Managers of a firm are trying to determine which of three programs is the best.

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 16 1 * * Interaction 1.5 3 * * Error 4.5 4 * Total 53 11 What advice would you give managers about the influence of sex and interaction? Use a .05 level of significance

Explanation / Answer

Mean square is calculated by dividing the corresponding sum of squares with corresponding df.

F value is calculated by dividing mean square of the corresponding factor or interactio with the mean square of the error. The P-value can be found by using the F-table with df1 as the degree of freedom for the row and df2 as the degree of freedom of error.

Since the P-value for both factors is less than the significance level, the factors are significant but the interaction between them is not.Thus the effectiveness of the program may be influenced by sex but it will not be affected by interaction.

Source Of Variation Sum of Squares Df Mean Square F P-value Programs 31 3 10.33 9.19 0.029 Sex 16 1 16.00 14.22 0.020 Interaction 1.5 3 0.50 0.44 0.734 Error 4.5 4 1.13 Total 53 11

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