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Power Fifteen

Power Fifteen. Analysis of Variance (ANOVA). Analysis of Variance. One-Way ANOVA Tabular Regression Two-Way ANOVA Tabular Regression. One-Way ANOVA. Apple Juice Concentrate Example, Data File xm 15-01 New product Try 3 different advertising strategies, one in each of three cities

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Power Fifteen

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  1. Power Fifteen Analysis of Variance (ANOVA)

  2. Analysis of Variance • One-Way ANOVA • Tabular • Regression • Two-Way ANOVA • Tabular • Regression

  3. One-Way ANOVA • Apple Juice Concentrate Example, Data File xm 15-01 • New product • Try 3 different advertising strategies, one in each of three cities • City 1: convenience of use • City 2: quality of product • City 3: price • Record Weekly Sales

  4. Advertising Strategies & Weekly Sales for 20 Weeks

  5. Is There a Significant Difference in Average Sales? Null Hypothesis, H0 : m1 = m2 = m3 Alternative Hypothesis: m1 ≠ m2 ,or m1 ≠ m3, or m2 ≠ m3

  6. Fk-1, n-k = [ESS/(k-1)]/[USS/(n-k)]

  7. Apple Juice Concentrate ANOVA F2, 57 = 28,756.12/8894.45 = 3.23

  8. F-Distribution Test of the Null Hypothesis of No Difference in Mean Sales with Advertising Strategy F2, 60 (critical) @ 5% =3.15

  9. Regression Set-Up: y(1) is column of 20 sales observations For city 1, 1 is a column of 20 ones, 0 is a column of 20 Zeros. Regression of a quantitative variable on three dummies Y = C(1)*Dummy(city 1) + C(2)*Dummy(city 2) + C(3)*Dummy(city 3) + e

  10. One-Way ANOVA and Regression Regression Coefficients are the City Means; F statistic

  11. Two-Way ANOVA • Apple Juice Concentrate • Two Factors • 3 advertising strategies • 2 advertising media: TV & Newspapers • 6 cities • City 1: convenience on TV • City 2: convenience in Newspapers • City 3: quality on TV • Etc.

  12. Advertising Strategies In Two Media: Weekly Sales

  13. Mean Weekly Sales By Strategy and Medium

  14. price

  15. Is There Any Difference In Mean Sales Among the Six Cities?

  16. Table of ANOVA for Two-Way

  17. Formulas For Sums of Squares a is the # of treatments for strategies =3 b is the # of treatments for media =2 r is the # of replicates or observations =10 The Grand Mean:

  18. Formulas For Sums of Squares (Cont.) Where the mean for treatment i, strategy, is:

  19. Mean Weekly Sales By Strategy and Medium

  20. Formulas For Sums of Squares (Cont.) Where the mean for treatment j, medium, is:

  21. Formulas For Sums of Squares (Cont.) Where is the mean for each city

  22. Table of Two-Way ANOVA for Apple Juice Sales

  23. F-Distribution Tests Test for Interaction: Test for Advertising Medium: Test for Advertising Strategy:

  24. Regression Set-Up Convenience dummy Quality dummy constant TV dummy =

  25. SALESAPJ CONVENIENCE QUALITY PRICE TELEVISION NEWSPAPERS 491 1 0 0 1 0 712 1 0 0 1 0 558 1 0 0 1 0 447 1 0 0 1 0 479 1 0 0 1 0 624 1 0 0 1 0 546 1 0 0 1 0 444 1 0 0 1 0 582 1 0 0 1 0 672 1 0 0 1 0 464 1 0 0 0 1 559 1 0 0 0 1 759 1 0 0 0 1 557 1 0 0 0 1 528 1 0 0 0 1 670 1 0 0 0 1 534 1 0 0 0 1 657 1 0 0 0 1 557 1 0 0 0 1 474 1 0 0 0 1 677 0 1 0 1 0 627 0 1 0 1 0

  26. Dependent Variable: SALESAPJ Method: Least Squares Sample: 1 60 Included observations: 60 Variable Coefficient Std. Error t-Statistic Prob. CONVENIENCE -48.50000 43.08204 -1.125759 0.2652 QUALITY 62.70000 43.08204 1.455363 0.1514 TELEVISION -24.40000 43.08204 -0.566361 0.5735 C 624.4000 30.46360 20.49659 0.0000 CONVENIENCE*TELEVISION 4.000000 60.92720 0.065652 0.9479 QUALITY*TELEVISION -19.70000 60.92720 -0.323337 0.7477

  27. R-squared 0.184821 Mean dependent var 614.3167 Adjusted R-squared 0.109342 S.D. dependent var 102.0765 S.E. of regression 96.33436 Akaike info criterion 12.06817 Sum squared resid 501136.7 Schwarz criterion 12.27760 Log likelihood -356.0450 F-statistic 2.448631 Durbin-Watson stat 2.452725 Prob(F-statistic) 0.045165

  28. Dependent Variable: SALESAPJ Method: Least Squares Sample: 1 60 Included observations: 60 Variable Coefficient Std. Error t-Statistic Prob. CONVENIENCE -46.50000 29.96267 -1.551931 0.1263 QUALITY 52.85000 29.96267 1.763862 0.0832 TELEVISION -29.63333 24.46441 -1.211283 0.2309 C 627.0167 24.46441 25.62974 0.0000 R-squared 0.182203 Mean dependent var 614.31 Adjusted R-squared 0.138393 S.D. dependent var 102.0765 S.E. of regression 94.75027 Akaike info criterion 12.00471 Sum squared resid 502746.3 Schwarz criterion 12.14433 Log likelihood -356.1412 F-statistic 4.158888 Durbin-Watson stat 2.456222 Prob(F-statistic) 0.009921

  29. Dependent Variable: SALESAPJ Method: Least Squares Sample: 1 60 Included observations: 60 Variable Coefficient Std. Error t-Statistic Prob. CONVENIENCE -46.50000 30.08521 -1.545610 0.1277 QUALITY 52.85000 30.08521 1.756677 0.0843 C 612.2000 21.27346 28.77765 0.0000 R-squared 0.160777 Mean dependent var 614.31 Adjusted R-squared 0.131330 S.D. dependent var 102.07 S.E. of regression 95.13779 Akaike info criterion 11.99724 Sum squared resid 515918.3 Schwarz criterion 12.101 Log likelihood -356.9171 F-statistic 5.459975 Durbin-Watson stat 2.379774 Prob(F-statistic) 0.006769

  30. Wald Test: Equation: Untitled Null Hypothesis: C(2)=C(3) F-statistic 138.2678 Probability 0.000000 Chi-square 138.2678 Probability 0.000000

  31. ANOVA By Difference • Regression with interaction terms, USS = 501,136.7 • Regression dropping interaction terms< USS = 502746.3 • Difference is 1,609.6 and is the sum of squares explained by interaction terms • F-test of the interaction terms: F2, 54 = [1609.6/2]/[501,136.7/54]

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