[信息與通信]第六章英文-簡(jiǎn)化版-方差分析參考資料-ch10-designofexperimentsandanalysis-資料下載頁(yè)
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【正文】 Types of Regression ModelsExperimentalDesignsOneWay AnovaCompletely RandomizedRandomized BlockTwoWay AnovaFactorial 10 59169。 2022 Pearson Prentice HallFactorial Design1. Experimental Units (Subjects) Are Assigned Randomly to Treatmentsn Subjects are Assumed Homogeneous2. Two or More Factors or Independent Variablesn Each Has 2 or More Treatments (Levels)3. Analyzed by TwoWay ANOVA10 60169。 2022 Pearson Prentice HallFactorial Design Example TreatmentFactor 2 (Training Method)FactorLevelsLevel 1 Level 2 Level 3Level 1 19 hr.? 20 hr.? 22 hr.?Factor 1 (High) 11 hr.? 17 hr.? 31 hr.?(Motivation)Level 2 27 hr.? 25 hr.? 31 hr.?(Low) 29 hr.? 30 hr.? 49 hr.?10 61169。 2022 Pearson Prentice HallAdvantages of Factorial Designs1. Saves Time amp。 Effortn ., Could Use Separate Completely Randomized Designs for Each Variable2. Controls Confounding Effects by Putting Other Variables into Model3. Can Explore Interaction Between Variables10 62169。 2022 Pearson Prentice HallTwoWay ANOVA10 63169。 2022 Pearson Prentice HallTypes of Regression ModelsExperimentalDesignsOneWay AnovaCompletely RandomizedRandomized BlockTwoWay AnovaFactorial 10 64169。 2022 Pearson Prentice HallTwoWay ANOVA1. Tests the Equality of 2 or More Population Means When Several Independent Variables Are Used2. Same Results as Separate OneWay ANOVA on Each Variablen But Interaction Can Be Tested3. Used to Analyze Factorial Designs 10 65169。 2022 Pearson Prentice HallTwoWay ANOVA Assumptions1. Normalityn Populations are Normally Distributed2. Homogeneity of Variancen Populations have Equal Variances3. Independence of Errorsn Independent Random Samples are Drawn10 66169。 2022 Pearson Prentice HallTwoWay ANOVA Data TableXijkLevel i Factor ALevel j Factor BObservation kFactor Factor BA 1 2 ... b1 X111 X121 ... X1b1X112 X122 ... X1b22 X211 X221 ... X2b1X212 X222 ... X2b2: : : : :a Xa11 Xa21 ... Xab1Xa12 Xa22 ... Xab210 67169。 2022 Pearson Prentice HallTwoWay ANOVA Null Hypotheses1. No Difference in Means Due to Factor An H0: ?1.. = ?2.. =... = ?a..2. No Difference in Means Due to Factor Bn H0: ?.1. = ?.2. =... = ?.b.3. No Interaction of Factors A amp。 Bn H0: ABij = 010 68169。 2022 Pearson Prentice HallTotal VariationTwoWay ANOVA Total Variation Partitioning Variation Due to Treatment AVariation Due to Random SamplingVariation Due to InteractionSSESSASS(AB)SS(Total)Variation Due to Treatment BSSB10 69169。 2022 Pearson Prentice HallSource ofVariationDegrees ofFreedomSum ofSquaresMeanSquareFA(Row)a 1 SS(A) MS(A) MS(A)MSEB(Column)b 1 SS(B) MS(B) MS(B)MSEAB(Interaction)(a1)(b1) SS(AB) MS(AB) MS(AB)MSEError n ab SSE MSETotal n 1 SS(Total)TwoWay ANOVA Summary TableSame as Other Designs10 70169。 2022 Pearson Prentice HallInteraction1. Occurs When Effects of One Factor Vary According to Levels of Other Factor2. When Significant, Interpretation of Main Effects (A amp。 B) Is Complicated3. Can Be Detectedn In Data Table, Pattern of Cell Means in One Row Differs From Another Rown In Graph of Cell Means, Lines Cross10 71169。 2022 Pearson Prentice HallGraphs of InteractionEffects of Motivation (High or Low) amp。 Training Method (A, B, C) on Mean Learning TimeInteraction No InteractionAverageResponseA B CHighLowAverageResponseA B CHighLow10 72169。 2022 Pearson Prentice HallExercise 10 73169。 2022 Pearson Prentice HallConclusion1. Described Analysis of Variance (ANOVA)2. Explained the Rationale of ANOVA3. Compared Experimental Designs4. Tested the Equality of 2 or More Meansn Completely Randomized Designn Factorial Desig
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