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Unformatted text preview: 1 MA 214: Applied Statistics Instructor : Remus Oşan Lecture 11 – July 15, 2010 Chapter 10: Analysis of Variance: Comparing More Than Two Means 10.3 Multiple Comparisons of Means 10.4 The Randomized Block Design 10.5 Factorial Experiments 2 Chapter 10: Analysis of Variance: Comparing More Than Two Means s 10.1 Elements of a Designed Experiment s 10.2 The Completely Randomized Design s 10.3 Multiple Comparisons of Means s 10.4 The Randomized Block Design s 10.5 Factorial Experiments s STATISTICS IN ACTION On the Trail of the Dogs: Do Dogs Travel at Random? 3 Chapter 10.3: Analysis of Variance The completely Randomized Design s Steps for Conducting an ANOVA for a Completely Randomized Design s 1. Make sure that the design is truly completely randomized, with independent random samples for each treatment. s 2. Check the assumptions of normality and equal variances. 4 Chapter 10.2: Analysis of Variance The completely Randomized Design s 3. Create an ANOVA summary table s Use a statistical software program s Or calculation formulas in Appendix B 5 Chapter 10.2: Analysis of Variance The completely Randomized Design s 4. If the Ftest leads to the conclusion that the means differ, s a. Conduct a multiplecomparisons procedure for as many of the pairs of meams as you wish to compare. (See 10.3.) s Use the results to summarize the statistically significant differences among the treatment means. s b. If desired, form confidence intervals for one or more individual treatment means 6 Chapter 10.2: Analysis of Variance The completely Randomized Design s 5. If the Ftest leads to the nonrejection of the null hypothesis that the treatment means are equal, consider the following possibilities: s a. The treatment means are equal; that is, the null hypothesis is true. s b. The treatment means really differ, but other important factors affecting the response are not accounted for by the completely randomized design. s Either increase the sample size for each treatment, or use a different experimental design 2 7 Chapter 10.2: Analysis of Variance The completely Randomized Design s Statistics in action: A OneWay Analysis of the Doggie Data s H : μ male = μ male = μ female = μ gravid = μ nymph s A MINITAB printout of the ANOVA s The pvalue of the test (highlighted on the printout) is 0 s At α = .05, we reject the null hypothesis and conclude that the mean deviation from the extract trail differs among the populations of adult male, adult female, gravid, and nymph dogs. 8 Chapter 10.2: Analysis of Variance The completely Randomized Design 9 Chapter 10.2: Analysis of Variance The completely Randomized Design 10 Chapter 10.2: Analysis of Variance The completely Randomized Design s Problems s 10.13 and 10.15 from page 499 s 10.21 and 10.23 from page 500 s 10.27, 10.29 and 10.31 from pages 501502 11 Chapter 10.3: Analysis of Variance Multiple Comparisons of Means s Assuming that the ANOVA test indicates that there is a significant difference between at least two means, usually...
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This note was uploaded on 08/09/2011 for the course STATISTICS  taught by Professor Montilla during the Spring '11 term at Universidad Iberoamericana.
 Spring '11
 Montilla
 Statistics, Variance

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