2660.405
|
39
|
|
|
|
|
One-way ANOVA
|
Sum of Squares
|
Degrees of Freedom
|
Mean Squares
|
F-Ratio
|
p-Value
|
|
Between Variation
|
1648.282
|
3
|
549.427
|
35.771
|
< 0.0001
|
|
Within Variation
|
552.941
|
36
|
15.359
|
|
|
|
Total Variation
|
2201.223
|
39
|
|
|
|
|
One-way ANOVA
|
Sum of Squares
|
Degrees of Freedom
|
Mean Squares
|
F-Ratio
|
p-Value
|
|
Between Variation
|
22.091
|
3
|
7.364
|
0.389
|
0.7617
|
|
Within Variation
|
681.733
|
36
|
18.937
|
|
|
|
Total Variation
|
703.824
|
39
|
|
|
|