17-2 Learning Objectives Understand... The nature and logic of hypothesis testing. A statistically significant difference The six-step hypothesis testing procedure.
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
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
17-5 PulsePoint: Research Revelation $28 The amount, in billions, saved by North American companies by having employees use a company purchasing card.
17-9 Hypothesis Testing and the Research Process
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.
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
17-16 Decision Rule Take no corrective action if the analysis shows that one cannot reject the null hypothesis.
17-17 Statistical Decisions
17-18 Probability of Making a Type I Error
17-19 Critical Values
17-20 Exhibit 17-4 Probability of Making A Type I Error
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
17-22 Probability of Making A Type II Error
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
17-24 Tests of Significance NonparametricParametric
17-25 Assumptions for Using Parametric Tests Independent observations Normal distribution Equal variances Interval or ratio scales
17-26 Probability Plot
17-27 Probability Plot
17-28 Probability Plot
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
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?
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
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?
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
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)
17-37 Two-Sample Parametric Tests
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
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)
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
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)
17-47 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor AB Do Not Favor CD
17-48 Related Samples Nonparametric Tests: McNemar Test Before After Do Not Favor After Favor A=10B=90 Do Not Favor C=60D=40
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
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
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)
17-52 Post Hoc: Scheffe’s S Multiple Comparison Procedure VersesDiff Crit. Diff. p Value LufthansaMalaysia Airlines 19, Cathay Pacific Malaysia Airlines Cathay Pacific
17-54 ANOVA Plots Lufthansa Business Class Lounge
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
17-56 k-Related-Samples Tests More than two levels in grouping factor Observations are matched Data are interval or ratio
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
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
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
17-60 Key Terms Two-related-samples tests Two-tailed test Type I error Type II error Z distribution Z test