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Power 16. Review. Post-Midterm Cumulative. Projects. Logistics. Put power point slide show on a high density floppy disk, or e-mail as an attachment, for a WINTEL machine. Email [email protected] the slide-show as a PowerPoint attachment. Assignments. 1. Project choice

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Power 16

Power 16


Review

Review

  • Post-Midterm

  • Cumulative


Projects

Projects


Logistics

Logistics

  • Put power point slide show on a high density floppy disk, or e-mail as an attachment, for a WINTEL machine.

  • Email [email protected] the slide-show as a PowerPoint attachment


Assignments

Assignments

  • 1. Project choice

  • 2. Data Retrieval

  • 3. Statistical Analysis

  • 4. PowerPoint Presentation

  • 5. Executive Summary

  • 6. Technical Appendix

  • 7. Graphics

Power_13


Powerpoint presentations member 4

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


Executive summary and technical appendix

Executive Summary and Technical Appendix


Technical appendix

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


Technical appendix cont

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.


Post midterm review

Post-Midterm Review

  • Project I: Power 16

  • Contingency Table Analysis: Power 14, Lab 8

  • ANOVA: Power 15, Lab 9

  • Survival Analysis: Power 12, Power 11, Lab 7

  • Multi-variate Regression: Power 11 , Lab 6


Slide show

Slide Show

  • Challenger disaster


Project i

Project I

  • Number of O-Rings Failing On Launch i: yi(#) = a + b*tempi + ei

    • Biased because of zeros, even if divide equation by 6

  • Two Ways to Proceed

    • Tobit, non-linear estimation: yi(#) = a + b*tempi + ei

    • Bernoulli variable: probability models

  • Probability Models: yi(0,1) = a + b*tempi + ei


Project i cont

Project I (Cont.)

  • Probability Models: yi(0,1) = a + b*tempi + ei

    • OLS, Linear Probability Model, linear approximation to the sigmoid

    • Probit, non-linear estimate of the sigmoid

    • Logit, non-linear estimate of the sigmoid

  • Significant Dependence on Temperature

    • t-test (or z-test) on slope, H0 : b=0

    • F-test

    • Wald test


Project i cont1

Project I (Cont.)

  • Plots of Number or Probability Vs Temp.

    • Label the axes

  • Answer all parts, a-f

    • The most frequent sins

      • Did not explicitly address significance

      • Did not answer b, 660 : all launches at lower temperatures had one or more o-ring failures

      • Did not execute c, estimate linear probability model


Challenger disaster

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?


Challenger disaster1

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


Launches before challenger

Launches Before Challenger

  • Data

    • number of o-rings that failed

    • launch temperature


Exploratory analysis

Exploratory Analysis

  • Launches where there was a problem


Power 16

Orings temperature

158

157

170

163

170

275

353


Power 16

.


Exploratory analysis1

Exploratory Analysis

  • All Launches

Plot of failures per observation versus temperature range shows

temperature dependence:

Mean temperature for the 7 launches with o-ring failures was

lower, 63.7, than for the 17 launches without o-ring failures,

72.6. -

Contingency table analysis


Launches and o ring failures yes no

Launches and O-Ring Failures (Yes/No)


Launches and o ring failures yes no expected observed

Launches and O-Ring Failures (Yes/No) Expected/Observed


Launches and o ring failures chi square 2dof 9 08 crit 0 05 6

Launches and O-Ring Failures Chi-Square, 2dof=9.08, crit(=0.05)=6


Power 16

Number of O-ring Failures Vs. Temperature


Power 16

Logit Extrapolated to 31F:

Probit extrapolated to 31F:


Power 16

Extrapolating OLS to 31F: OLS:

Tobit:


Conclusions

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:


Conclusions1

Conclusions

  • Decision theory argument: expected cost/benefit ratio:


Ways to analyze challenger

Ways to Analyze Challenger

Difference in mean temperatures for failures and successes

Difference in probability of one or more o-ring failures for high and low temperature ranges

Probabilty models: LPM (OLS), probit, logit

Number of o-ring failure per launch Vs. Temp.

