Managers of a firm are trying
Managers of a firm are trying to determine which of threeprograms is the best. They believe that the effectiveness of theprograms may be influenced by sex and interaction. A factorialexperiment was performed and you are given the following ANOVAtable: Source of Variation Sum of Squares df Mean Square F FactorA: Programs 31 3 * * Factor B: Sex 11 1 * * Interaction 1.5 3 * *Error 4.5 4 * Total 48 11 What advice would you give managers aboutthe influence of sex and interaction? Use a .05 level ofsignificance.
Answer:
Complete ANOVA table is given below
| Source of Variation | Source of Variation | df | Mean Square | F | P.Value | |||||
| Factor A: Programs | 31 | 3 | 10.33 | 9.14159292 | 0.0291 | |||||
| Factor B: Sex | 11 | 1 | 11 | 9.734513274 | 0.0355 | |||||
| Interaction | 1.5 | 3 | 0.5 | 0.442477876 | 0.7355 | |||||
| Error | 4.5 | 4 | 1.13 | |||||||
| Total | 48 | 11 |
where Mean Square = (Sourceof Variation / df)
FA= (Mean Square Factor A: Programs / MeanSquare Error)
F B= (Mean Square Factor B: Sex/ Mean SquareError)
FAB= (Mean Square Interaction/ Mean SquareError)
P.Values are calculated from F-Table for particularvalue for degrees of freedoms.
Calculated p.value for Factor B: Sex = 0.0355 which isless then 0.05 imply that Factor B: Sex have significant effect onthe effectiveness of the programs while as p.value for interaction= 0.7355 which is much greater then 0.05 imply thatinteraction have not significant effect on the effectiveness of theprograms.
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