Chapter 12 - Analysis of variance. Learning objectives of this chapter include: List the characteristics of the F distribution, conduct a test of hypothesis to determine whether the variances of two populations are equal, discuss the general idea of analysis of variance, organize data into a one-way and a two-way ANOVA table, conduct a test of hypothesis among three or more treatment means. | Analysis of Variance Chapter 12 McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. We continue our discussion of hypothesis testing in this chapter. Recall that in chapters 10 and 11, we examined the general theory of hypothesis testing. In chapter 11, we learned the different procedures for testing one population parameter, and in chapter 12 we learned how to compare two population parameters. In this chapter, we will learn a procedure for comparing the means of three or more populations using the F distribution. Additionally, we will learn the other major uses of the F distribution. Learning Objectives LO 12-1 List the characteristics of the F distribution and locate values in an F table. LO 12-2 Perform a test of hypothesis to determine whether the variances of two populations are equal. LO 12-3 Describe the ANOVA approach for testing differences in sample means. LO 12-4 Organize data into appropriate ANOVA tables for analysis. LO 12-5 Conduct a test of hypothesis among three or more treatment means and describe the results. LO 12-6 Develop confidence intervals for the difference in treatment means and interpret the results. 12- The F Distribution Uses of the F distribution test whether two samples are from populations having equal variances. to compare several population means simultaneously. The simultaneous comparison of several population means is called analysis of variance (ANOVA). Assumption: In both of the uses above, the populations must follow a normal distribution, and the data must be at least interval-scale. Characteristics of the F distribution There is a “family” of F Distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator. The F distribution is continuous. F cannot be negative. The F distribution is positively skewed. It is asymptotic. As F the curve approaches the X-axis but never | Analysis of Variance Chapter 12 McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. We continue our discussion of hypothesis testing in this chapter. Recall that in chapters 10 and 11, we examined the general theory of hypothesis testing. In chapter 11, we learned the different procedures for testing one population parameter, and in chapter 12 we learned how to compare two population parameters. In this chapter, we will learn a procedure for comparing the means of three or more populations using the F distribution. Additionally, we will learn the other major uses of the F distribution. Learning Objectives LO 12-1 List the characteristics of the F distribution and locate values in an F table. LO 12-2 Perform a test of hypothesis to determine whether the variances of two populations are equal. LO 12-3 Describe the ANOVA approach for testing differences in sample means. LO 12-4 Organize data into appropriate ANOVA tables for analysis. LO 12-5 .
