1. McGraw-Hill/IrwinCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. HYPOTHESIS TESTING Chapter 17

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

3. 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

4. 17-4 Pull Quote “A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective.” Edward Teller, theoretical physicist, “father of the hydrogen bomb” (1908–2003)

5. 17-5 Hypothesis Testing Deductive Reasoning Inductive Reasoning

6. 17-6 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

7. 17-7 Statistical Procedures Descriptive Statistics Inferential Statistics

8. 17-8 Hypothesis Testing and the Research Process

9. 17-9 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.

10. 17-10 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

11. 17-11 Statistical Significance

12. 17-12 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

13. 17-13 Two-Tailed Test of Significance

14. 17-14 One-Tailed Test of Significance

15. 17-15 Decision Rule Take no corrective action if the analysis shows that one cannot reject the null hypothesis.

16. 17-16 Statistical Decisions

17. 17-17 Probability of Making a Type I Error

18. 17-18 Critical Values

19. 17-19 Probability of Making A Type I Error

20. 17-20 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

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

22. 17-22 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

23. 17-23 Tests of Significance NonparametricParametric

24. 17-24 Assumptions for Using Parametric Tests Independent observations Normal distribution Equal variances Interval or ratio scales

25. 17-25 Probability Plot

26. 17-26 Probability Plot

27. 17-27 Probability Plot

28. 17-28 Advantages of Nonparametric Tests Easy to understand and use Usable with nominal data Appropriate for ordinal data Appropriate for non-normal population distributions

29. 17-29 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?

30. 17-30 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

31. 17-31 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?

32. 17-32 Parametric Tests t-testZ-test

33. 17-33 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)

34. 17-34 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

35. 17-35 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)

36. 17-36 Two-Sample Parametric Tests

37. 17-37 Two-Sample t-Test Example A GroupB Group Average hourly sales X 1 = $1,500 X2 = $1,300 Standard deviation s 1 = 225s2 = 251

38. 17-38 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)

39. 17-39 Two-Sample Nonparametric Tests: Chi-Square On-the-Job-Accident Cell Designation Count Expected Values YesNoRow 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

40. 17-40 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)

41. 17-41 SPSS Cross-Tabulation Procedure

42. 17-42 Two-Related-Samples Tests NonparametricParametric

43. 17-43 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.

44. 17-44 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)

45. 17-45 SPSS Output for Paired-Samples t-Test

46. 17-46 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor AB Do Not Favor CD

47. 17-47 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor A=10B=90 Do Not Favor C=60D=40

48. 17-48 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.

49. 17-49 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 Lufthansa2038.95014.0063.132 Malaysia Airlines2058.90015.0893.374 Cathay Pacific2072.90013.9023.108 All data are hypothetical

50. 17-50 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)

51. 17-51 Post Hoc: Scheffe’s S Multiple Comparison Procedure VersesDiff Crit. Diff. p Value LufthansaMalaysia Airlines 19,95011.400.0002 Cathay Pacific 33.95011.400.0001 Malaysia Airlines Cathay Pacific 14.00011.400.0122

52. 17-52 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

53. 17-53 ANOVA Plots

54. 17-54 Two-Way ANOVA Example ________________________________Model Summary________________________ Sourced.f. Sum of Squares Mean SquareF Valuep Value Airline211644.0335822.01739.1780.0001 Seat selection13182.817 21.4180.0001 Airline by seat selection 2517.033258.5171.7400.1853 Residual548024.700148.606 Means Table Effect: Airline by Seat Selection CountMeanStd. Dev.Std. Error Lufthansa economy 1035.60012.1403.839 Lufthansa business 1042.30015.5504.917 Malaysia Airlines economy 1048.50012.5013.953 Malaysia Airlines business 1069.3009.1662.898 Cathay Pacific economy 1064.80013.0374.123 Cathay Pacific business 1081.0009.6033.037 All data are hypothetical

55. 17-55 k-Related-Samples Tests More than two levels in grouping factor Observations are matched Data are interval or ratio

56. 17-56 Repeated- Measures ANOVA Example __________________Model Summary____________________ Sourced.f. Sum of Squares Mean 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 ___________________Means Table Effect: Ratings_________________________ CountMeanStd. Dev.Std. Error Rating 16056.91719.9022.569 Rating 26061.48323.2082.996 All data are hypothetical. ______________________Means Table by Airline _____________________ CountMeanStd. Dev.Std. Error Rating 1, Lufthansa2038.95014.0063.132 Rating 1, Malaysia Airlines2058.90015.0893.374 Rating 1, Cathay Pacific2072.90013.9023.108 Rating 2, Lufthansa2032.4008.2681.849 Rating 2, Malaysia Airlines2072.25010.5722.364 Rating 2, Cathay Pacific2079.80011.2652.519

57. 17-57 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

58. 17-58 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

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

60. McGraw-Hill/IrwinCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. ADDITIONAL DISCUSSION OPPORTUNITIES Chapter 17

61. 17-61 Snapshot: Troy-Bilt What elements in TV advertising build recall and consideration? Those who are market ready in category process TV ads differently than those who aren’t market ready. Test and control groups used. Test ads embedded in DIY House Crashers.

62. 17-62 Snapshot: Drug use in Movies Top 200 rental movies during 2 years. Trained coders. Prevalence of use, frequency of use, percentage of characters using. Content analysis of drinking, smoking, illicit drugs, prescriptions and OLC drugs.

63. 17-63 Snapshot: A/B Testing Does web page design alter click behavior? Test one or multiple factors. What hypothesis could drive A/B tests? Are we being tested whenever we visit a web page?

64. 17-64 PullQuote: 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

65. 17-65 PulsePoint: Research Revelation $28 The amount, in billions, saved by North American companies by having employees use a company purchasing card.

66. McGraw-Hill/IrwinCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. HYPOTHESIS TESTING Chapter 17

67. 17-67 Photo Attributions