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© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 4/14/2014, Spring 2014 Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 8: Analysis of Variance 1

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© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved Understand the logic of analysis of variance Understand and calculate the sum of squares Understand and calculate the mean square Understand and calculate the F ratio Conduct a multiple comparison of means to determine where a significant difference lies CHAPTER OBJECTIVES Understand the requirements for using the F ratio

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Understand the logic of analysis of variance Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.1

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Comparing More than Two Groups 8.1 Multiple t Ratios Analysis of Variance vs. Combing t ratios increases the chance of making a Type I error A single overall decision as to whether a significant difference exists

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The Logic of Analysis of Variance 8.1

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Figure 8.1

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8.1 Figure 8.2

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The Logic of Analysis of Variance 8.1

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Understand and calculate the sum of squares Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.2

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10 The sum of squared deviations from the mean Total sum of squares Between-group sum of squares Within-group sum of squares The Sum of Squares Definitional FormulasComputational Formulas

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Understand and calculate the mean square Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.3

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12 The value of the sum of squares grows as variation and sample size increase The mean square (or variance) controls for these influences The Mean Square

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Understand and calculate the F ratio Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.4

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14 A comparison of the variation between groups and variation within groups It must be evaluated for significance – The larger the F ratio, the more likely it is to be statistically significant – Interpret the F ratio with Table D in Appendix C (pages ) The F ratio

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8.4 Table 8.4

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Conduct a multiple comparison of means to determine where a significant difference lies Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.5

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17 A significant F ratio does not tell us where the difference lies We can use Tukey’s Honesty Significant Difference (HSD) to determine this Allows for a comparison of any two means against HSD Takes into account Type I error A Multiple Comparison of Means A set of several t-test are also acceptable but take more time Now just compare the values of the difference between each pair of means and HSD. A difference is significant if it is greater than the HSD (Page 556)

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Understand the requirements for using the F ratio Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 8.6

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Requirements for Using the F Ratio 8.6 A Comparison between Three or More Independent Means Interval Data Random Sampling A Normal Distribution Equal Variances

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Example 20 Problem Problem 37

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Homework 21 Chapter 8 Problems: 28 and Also Chapter 7 Problem 42

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Exam #2 22 Confidence Intervals Hypothesis Testing (two-sided only) ANOVA I’ll give you some statistics

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© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved Analysis of variance examines the variance between and within groups to determine if a significant difference exists The sum of squares examines the total deviation, the between- group deviation and the within-group deviation The mean square controls for the increase in the sum of squares that naturally occurs as variation and sample size increase The F ratio compares variation between groups and variation within groups CHAPTER SUMMARY Tukey’s HSD is used to determine where a significant difference lies once a significant F ratio has been found There are several requirements that must be met in order to conduct an analysis of variance test

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