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Ch15-2 - Chapter 15 continued Analysis of Variance 15.5...

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Analysis of Variance Chapter 15 - continued
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15.5 Two-Factor Analysis of Variance - Example 15.3 Suppose in Example 15.1, two factors are to be examined: The effects of the marketing strategy on sales. Emphasis on convenience Emphasis on quality Emphasis on price The effects of the selected media on sales. Advertise on TV Advertise in newspapers
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Solution We may attempt to analyze combinations of levels, one from each factor using one-way ANOVA. The treatments will be: Treatment 1: Emphasize convenience and advertise in TV Treatment 2: Emphasize convenience and advertise in newspapers ……………………………………………………………… ……. Treatment 6: Emphasize price and advertise in newspapers Attempting one-way ANOVA
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Solution The hypotheses tested are: H 0 : μ 1 = μ 2 = μ 3 = μ 4 = μ 5 = μ 6 H 1 : At least two means differ. Attempting one-way ANOVA
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City1 City2 City3 City4 City5 City6 Convnce Convnce Quality Quality Price Price TV Paper TV Paper TV Paper In each one of six cities sales are recorded for ten weeks. In each city a different combination of marketing emphasis and media usage is employed. Solutio n Attempting one-way ANOVA
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The p-value =.0452. We conclude that there is evidence that differences exist in the mean weekly sales among the six cities. City1 City2 City3 City4 City5 City6 Convnce Convnce Quality Quality Price Price TV Paper TV Paper TV Paper Solution Xm15-03 Attempting one-way ANOVA
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These result raises some questions: Are the differences in sales caused by the different marketing strategies? Are the differences in sales caused by the different media used for advertising? Are there combinations of marketing strategy and media that interact to affect the weekly sales? Interesting questions – no answers
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The current experimental design cannot provide answers to these questions. A new experimental design is needed. Two-way ANOVA (two factors)
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Two-way ANOVA (two factors) City 1 sales City3 sales City 5 sales City 2 sales City 4 sales City 6 sales TV Newspapers Convenience Quality Price Are there differences in the mean sales caused by different marketing strategies? Factor A: Marketing strategy Factor B: Advertising media
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Test whether mean sales of “Convenience”, “Quality”, and “Price” significantly differ from one another. H 0 : μ Conv. = μ Quality = μ Price H 1 : At least two means differ Calculations are based on the sum of square for factor A SS(A) Two-way ANOVA (two factors)
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Two-way ANOVA (two factors) City 1 sales City 3 sales City 5 sales City 2 sales City 4 sales City 6 sales Factor A: Marketing strategy Factor B: Advertising media Are there differences in the mean sales caused by different advertising media?
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