Homework SourseThe calculations for a factorial experiment involving four l
The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 299, SSA = 23, SSB = 24, SSAB = 195.
Set up the ANOVA table and test for significance using = .05. Show entries to 2 decimals, if necessary.
The p-value for Factor A is
What is your conclusion with respect to Factor A?
The p-value for Factor B is
What is your conclusion with respect to Factor B?
The p-value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
| Factor A | ||||
| Factor B | ||||
| Interaction | ||||
| Error | ||||
| Total |
Solution
Interaction
The p-value of factor A with degree of freedom is (3,24) is 0.100
The conclusion with respect to Factor A is that the p-value is grater than 0.05, there is no significant difference in mean
The p-value of factor B with degree of freedom is (2,24) is (0.01, 0.25)
The conclusion with respect to Factor B is that the p-value is less than 0.05, there is significant difference in mean
The p-value for the interaction of factors A and B with degree of freedom is (6,24) is less than 0.001
The conclusion with respect for the interaction of factors A and Factor B is that the p-value is less than 0.05, there is significant difference in mean
| Sourace of variation | Sum of squares | degree of freedom | mean square | F |
| Factor A | 23 | 3 | 23/4=5.75 | 5.75/2.375=2.42 |
| Factor B | 24 | 2 | 24/2=12 | 12/2.375=5.05 |
| Interaction | 195 | 6 | 195/6=32.5 | 32.5/2.375=13.68 |
| Error | 57 | 24 | 57/24=2.375 | |
| Total | 299 | 35 |
