CHAPTER12AnalysisofVarianceTests.ppt

CHAPTER 12Analysis of Variance Tests to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel ? 2002 The Wadsworth Group Chapter 12 - Learning Objectives Describe the relationship between analysis of variance, the design of experiments, and the types of applications to which the experiments are applied. Differentiate one-way, randomized block, and two-way analysis of variance techniques. Arrange data into a format that facilitates their analysis by the appropriate analysis of variance technique. Use the appropriate methods in testing hypotheses relative to the experimental data. Chapter 12 - Key Terms Factor level, treatment, block, interaction Within-group variation Between-group variation Completely randomized design Randomized block design Two-way analysis of variance, factorial experiment Sum of squares: Treatment Error Block Interaction Total Chapter 12 - Key Concepts Differences in outcomes on a dependent variable may be explained to some degree by differences in the independent variables. Variation between treatment groups captures the effect of the treatment. Variation within treatment groups represents random error not explained by the experimental treatments. One-Way ANOVA Purpose: Examines two or more levels of an independent variable to determine if their population means could be equal. Hypotheses: H0: μ1 = μ2 = ... = μt * H1: At least one of the treatment group means differs from the rest. OR At least two of the population means are not equal. * where t = number of treatment groups or levels One-Way ANOVA, cont. Format for data: Data appear in separate columns or rows, organized as treatment groups. Sample size of each group may differ. Calculations: SST = SSTR + SSE (definitions follow) Sum of squares total (SST) = sum of squared differences between each individual data value (regardless of group membership) minus the grand mean,