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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

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

18-4 Hypothesis Testing Deductive Reasoning Inductive Reasoning

18-5 Statistical Procedures Descriptive Statistics Inferential Statistics

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

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

18-8 Statistical Significance

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

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

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

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

18-13 Exhibit 18-3 Statistical Decisions

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

18-15 Critical Values

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

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

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

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

18-20 Tests of Significance NonparametricParametric

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

18-22 Exhibit 18-6

18-23 Exhibit 18-6

18-24 Exhibit 18-6

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

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?

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

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?

18-29 Parametric Tests t-testZ-test

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)

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/fraternity16904527 Apartment/rooming house, nearby 13402012 Apartment/rooming house, distant 16402012 Live at home 15 _____ 30 _____ 15 _____ 9 _____ Total6020010060

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)

18-33 Two-Sample Parametric Tests

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

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)

18-36 Two-Sample Nonparametric Tests: Chi-Square On-the-Job-Accident Cell Designation Count Expected ValuesYesNoRow Total Smoker Heavy Smoker 1,1 12, 8.24 1,2 4 7.75 16 Moderate 2,1 9 7.73 2,2 6 7.27 15 Nonsmoker 3,1 13 18.03 3,2 22 16.97 35 Column Total 343266

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)

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

18-39 Two-Related-Samples Tests NonparametricParametric

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 126932 54574 86656 62710 96146 36112 50220 35099 53794 23966 123505 49662 78944 59512 92300 35173 48111 32427 49975 20779 3427 4912 7712 3192 3846 939 2109 2632 3819 3187 ΣD = 35781. 11744329 24127744 59474944 10227204 14971716 881721 4447881 6927424 14584761 10156969 ΣD = 157364693.

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)

18-42 Exhibit 18-10 SPSS Output for Paired-Samples t-Test

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

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

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

18-46 Exhibit 18-12 ANOVA Example __________________________________________Model Summary_________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Model (airline)211644.0335822.01728.3040.0001 Residual (error)5711724.550205.694 Total5923368.583 _______________________Means Table________________________ CountMeanStd. Dev.Std. Error Delta2038.95014.0063.132 Lufthansa2058.90015.0893.374 KLM2072.90013.9023.108 All data are hypothetical

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)

18-48 Post Hoc: Scheffe’s S Multiple Comparison Procedure VersesDiff Crit. Diff. p Value DeltaLufthansa19,95011.400.0002 KLM33.95011.400.0001 LufthansaKLM14.00011.400.0122

18-49 Exhibit 18-13 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

18-50 Exhibit 18-14 ANOVA Plots

18-51 Exhibit 18-15 Two-Way ANOVA Example __________________________________________Model Summary_________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Airline211644.0335822.01739.1780.0001 Seat selection13182.817 21.4180.0001 Airline by seat selection2517.033258.5171.7400.1853 Residual548024.700148.606 All data are hypothetical __________Means Table Effect: Airline by Seat Selection___________ CountMeanStd. Dev.Std. Error Delta economy1035.60012.1403.839 Delta business1042.30015.5504.917 Lufthansa economy1048.50012.5013.953 Lufthansa business1069.3009.1662.898 KLM economy1064.80013.0374.123 KLM business1081.0009.6033.037

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

18-53 Exhibit 18-17 Repeated- Measures ANOVA Example ___________________________________Means Table by Airline _________________________________________________________________________ CountMeanStd. Dev.Std. Error Rating 1, Delta2038.95014.0063.132 Rating 1, Lufthansa2058.90015.0893.374 Rating 1, KLM2072.90013.9023.108 Rating 2, Delta2032.4008.2681.849 Rating 2, Lufthansa2072.25010.5722.364 Rating 2, KLM2079.80011.2652.519 __________________________________________________________Model Summary_________________________________________________________ Sourced.f.Sum of SquaresMean SquareF Valuep Value Airline23552735.5017763.77567.1990.0001 Subject (group)5715067.650264.345 Ratings1625.633 14.3180.0004 Ratings by air.......22061.7171030.85823.5920.0001 Ratings by subj.....572490.65043.696 All data are hypothetical. ______________________________________Means Table Effect: Ratings_________________________________________________________________ CountMeanStd. Dev.Std. Error Rating 16056.91719.9022.569 Rating 26061.48323.2082.996

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

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

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