[信息與通信]第六章英文-簡化版-方差分析參考資料-ch10-designofexperimentsandanalysis(參考版)
2025-01-22 09:40本頁面
【正文】 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 Design。 Training Method (A, B, C) on Mean Learning TimeInteraction No InteractionAverageResponseA B CHighLowAverageResponseA B CHighLow10 72169。 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 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。 Bn H0: ABij = 010 68169。 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 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 ANOVA10 63169。 2022 Pearson Prentice HallAdvantages of Factorial Designs1. Saves Time amp。 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 Experiments10 58169。 2022 Pearson Prentice HallF0 Randomized Block FTest SolutionH0: ?1 = ?2 = ?3= ?4Ha: Not All Equal? = .05?1 = 3 ?2 = 12 Critical Value(s):Test Statistic: Decision:Conclusion:Reject at ? = .05There Is Evidence Pop. Means Are Different? = .05F = 10 56169。52,000 B:51,000 A:43,000Car38,000 D:4 A:36,000 A:48,000 D:50,000Car48,000 A:2 B:38,000 D:42,000 C:RearCarFront LeftLocationBlock Left 19841994 T/Maker Co.10 54169。 2022 Pearson Prentice HallRandomized Block FTest Test Statistic1. Test Statisticn F = MST / MSEl MST Is Mean Square for Treatmentl MSE Is Mean Square for Error2. Degrees of Freedomn ?1 = p 1n ?2 = n – b – p +1l p = Treatments, b = Blocks, n = Total Sample Size10 53169。 2022 Pearson Prentice HallRandomized Block FTest HypothesesH0: ?1 = ?2 = ?3 = ... = ?pnAll Population Means are EqualnNo Treatment EffectHa: Not All ?j Are EqualnAt Least 1 Pop. Mean is DifferentnTreatment Effectn?1 ? ?2 ? ... ? ?p Is Wrong 10 50169。 2022 Pearson Prentice HallRandomized Block FTest1. Tests the Equality of 2 or More (p) Population Means2. Variablesn One Nominal Scaled Independent Variablel 2 or More (p) Treatment Levels or Classificationsn One Nominal Scaled Blocking Variablen One Interval or Ratio Scaled Dependent Variable3. Used with Randomized Block Designs 10 48169。3 B A D C . . .............Block1 A C D BBlockwithinrandomlyTreatmentsExperimentalD B,Levels: 2022 Pearson Prentice HallRandomized Block Design1. Experimental Units (Subjects) Are Assigned Randomly to Blocksn Blocks are Assumed Homogeneous2. One Factor or Independent Variable of Interestn 2 or More Treatment Levels or Classifications3. One Blocking Fact
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