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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 7: Testing Differences between Means. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 4/7/2014 , Spring 2014. Midterm Exam Results. Midterm Exam Morning Group Mean: 80.62

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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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  1. Fox/Levin/Forde, Elementary Statistics in Social Research, 12e • Chapter 7: Testing Differences between Means HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D. 4/7/2014, Spring 2014

  2. Midterm Exam Results Midterm Exam Morning Group Mean: 80.62 Afternoon Group Mean: 85.65 HW#7: Add explanation, formula and example about the Coefficient of Variation and I’ll to multiply your grade by =1.05263

  3. CHAPTER OBJECTIVES 7.1 • Distinguish between the null and research hypotheses • Understand the sampling distribution of differences between mean and use it to test hypotheses 7.2 7.3 • Understand the rationale behind levels of significance 7.4 • Test the differences between means 7.5 • Understand the logic of one-tailed tests 7.6 • Calculate Cohen’s d 7.7 • List the requirements for testing the differences between means

  4. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.1 Distinguish between the null and research hypotheses

  5. 7.1 Introduction We’ve learned that a population mean or proportion can be estimated Researchers really want to test hypotheses • These hypotheses typically refer to differences between groups In this chapter, we’ll learn how to test hypotheses about differences between sample means and proportions

  6. 7.1 The Null and Research Hypotheses The Null Hypothesis The Research Hypothesis vs. • There is no statistically significant difference between the sample means of two groups • Any observed difference is the result of sampling error alone • There is a statistically significant difference between the sample means of two groups • A true population difference does exist

  7. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.2 Understand the sampling distribution of differences between means and use it to test hypotheses

  8. 7.2 Figure 7.2

  9. 7.2 Testing Hypotheses with the Distribution of Differences between Means The sampling distribution approximates a normal curve • This provides the basis for testing hypotheses between sample means • We need to use standard scores or z scores

  10. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.3 Understand the rationale behind levels of significance

  11. 7.3 Figure 7.7

  12. 7.3 Levels of Significance Used to determine statistical significance Symbolized by αlpha • The level of probability where decisions can be made with confidence

  13. 7.3 Figure 7.6

  14. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.4 Test the differences between means

  15. Tests of Difference Means Proportions: Box 7.4, page 250 Dependent Samples Independent Samples Known σ1 and σ2 Unknown σ1 and σ2 Same & Matched Samples Box 7.2 &7.3, page 244&247 Not realistic “Same” Variance Box 7.1, page 239 Unequal Variance page 243

  16. Tests of Difference Means Proportions: Box 7.4, page 250 Dependent Samples Independent Samples Known σ1 and σ2 Unknown σ1 and σ2 Same & Matched Samples Box 7.2 &7.3, page 244&247 Not realistic “Same” Variance Box 7.1, page 239 Unequal Variance page 243

  17. 7.4 Test the Differences between Means Standard Error of the Differences between Means • The standard deviation of the distributions of differences can be estimated Testing differences between means • t is used instead of z because we don’t know the true population standard deviation

  18. Box 7.1 in page 239Problem 22

  19. Tests of Difference Means Proportions: Box 7.4, page 250 Dependent Samples Independent Samples Known σ1 and σ2 Unknown σ1 and σ2 Same & Matched Samples Box 7.2 &7.3, page 244&247 Not realistic “Same” Variance Box 7.1, page 239 Unequal Variance page 243

  20. 7.4 Adjustment for Unequal Variances The formula for estimating the standard error of the differences between means pools variance information from both samples • This assumes that the population variances are the same for the two groups • If either sample variance is more than twice as large as the other, we should use the following formula that does not pool the variances

  21. Example in page 243Problem 24

  22. Tests of Difference Means Proportions: Box 7.4, page 250 Dependent Samples Independent Samples Known σ1 and σ2 Unknown σ1 and σ2 Same & Matched Samples Box 7.2 &7.3, page 244&247 Not realistic “Same” Variance Box 7.1, page 239 Unequal Variance page 243

  23. 7.4 Comparing Dependent Samples The before-after or panel design consists of a single sample measured at two points in time • This means that the samples are no longer independent and therefore different formulas are required:

  24. Box 7.2 in page 244 and Box 7.3 in page 247Problem 34

  25. Tests of Difference Means Proportions: Box 7.4, page 250 Dependent Samples Independent Samples Known σ1 and σ2 Unknown σ1 and σ2 Same & Matched Samples Box 7.2 &7.3, page 244&247 Not realistic “Same” Variance Box 7.1, page 239 Unequal Variance page 243

  26. 7.4 Two Sample Test of Proportions The logic for testing the differences between two proportions is the same as when dealing with means • The formulas are just different

  27. Box 7.4 in page 250Problem 41

  28. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.5 Understand the logic of one-tailed tests

  29. 7.5 One-Tailed Tests vs. Two-Tailed One-Tailed

  30. 7.5 Figure 7.9

  31. Let’s review the examples, this time looking at the one-tailed test hypothesisNotice that now we use page 553Box 7.5 in page 254 Same sampleBox 7.6 in page 256 Independent Samples

  32. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 7.7 List the requirements for testing the difference between means

  33. 7.7 Requirements for Testing the Differences between Means • A Comparison between Two Means • Interval Data • Random Sampling • A Normal Distribution • Equal Variances

  34. Homework Chapter 7 Problems: 27, 28, 36

  35. CHAPTER SUMMARY • When testing for differences between means (or proportions), researchers begin with a null and research hypothesis 7.1 • The logic of the distribution of differences between means is integral for hypothesis testing 7.2 • The level of significance determines the level of probability at which the null hypothesis can be rejected with confidence 7.3

  36. CHAPTER SUMMARY • Researchers can use several different methods to test for differences between means and proportions 7.4 • One-tailed tests are used when the direction of a relationship is anticipated 7.5 7.6 • Cohen’s d can be calculated to determine effect size • There are several requirements that must be met in order to test the differences between means 7.7

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