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© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.McGraw-Hill/Irwin 18-1 Chapter 18 Hypothesis Testing

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18-2 Learning Objectives Understand... the nature and logic of hypothesis testing a statistically significant difference six-step hypothesis testing procedure

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18-3 Learning Objectives Understand... differences between parametric and nonparametric tests and when to use each factors that influence the selection of an appropriate test of statistical significance how to interpret the various test statistics

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18-4 Hypothesis Testing Deductive Reasoning Inductive Reasoning

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18-5 Statistical Procedures Descriptive Statistics Inferential Statistics

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18-6 Exhibit 18-1 Hypothesis Testing and the Research Process

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18-7 Approaches to Hypothesis Testing Classical statistics Objective view of probability Established hypothesis is rejected or fails to be rejected Analysis based on sample data Bayesian statistics Extension of classical approach Analysis based on sample data Also considers established subjective probability estimates

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18-8 Statistical Significance

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18-9 Types of Hypotheses Null –H 0 : = 50 mpg –H 0 : < 50 mpg –H 0 : > 50 mpg Alternate –H A : = 50 mpg –H A : > 50 mpg –H A : < 50 mpg

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18-10 Exhibit 18-2 Two-Tailed Test of Significance

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18-11 Exhibit 18-2 One-Tailed Test of Significance

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18-12 Decision Rule Take no corrective action if the analysis shows that one cannot reject the null hypothesis.

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18-13 Exhibit 18-3 Statistical Decisions

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18-14 Exhibit 18-4 Probability of Making a Type I Error

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18-15 Critical Values

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18-16 Exhibit 18-4 Probability of Making A Type I Error

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18-17 Factors Affecting Probability of Committing a Error True value of parameter Alpha level selected One or two-tailed test used Sample standard deviation Sample size

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18-18 Exhibit 18-5 Probability of Making A Type II Error

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18-19 Statistical Testing Procedures Obtain critical test value Interpret the test Interpret the test Stages Choose statistical test State null hypothesis Select level of significance Compute difference value

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18-20 Tests of Significance NonparametricParametric

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18-21 Assumptions for Using Parametric Tests Independent observations Normal distribution Equal variances Interval or ratio scales

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18-22 Exhibit 18-6

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18-23 Exhibit 18-6

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18-24 Exhibit 18-6

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18-25 Advantages of Nonparametric Tests Easy to understand and use Usable with nominal data Appropriate for ordinal data Appropriate for non-normal population distributions

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18-26 How To Select A Test How many samples are involved? If two or more samples are involved, are the individual cases independent or related? Is the measurement scale nominal, ordinal, interval, or ratio?

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18-27 Exhibit 18-7 Recommended Statistical Techniques Two-Sample Tests ____________________________________________ k-Sample Tests ____________________________________________ Measurement ScaleOne-Sample CaseRelated Samples Independent SamplesRelated Samples Independent Samples Nominal Binomial x 2 one-sample test McNemar Fisher exact test x 2 two-samples test Cochran Q x 2 for k samples Ordinal Kolmogorov-Smirnov one-sample test Runs test Sign test Wilcoxon matched-pairs test Median test Mann-Whitney U Kolmogorov- Smirnov Wald-Wolfowitz Friedman two- way ANOVA Median extension Kruskal-Wallis one-way ANOVA Interval and Ratio t-test Z test t-test for paired samples t-test Z test Repeated- measures ANOVA One-way ANOVA n-way ANOVA

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18-28 Questions Answered by One-Sample Tests Is there a difference between observed frequencies and the frequencies we would expect? Is there a difference between observed and expected proportions? Is there a significant difference between some measures of central tendency and the population parameter?

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18-29 Parametric Tests t-testZ-test

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18-30 One-Sample t-Test Example NullHo: = 50 mpg Statistical testt-test Significance level.05, n=100 Calculated value1.786 Critical test value1.66 (from Appendix C, Exhibit C-2)

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18-31 One Sample Chi-Square Test Example Living Arrangement Intend to Join Number Interviewed Percent (no. interviewed/200) Expected Frequencies (percent x 60) Dorm/fraternity Apartment/rooming house, nearby Apartment/rooming house, distant Live at home 15 _____ 30 _____ 15 _____ 9 _____ Total

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18-32 One-Sample Chi-Square Example NullHo: 0 = E Statistical testOne-sample chi-square Significance level.05 Calculated value9.89 Critical test value7.82 (from Appendix C, Exhibit C-3)

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18-33 Two-Sample Parametric Tests

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18-34 Two-Sample t-Test Example A GroupB Group Average hourly salesX 1 = $1,500X2 = $1,300 Standard deviations 1 = 225s2 = 251