OLS, Tobit

Contingency table analysis

ANOVA


Contingency table analysis

Contingency Table Analysis

  • Challenger example


Launches and o ring failures yes no1

Launches and O-Ring Failures (Yes/No)


Anova and o rings

ANOVA and O-Rings

  • Probability one or more o-rings fail

    • Low temp: 53-62 degrees

    • Medium temp: 63-71 degrees

    • High temp: 72-81 degrees

  • Average number of o-rings failing per launch

    • Low temp: 53-62 degrees

    • Medium temp: 63-71 degrees

    • High temp: 72-81 degrees


Power 16

Probability one or more o-rings fails


Power 16

Number of o-rings failing per launch


Outline

Outline

  • ANOVA and Regression

  • (Non-Parametric Statistics)

  • (Goodman Log-Linear Model)


Anova and regression one way

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)


Power 16

One-Way ANOVA and Regression

Regression Coefficients are the City Means; F statistic


Anova and regression one way alternative specification

Anova and Regression: One-WayAlternative 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)


Anova and regression one way alternative specification1

Anova and Regression: One-WayAlternative 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)


Anova and regression two way series of regressions compare to table 11 lecture 15

ANOVA and Regression: Two-WaySeries 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: F2, 54 = [(502746.3-501136.7)/2]/(501136.7/54) = (1609.6/2)/9280.3 = 0.09


Power 16

Table of Two-Way ANOVA for Apple Juice Sales


Anova and regression two way series of regressions

ANOVA and Regression: Two-WaySeries of Regressions

  • Salesaj = c(1) + c(2)*convenience + c(3)* quality + e, SSR=515,918.3

  • Test for media effect: F1, 54 = [(515918.3-502746.3)/1]/(501136.7/54) = 13172/9280.3 = 1.42

  • Salesaj = c(1) +e, SSR = 614757

  • Test for strategy effect: F2, 54 = [(614757-515918.3)/2]/(501136.7/54) = (98838.7/2)/(9280.3) = 5.32


Survival analysis

Survival Analysis

  • Density, f(t)

  • Cumulative distribution function, CDF, F(t)

    • Probability you failed up to time t* =F(t*)

  • Survivor Function, S(t) = 1-F(t)

    • Probability you survived longer than t*, S(t*)

    • Kaplan-Meier estimates:

      (#at risk- # ending)/# at risk

  • Applications

    • Testing a new drug


Chemotherapy drug taxol

Chemotherapy Drug Taxol

  • Current standard for ovarian cancer is taxol and a platinate such as cisplatin

  • Previous standard was cyclophosphamide and cisplatin

  • Kaplan-Meier Survival curves comparing the two regimens

    • Lab 7: ( # at risk- #ending)/# at riak


Power 16

Taxol ( Bristol-Myers Squibb)

interrupts cell division (mitosis)

It is a cyclical hydrocarbon


Power 16

Top Panel: European

Canadian and Scottish,

342 at risk for Tc, 292

Survived 1 year

Bottom Panel:

Gynecological Oncology

Group, 196 at risk

For Tc, 168 survived

1 year


2003 final

2003 Final


Nonparametric statistics

Nonparametric Statistics

  • What to do when the sample of observations is not distributed normally?


3 nonparametric techniques

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


Wilcoxon rank sum test for independent samples

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


Rating scheme

Rating scheme


Power 16

Ratings


Rank the 30 ratings

Rank the 30 Ratings

  • 30 total ratings for both samples

  • 3 ratings of 1

  • 5 ratings of 2

  • etc


Power 16

3 15 12


Power 16

continued

5 30 27


Power 16

4 19.5 5 27

Rank Sum 276.5 188.5


Rank sum t

Rank Sum, T

  • E (T )= n1 (n1 + n2 + 1)/2 = 15*31/2 = 232.5

  • VAR (T) = n1 * n2 (n1 + n2 + 1)/12

  • VAR (T) = 15*31/12 , sT = 24.1

  • For sample sizes larger than 10, T is normal

  • Z = [T-E(T)]/ sT = (276.5 - 232.5)/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


Power 16

5%

1.645


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