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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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