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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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Presentation on theme: "Chapter 17 Hypothesis Testing McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved."— Presentation transcript:

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

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 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

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

6 17-6 Hypothesis Testing Deductive Reasoning Inductive Reasoning

7 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

8 17-8 Statistical Procedures Descriptive Statistics Inferential Statistics

9 17-9 Hypothesis Testing and the Research Process

10 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.

11 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

12 17-12 Statistical Significance

13 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

14 17-14 Two-Tailed Test of Significance

15 17-15 One-Tailed Test of Significance

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

17 17-17 Statistical Decisions

18 17-18 Probability of Making a Type I Error

19 17-19 Critical Values

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

21 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

22 17-22 Probability of Making A Type II Error

23 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

24 17-24 Tests of Significance NonparametricParametric

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

26 17-26 Probability Plot

27 17-27 Probability Plot

28 17-28 Probability Plot

29 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

30 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?

31 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

32 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?

33 17-33 Parametric Tests t-testZ-test

34 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)

35 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

36 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)

37 17-37 Two-Sample Parametric Tests

38 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

39 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)

40 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

41 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)

42 17-42 SPSS Cross-Tabulation Procedure

43 17-43 Two-Related-Samples Tests NonparametricParametric

44 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 =

45 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)

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

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

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

49 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

50 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

51 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)

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

53 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

54 17-54 ANOVA Plots Lufthansa Business Class Lounge

55 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

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

57 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

58 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

59 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

60 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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