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Chapter 17 Hypothesis Testing McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved.

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17-2 Learning Objectives Understand... The nature and logic of hypothesis testing. A statistically significant difference The six-step hypothesis testing procedure.

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17-3 Learning Objectives Understand... The differences between parametric and nonparametric tests and when to use each. The factors that influence the selection of an appropriate test of statistical significance. How to interpret the various test statistics

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17-4 Hypothesis Testing vs. Theory “Don’t confuse “hypothesis” and “theory.” The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.” Martin H. Fischer professor emeritus. physiology University of Cincinnati

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17-5 PulsePoint: Research Revelation $28 The amount, in billions, saved by North American companies by having employees use a company purchasing card.

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17-6 Hypothesis Testing Deductive Reasoning Inductive Reasoning

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17-7 Hypothesis Testing Finds Truth “One finds the truth by making a hypothesis and comparing the truth to the hypothesis.” David Douglass physicist University of Rochester

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17-8 Statistical Procedures Descriptive Statistics Inferential Statistics

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17-9 Hypothesis Testing and the Research Process

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17-10 When Data Present a Clear Picture As Abacus states in this ad, when researchers ‘sift through the chaos’ and ‘find what matters’ they experience the “ah ha!” moment.

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17-11 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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17-12 Statistical Significance

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17-13 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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17-14 Two-Tailed Test of Significance

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17-15 One-Tailed Test of Significance

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17-16 Decision Rule Take no corrective action if the analysis shows that one cannot reject the null hypothesis.

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17-17 Statistical Decisions

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17-18 Probability of Making a Type I Error

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17-19 Critical Values

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17-20 Exhibit 17-4 Probability of Making A Type I Error

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17-21 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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17-22 Probability of Making A Type II Error

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17-23 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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17-24 Tests of Significance NonparametricParametric

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17-25 Assumptions for Using Parametric Tests Independent observations Normal distribution Equal variances Interval or ratio scales

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17-26 Probability Plot

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17-27 Probability Plot

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17-28 Probability Plot

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17-29 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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17-30 How to Select a Test How many samples are involved? If two or more samples: are the individual cases independent or related? Is the measurement scale nominal, ordinal, interval, or ratio?

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17-31 Recommended Statistical Techniques Two-Sample Tests ________________________________________ ____ k-Sample Tests ________________________________________ ____ Measureme nt Scale One-Sample Case Related Samples Independent Samples Related 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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17-32 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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17-33 Parametric Tests t-testZ-test

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17-34 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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17-35 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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17-36 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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17-37 Two-Sample Parametric Tests

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17-38 Two-Sample t-Test Example A GroupB Group Average hourly sales X 1 = $1,500 X2 = $1,300 Standard deviation s 1 = 225s2 = 251

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17-39 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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17-40 Two-Sample Nonparametric Tests: Chi-Square On-the-Job-Accident Cell Designation Count Expected Values YesNoRow Total Smoker Heavy Smoker 1,1 12, , Moderate 2, , Nonsmoker 3, , Column Total

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17-41 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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17-42 SPSS Cross-Tabulation Procedure

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17-43 Two-Related-Samples Tests NonparametricParametric

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17-44 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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17-45 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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17-46 SPSS Output for Paired- Samples t-Test

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17-47 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor AB Do Not Favor CD

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17-48 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor A=10B=90 Do Not Favor C=60D=40

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17-49 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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17-50 ANOVA Example __________________________________________Model Summary_________________________________________ Sourced.f. Sum of SquaresMean SquareF Valuep Value Model (airline) Residual (error) Total _______________________Means Table________________________ CountMeanStd. Dev.Std. Error Lufthansa Malaysia Airlines Cathay Pacific All data are hypothetical

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17-51 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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17-52 Post Hoc: Scheffe’s S Multiple Comparison Procedure VersesDiff Crit. Diff. p Value LufthansaMalaysia Airlines 19, Cathay Pacific Malaysia Airlines Cathay Pacific

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17-53 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- Forsythe XXXX Newman-KeulsXX DuncanXX Dunnet’s T3X Dunnet’s CX

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17-54 ANOVA Plots Lufthansa Business Class Lounge

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17-55 Two-Way ANOVA Example _______________________________________Model Summary___________________________ Sourced.f. Sum of Squares Mean 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 Lufthansa economy Lufthansa business Malaysia Airlines economy Malaysia Airlines business Cathay Pacific economy Cathay Pacific business

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17-56 k-Related-Samples Tests More than two levels in grouping factor Observations are matched Data are interval or ratio

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17-57 Repeated-Measures ANOVA Example All data are hypothetical. ___________________________________Means Table by Airline _________________________________________________________________________ CountMeanStd. Dev.Std. Error Rating 1, Lufthansa Rating 1, Malaysia Airlines Rating 1, Cathay Pacific Rating 2, Lufthansa Rating 2, Malaysia Airlines Rating 2, Cathay Pacific __________________________________________________________Model Summary_________________________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Airline Subject (group) Ratings Ratings by air Ratings by subj ______________________________________Means Table Effect: Ratings_________________________________________________________________ CountMeanStd. Dev.Std. Error Rating Rating

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17-58 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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17-59 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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17-60 Key Terms Two-related-samples tests Two-tailed test Type I error Type II error Z distribution Z test

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