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1. Chapter 17 Hypothesis Testing

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

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. 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

5. Hypothesis Testing Inductive Reasoning Deductive Reasoning

6. Statistical Procedures Inferential Statistics Descriptive Statistics

7. Hypothesis Testing and the Research Process

8. When Data Present a Clear Picture Researchers use hypothesis testing to hunt for truth. As Abacus states in this ad, when researchers ‘sift through the chaos’ and ‘find what matters’ they experience the “ah ha!” moment.

9. 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 Approaches to Hypothesis Testing

10. Statistical Significance

11. Types of Hypotheses • Null • H0:  = 50 mpg • H0:  < 50 mpg • H0:  > 50 mpg • Alternate • HA:  = 50 mpg • HA:  > 50 mpg • HA:  < 50 mpg

12. Two-Tailed Test of Significance

13. One-Tailed Test of Significance

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

15. Statistical Decisions

16. Probability of Making a Type I Error

17. Critical Values

18. Exhibit 17-4 Probability of Making A Type I Error

19. 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

20. Probability of Making A Type II Error

21. State null hypothesis Interpret the test Choose statistical test Obtain critical test value Select level of significance Compute difference value Statistical Testing Procedures Stages

22. Tests of Significance Parametric Nonparametric

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

24. Probability Plot

25. Probability Plot

26. Probability Plot

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

28. 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?

29. Recommended Statistical Techniques

30. 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?

31. Parametric Tests Z-test t-test

32. One-Sample t-Test Example

33. One Sample Chi-Square Test Example

34. One-Sample Chi-Square Example (from Appendix C, Exhibit C-3)

35. Two-Sample Parametric Tests

36. Two-Sample t-Test Example

37. Two-Sample t-Test Example (from Appendix C, Exhibit C-2)

38. Two-Sample Nonparametric Tests: Chi-Square

39. Two-Sample Chi-Square Example (from Appendix C, Exhibit C-3)

40. SPSS Cross-Tab Procedure

41. Two-Related-Samples Tests Parametric Nonparametric

42. Sales Data for Paired-Samples t-Test

43. Paired-Samples t-Test Example (from Appendix C, Exhibit C-2)

44. SPSS Output for Paired-Samples t-Test

45. Related Samples Nonparametric Tests: McNemar Test

46. Related Samples Nonparametric Tests: McNemar Test

47. 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

48. ANOVA Example All data are hypothetical

49. ANOVA Example Continued (from Appendix C, Exhibit C-9)

50. Post Hoc: Scheffe’s S Multiple Comparison Procedure