[第六章.英文-简化版.-方差分析参考资料-ch10-DesignofExperimentsandAnalysis.ppt

Chapter 10 Design of Experiments and Analysis of Variance One-Way ANOVA F-Test Types of Regression Models One-Way ANOVA F-Test 1. Tests the Equality of 2 or More (p) Population Means 2. Variables One Nominal Scaled Independent Variable 2 or More (p) Treatment Levels or Classifications One Interval or Ratio Scaled Dependent Variable 3. Used to Analyze Completely Randomized Experimental Designs One-Way ANOVA F-Test Assumptions 1. Randomness Independence of Errors Independent Random Samples are Drawn for each condition 2. Normality Populations (for each condition) are Normally Distributed 3. Homogeneity of Variance Populations (for each condition) have Equal Variances One-Way ANOVA F-Test Hypotheses H0: ?1 = ?2 = ?3 = ... = ?p All Population Means are Equal No Treatment Effect Ha: Not All ?j Are Equal At Least 1 Pop. Mean is Different Treatment Effect NOT ?1 ? ?2 ? ... ? ?p One-Way ANOVA F-Test Hypotheses H0: ?1 = ?2 = ?3 = ... = ?p All Population Means are Equal No Treatment Effect Ha: Not All ?j Are Equal At Least 1 Pop. Mean is Different Treatment Effect NOT ?1 ? ?2 ? ... ? ?p Why Variances? Two PossibleExperiment Outcomes Same treatment variation Different random variation Two More PossibleExperiment Outcomes Same treatment variation Different random variation One-Way ANOVA Basic Idea 1. Compares 2 Types of Variation to Test Equality of Means 2. Comparison Basis Is Ratio of Variances 3. If Treatment Variation Is Significantly Greater Than Random Variation then Means Are Not Equal 4. Variation Measures Are Obtained by ‘Partitioning’ Total Variation One-Way ANOVA Partitions Total Variation One-Way ANOVA Partitions Total Variation One-Way ANOVA Partitions Total Variation One-Way ANOVA Partitions Total Variation One-Way ANOVA Partitions Total Variation Sum of Squares Among Sum of Squares Between Sum of Squares Treatment Among Groups Variation One-Way ANOVA Partitions Total Variation Sum of Squares Within Sum of Squares Error (SSE) Within Groups Variation