1 Power 16

2 Projects

3 Logistics Put power point slide show on a high density floppy disk for a WINTEL machine. the slide-show as a PowerPoint attachment

4 Assignments 1. Project choice 2. Data Retrieval 3. Statistical Analysis 4. PowerPoint Presentation 5. Executive Summary 6. Technical Appendix Power_13

5 PowerPoint Presentations: Member 4 1. Introduction: Members 1,2, 3 –What –Why –How 2. Executive Summary: Member 5 3. Exploratory Data Analysis: Member 3 4. Descriptive Statistics: Member 3 5. Statistical Analysis: Member 3 6. Conclusions: Members 3 & 5 7. Technical Appendix: Table of Contents, Member 6

6 Executive Summary and Technical Appendix

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8 Technical Appendix Table of Contents Spreadsheet of data used and sources or if extensive, a subsample of the data Descriptive Statistics and Histograms for the variables in the study If time series data, a plot of each variable against time If relevant, plot of the dependent Vs. each of the explanatory variables

9 Technical Appendix (Cont.) Statistical Results, for example regression Plot of the actual, fitted and error and other diagnostics Brief summary of the conclusions, meanings drawn from the exploratory, descriptive, and statistical analysis.

10 Slide Show Challenger disaster

11 Challenger Disaster Failure of O-rings that sealed grooves on the booster rockets Was there any relationship between o-ring failure and temperature? Engineers knew that the rubber o-rings hardened and were less flexible at low temperatures But was there launch data that showed a problem?

12 Challenger Disaster What: Was there a relationship between launch temperature and o-ring failure prior to the Challenger disaster? Why: Should the launch have proceeded? How: Analyze the relationship between launch temperature and o-ring failure

13 Launches Before Challenger Data –number of o-rings that failed –launch temperature

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17 Exploratory Analysis Launches where there was a problem

Orings temperature

David Rhodes and Katie Wohletz show relationship changes if you drop a point.

20 Exploratory Analysis All Launches Plot of failures per observation versus temperature range shows temperature dependence: David Wagner Mean temperature for the 7 launches with o-ring failures was lower, 63.7, than for the 17 launches without o-ring failures, Yuan Yuan, Hung Lam

21 Launches and O-Ring Failures (Yes/No)

Number of O-ring Failures Vs. Temperature

23 Logit Extrapolated to 31F: James Young Probit extrapolated to 31F: Ken Morino

24 Extrapolating OLS to 31F: Adams, Rhodes, Wohletz, Wagner, Jelmini, Hatanaka

25 Conclusions From extrapolating the probability models to 31 F, Linear Probability, Probit, or Logit, there was a high probability of one or more o-rings failing From extrapolating the Number of O-rings failing to 31 F, OLS or Tobit, 3 or more o- rings would fail. There had been only one launch out of 24 where as many as 3 o-rings had failed. Decision theory argument: expected cost/benefit ratio: David Wagner

26 Outline ANOVA and Regression Non-Parametric Statistics Goodman Log-Linear Model

27 Anova and Regression: One-Way Salesaj = c(1)*convenience+c(2)*quality+c(3)*price+ e E[salesaj/(convenience=1, quality=0, price=0)] =c(1) = mean for city(1) –c(1) = mean for city(1) (convenience) –c(2) = mean for city(2) (quality) –c(3) = mean for city(3) (price) –Test the null hypothesis that the means are equal using a Wald test: c(1) = c(2) = c(3)

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

29 Anova and Regression: One-Way Alternative Specification Salesaj = c(1) + c(2)*convenience+c(3)*quality+e E[Salesaj/(convenience=0, quality=0)] = c(1) = mean for city(3) (price, the omitted one) E[Salesaj/(convenience=1, quality=0)] = c(1) + c(2) = mean for city(1) (convenience) –c(1) = mean for city(3), the omitted city –c(2) = mean for city(1) minus mean for city(3) –Test that the mean for city(1) = mean for city(3) –Using the t-statistic for c(2)

30 Anova and Regression: One-Way Alternative Specification Salesaj = c(1) + c(2)*convenience+c(3)*price+e E[Salesaj/(convenience=0, price=0)] = c(1) = mean for city(2) (quality, the omitted one) E[Salesaj/(convenience=1, price=0)] = c(1) + c(2) = mean for city(1) (convenience) –c(1) = mean for city(2), the omitted city –c(2) = mean for city(1) minus mean for city(2) –Test that the mean for city(1) = mean for city(2) –Using the t-statistic for c(2)

31 ANOVA and Regression: Two-Way Series of Regressions; Compare to Table 11, Lecture 15 Salesaj = c(1) + c(2)*convenience + c(3)* quality + c(4)*television + c(5)*convenience*television + c(6)*quality*television + e, SSR=501,136.7 Salesaj = c(1) + c(2)*convenience + c(3)* quality + c(4)*television + e, SSR=502,746.3 Test for interaction effect: F 2, 54 = [( )/2]/( /54) = (1609.6/2)/ = 0.09

Table of Two-Way ANOVA for Apple Juice Sales

33 ANOVA and Regression: Two-Way Series of Regressions Salesaj = c(1) + c(2)*convenience + c(3)* quality + e, SSR=515,918.3 Test for media effect: F 1, 54 = [( )/1]/( /54) = 13172/ = 1.42 Salesaj = c(1) +e, SSR = Test for strategy effect: F 2, 54 = [( )/2]/( /54) = ( /2)/(9280.3) = 5.32

34 Nonparametric Statistics What to do when the sample of observations is not distributed normally?

35 3 Nonparametric Techniques Wilcoxon Rank Sum Test for independent samples –Data Analysis Plus Signs Test for Matched Pairs: Rated Data –Eviews, Descriptive Statistics Wilcoxon Signed Rank Sum Test for Matched Pairs: Quantitative Data –Eviews

36 Wilcoxon Rank Sum Test for Independent Samples Testing the difference between the means of two populations when they are non-normal A New Painkiller Vs. Aspirin, Xm17-02

37 Rating scheme

38 Ratings

39 Rank the 30 Ratings 30 total ratings for both samples 3 ratings of 1 5 ratings of 2 etc

continued

Rank Sum

43 Rank Sum, T E (T )= n 1 (n 1 + n 2 + 1)/2 = 15*31/2 = VAR (T) = n 1 * n 2 (n 1 + n 2 + 1)/12 VAR (T) = 15*31/12,  T = 24.1 For sample sizes larger than 10, T is normal Z = [T-E(T)]/  T = ( )/24.1 = 1.83 Null Hypothesis is that the central tendency for the two drugs is the same Alternative hypothesis: central tendency for the new drug is greater than for aspirin: 1- tailed test

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