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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. Pull Quote • “A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective.” • Edward Teller, theoretical physicist, • “father of the hydrogen bomb” • (1908–2003)

  5. Hypothesis Testing Inductive Reasoning Deductive Reasoning

  6. 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

  7. Statistical Procedures Inferential Statistics Descriptive Statistics

  8. Hypothesis Testing and the Research Process

  9. 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.

  10. 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

  11. Statistical Significance

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

  13. Two-Tailed Test of Significance

  14. One-Tailed Test of Significance

  15. Take no corrective action if the analysis shows that one cannotreject the null hypothesis. Decision Rule

  16. Statistical Decisions

  17. Probability of Making a Type I Error

  18. Critical Values

  19. Probability of Making A Type I Error

  20. 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

  21. Probability of Making A Type II Error

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

  23. Tests of Significance Parametric Nonparametric

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

  25. Probability Plot

  26. Probability Plot

  27. Probability Plot

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

  29. 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?

  30. Recommended Statistical Techniques

  31. 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?

  32. Parametric Tests Z-test t-test

  33. One-Sample t-Test Example

  34. One Sample Chi-Square Test Example

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

  36. Two-Sample Parametric Tests

  37. Two-Sample t-Test Example

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

  39. Two-Sample Nonparametric Tests: Chi-Square

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

  41. SPSS Cross-Tabulation Procedure

  42. Two-Related-Samples Tests Parametric Nonparametric

  43. Sales Data for Paired-Samples t-Test

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

  45. SPSS Output for Paired-Samples t-Test

  46. Related Samples Nonparametric Tests: McNemar Test

  47. Related Samples Nonparametric Tests: McNemar Test

  48. 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.

  49. ANOVA Example All data are hypothetical

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

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