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18-35 Two-Sample t-Test Example NullHo: A sales = B sales Statistical testt-test Significance level.05 (one-tailed) Calculated value1.97, d.f. = 20 Critical test value1.725 (from Appendix C, Exhibit C-2)

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18-36 Two-Sample Nonparametric Tests: Chi-Square On-the-Job-Accident Cell Designation Count Expected ValuesYesNoRow Total Smoker Heavy Smoker 1,1 12, , Moderate 2, , Nonsmoker 3, , Column Total

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18-37 Two-Sample Chi-Square Example NullThere is no difference in distribution channel for age categories. Statistical testChi-square Significance level.05 Calculated value6.86, d.f. = 2 Critical test value5.99 (from Appendix C, Exhibit C-3)

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18-38 Exhibit 18-8 SPSS Cross- Tab Procedure

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18-39 Two-Related-Samples Tests NonparametricParametric

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18-40 Exhibit 18-9 Sales Data for Paired-Samples t-Test Company Sales Year 2 Sales Year 1Difference DD2D2 GM GE Exxon IBM Ford AT&T Mobil DuPont Sears Amoco Total ΣD = ΣD =

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18-41 Paired-Samples t-Test Example NullYear 1 sales = Year 2 sales Statistical testPaired sample t-test Significance level.01 Calculated value6.28, d.f. = 9 Critical test value3.25 (from Appendix C, Exhibit C-2)

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18-42 Exhibit SPSS Output for Paired-Samples t-Test

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18-43 Related-Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor AB Do Not Favor CD

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18-44 An Example of the McNemar Test Before After Do Not Favor After Favor A=10B=90 Do Not Favor C=60D=40

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18-45 k-Independent-Samples Tests: ANOVA Tests the null hypothesis that the means of three or more populations are equal One-way: Uses a single-factor, fixed- effects model to compare the effects of a treatment or factor on a continuous dependent variable

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18-46 Exhibit ANOVA Example __________________________________________Model Summary_________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Model (airline) Residual (error) Total _______________________Means Table________________________ CountMeanStd. Dev.Std. Error Delta Lufthansa KLM All data are hypothetical

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18-47 ANOVA Example Continued Null A1 = A2 = A3 Statistical testANOVA and F ratio Significance level.05 Calculated value28.304, d.f. = 2, 57 Critical test value3.16 (from Appendix C, Exhibit C-9)

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18-48 Post Hoc: Scheffe’s S Multiple Comparison Procedure VersesDiff Crit. Diff. p Value DeltaLufthansa19, KLM LufthansaKLM

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18-49 Exhibit Multiple Comparison Procedures Test Complex Comparisons Pairwise Comparisons Equal n’s Only Unequal n’s Equal Variances Assumed Unequal Variances Not Assumed Fisher LSDXXX BonferroniXXX Tukey HSDXXX Tukey-KramerXXX Games-HowellXXX Tamhane T2XXX Scheffé SXXXX Brown-ForsytheXXXX Newman-KeulsXX DuncanXX Dunnet’s T3X Dunnet’s CX

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18-50 Exhibit ANOVA Plots

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18-51 Exhibit Two-Way ANOVA Example __________________________________________Model Summary_________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Airline Seat selection Airline by seat selection Residual All data are hypothetical __________Means Table Effect: Airline by Seat Selection___________ CountMeanStd. Dev.Std. Error Delta economy Delta business Lufthansa economy Lufthansa business KLM economy KLM business

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18-52 k-Related-Samples Tests More than two levels in grouping factor Observations are matched Data are interval or ratio

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18-53 Exhibit Repeated- Measures ANOVA Example ___________________________________Means Table by Airline _________________________________________________________________________ CountMeanStd. Dev.Std. Error Rating 1, Delta Rating 1, Lufthansa Rating 1, KLM Rating 2, Delta Rating 2, Lufthansa Rating 2, KLM __________________________________________________________Model Summary_________________________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Airline Subject (group) Ratings Ratings by air Ratings by subj All data are hypothetical. ______________________________________Means Table Effect: Ratings_________________________________________________________________ CountMeanStd. Dev.Std. Error Rating Rating

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18-54 Key Terms a priori contrasts Alternative hypothesis Analysis of variance (ANOVA Bayesian statistics Chi-square test Classical statistics Critical value F ratio Inferential statistics K-independent-samples tests K-related-samples tests Level of significance Mean square Multiple comparison tests (range tests) Nonparametric tests Normal probability plot

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18-55 Key Terms Null hypothesis Observed significance level One-sample tests One-tailed test p value Parametric tests Power of the test Practical significance Region of acceptance Region of rejection Statistical significance t distribution Trials t-test Two-independent- samples tests

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18-56 Key Terms Two-related-samples tests Two-tailed test Type I error Type II error Z distribution Z test

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