Question

Managers of a firm are trying to determine which of three programs is the best. They believe that the effectiveness of the programs may be influenced by sex and interaction. A factorial experiment was performed and you are given the following ANOVA table: Source of Variation Sum of Squares df Mean Square F Factor A: 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 about the influence of sex and interaction? Use a .05 level of significance.

Answer 1

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 = (Source of Variation / df)

F_A= (Mean Square Factor A: Programs / Mean Square Error)

F _B= (Mean Square Factor B: Sex/ Mean Square Error)

F_AB= (Mean Square Interaction/ Mean Square Error)

P.Values are calculated from F-Table for particular value for degrees of freedoms.

Calculated p.value for Factor B: Sex = 0.0355 which is less then 0.05 imply that Factor B: Sex have significant effect on the effectiveness of the programs while as p.value for interaction = 0.7355  which is much greater then 0.05 imply that interaction have not significant effect on the effectiveness of the programs.