Lecture 9

# Lecture 9 - Lecture 9 Analysis of Variance Copyright 2012...

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© Copyright 2012, Team MGMT1050 Lecture 9 Lecture 9 Analysis of Variance

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© Copyright 2012, Team MGMT1050 ANOVA ANOVA > ANOVA stands for AN alysis O f VA riance > ANOVA allows us to: Do multiple tests at one time more than two groups Test for multiple effects simultaneously more than one variable
© Copyright 2012, Team MGMT1050 ANOVA Tests ANOVA Tests The types of ANOVA we will look at are: > One Way ANOVA > Randomized block design ANOVA > Two-Factor ANOVA > You will also see ANOVA in regression analysis next week

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© Copyright 2012, Team MGMT1050 One-Way ANOVA One-Way ANOVA > One-way ANOVA allows us to simultaneously test to determine if two or more population means are equal H O : μ 1 = μ 2 = μ 3 H A : At least two means differ
© Copyright 2012, Team MGMT1050 ANOVA Assumptions ANOVA Assumptions > All populations are normally distributed > The population variances are equal ANOVA tests assume that variances can be pooled > The observations are independent

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© Copyright 2012, Team MGMT1050 Example Example > We are interested in seeing if the advertising strategies employed in different cities made a difference > We assume that these cities have been shown to be similar in the past > The sales results for 20 randomly selected weeks in each of the these cities is displayed on the next slide
© Copyright 2012, Team MGMT1050 Example Data Example Data > There are three treatments , the advertising strategy used in the these cities AKA Factor Levels > We have a response variable , the level of weekly sales Convenience Quality Price 752 633 786 820 714 594 903 767 619 797 703 650 798 927 845 622 991 862 710 919 693 811 797 551 754 766 742 548 862 622 795 768 685 909 718 734 734 878 679 661 843 651 672 663 880 792 747 754 758 784 770 766 830 719 682 770 706 805 853 726

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© Copyright 2012, Team MGMT1050 Means and Grand Mean Means and Grand Mean 752 795 633 768 786 685 820 909 714 718 594 734 903 734 767 878 619 679 797 661 703 843 650 651 798 672 927 663 845 880 622 792 991 747 862 754 710 758 919 784 693 770 811 766 797 830 551 719 754 682 766 770 742 706 548 805 862 853 622 726 754.83 713.40 Grand Mean: 754.45 796.65 City 1 City 2 City 3 Convenience Quality Price = C x = Q x = P x = x
© Copyright 2012, Team MGMT1050 Discussion Discussion > There are differences between the means, but we are not sure if they are significant. > We could also observe that there is an amount of variation about the grand mean > There are two sources of variation: Some of this variation is explained by the treatments (advertising strategies) Some remains unexplained , i.e., due to other factors not modeled, or randomness

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© Copyright 2012, Team MGMT1050 Graphically Graphically 400 500 600 700 800 900 1000 1100 Sales City 1 - C City 2 - Q City 3 - P All Cities
© Copyright 2012, Team MGMT1050 A Closer Look as City #2’s Data A Closer Look as City #2’s Data x x x x x x x x x x x x x x x x x x x x Grand Mean 796.7 Treatment Mean Deviations from Grand Mean 754.8 747 770 853 784 830 878 843 663 City 2 - Q - Data Points 766 862 768 718 927 991 919 797 633 714 767 703 These orange bars represent the deviations of each point from the Grand Mean of the data. Their SSD is part of what we seek to explain.

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© Copyright 2012, Team MGMT1050 A Closer Look as City #2’s Data A Closer Look as City #2’s Data x x x x x x x x x x x x x x x x x x x x Residual Deviations Grand Mean 796.7 Treatment Mean 754.8 747 770 853 784 830 878 843 663 City 2 - Q - Data Points 766 862
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• Fall '12
• HilaCohen;OlgaKaminer;AlanMarshall;AlexShoumarov,DoritNevo
• SST, Team MGMT1050

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