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Chapter 17

Chapter 17. Hypothesis Testing. Learning Objectives. Understand . . . The nature and logic of hypothesis testing. A statistically significant difference The six-step hypothesis testing procedure. Learning Objectives. Understand . . .

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Chapter 17

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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

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