Analysis of Variance参考.ppt

Chapter 11Analysis of Variance Chapter Goals After completing this chapter, you should be able to: Recognize situations in which to use analysis of variance Understand different analysis of variance designs Perform a single-factor hypothesis test and interpret results Conduct and interpret post-analysis of variance pairwise comparisons procedures Set up and perform randomized blocks analysis Analyze two-factor analysis of variance test with replications results Chapter Overview General ANOVA Setting Investigator controls one or more independent variables Called factors (or treatment variables) Each factor contains two or more levels (or categories/classifications) Observe effects on dependent variable Response to levels of independent variable Experimental design: the plan used to test hypothesis One-Way Analysis of Variance Evaluate the difference among the means of three or more populations Examples: Accident rates for 1st, 2nd, and 3rd shift Expected mileage for five brands of tires Assumptions Populations are normally distributed Populations have equal variances Samples are randomly and independently drawn Completely Randomized Design Experimental units (subjects) are assigned randomly to treatments Only one factor or independent variable With two or more treatment levels Analyzed by One-factor analysis of variance (one-way ANOVA) Called a Balanced Design if all factor levels have equal sample size Hypotheses of One-Way ANOVA All population means are equal i.e., no treatment effect (no variation in means among groups) At least one population mean is different i.e., there is a treatment effect Does not mean that all population means are different (some pairs may be the same) One-Factor ANOVA One-Factor ANOVA Partitioning the Variation Total variation can be split into two parts: Partitioning the Variation Partition of Total Variation Commonly referred to as: Sum of Squares Within Sum of Squares Error Sum of Squares Unexplained