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# Chapter 18

Chapter 18. Hypothesis Testing. Learning Objectives. Understand . . . the nature and logic of hypothesis testing a statistically significant difference six-step hypothesis testing procedure. Learning Objectives. Understand . . .

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## Chapter 18

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1. Chapter 18 Hypothesis Testing

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

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

4. Hypothesis Testing Inductive Reasoning Deductive Reasoning

5. Statistical Procedures Inferential Statistics Descriptive Statistics

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

7. 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

8. Statistical Significance

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

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

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

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

13. Exhibit 18-3 Statistical Decisions

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

15. Critical Values

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

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

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

20. Tests of Significance Parametric Nonparametric

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

22. Exhibit 18-6

23. Exhibit 18-6

24. Exhibit 18-6

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

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?

27. Exhibit 18-7 Recommended Statistical Techniques

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?

29. Parametric Tests Z-test t-test

30. One-Sample t-Test Example

31. One Sample Chi-Square Test Example

32. One-Sample Chi-Square Example

33. Two-Sample Parametric Tests

34. Two-Sample t-Test Example

35. Two-Sample t-Test Example

36. Two-Sample Nonparametric Tests: Chi-Square

37. Two-Sample Chi-Square Example

38. Exhibit 18-8 SPSS Cross-Tab Procedure

39. Two-Related-Samples Tests Parametric Nonparametric

40. Exhibit 18-9 Sales Data for Paired-Samples t-Test

41. Paired-Samples t-Test Example

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

43. Related-Samples Nonparametric Tests: McNemar Test

44. An Example of the McNemar Test

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

46. Exhibit 18-12 ANOVA Example All data are hypothetical

47. ANOVA Example Continued

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

49. Exhibit 18-13 Multiple Comparison Procedures

50. Exhibit 18-14 ANOVA Plots

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