大三下资料 实验设计与方差分析 Final_summary

Summary of Chapter 6 11 Jingyuan Liu SOE and WISE Xiamen University DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 What have you learned in this course 1 Introduction to Design of Experiment DOE and Analysis of Variance ANOVA 2 Basic Statistical Methods 3 One way ANOVA 4 Multi factor ANOVA 5 Random and Mixed Eff ects Models 6 Regression Approach to ANOVA and ANCOVA 7 Introduction to DOE 8 Experiments with Blocking 9 Two level Factorial Designs 10 Two level Fractional Factorial Designs 11 Repeated Measures and Related DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 6 Regression Approach to ANOVA and ANCOVA Use regression approach to analyze ANOVA model yij i ij yij 1Iij1 a 1Iij a 1 ij Estimation of unknown parameters Regression ANOVA table ANCOVA with both factor and quantitative covariate yij i Xij X ij yij 1Iij1 a 1Iij a 1 Xij X ij Estimation of unknown parameters Fitted treatment regression lines Lack of fi t test for the treatment eff ects Test for the slope 1 parallel 2 zero DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 7 Introduction to Design of Experiment DOE DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 8 Experiments with Blocking Blocking Budget Block size How many block factors Randomized complete block design RCBD Each block with all treatments Analyzed with factorial ANOVA models with without replications Balanced incomplete block design BIBD Block size number of treatments Each block with only part of all treatments but they show up in a balanced manner every trt appears with every other trt the same number of times Only exist for certain combination of r nb rb npand n Analyzed using regression approach Latin square design Sudoku type Two block factors row and column Number of trts number of row blocks number of column blocks Each row and each column contains all treatments once the sparsest BIBD Analyzed using separate ANOVA model DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 9 Two level Factorial Designs Nothing more than the four essential questions 1 How to design the experiment Orthogonal coding fi rst design the main eff ect columns then interactions by multiplication 2 What eff ects can be estimated For 2kdesign we have 2k 1 factor eff ects to estimate 3 How to estimate these eff ects y y 4 Are these eff ects signifi cant ANOVA table t tests DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 10 Two level Fractional Factorial Designs General 2k pfractional factorial design N 2k pruns k p basic factors p generators How to design the experiment How to defi ne relation What are the aliases For each resolution R there is a minimum aberration design The best design is the minimum aberration with largest R Resolution III design Sparsest design only main eff ects are of interest For k factors only need N k 1 runs for N 2q 2k p design or N 4q Plackett Burman design 2kfull factorial design with blocking Generate the 2qblocks using q 2 level block factors Some higher interactions are sacrifi ced for blocking What can be estimated Analyses are identical with 2kfull factorial but with aliases DOE and ANOVA Summary of Chapter 6 11Summary of Chapter 6 11 Chapter 11 Repeated Measures and Related Repeatedly measure each subject Single factor with repeated measures Two factor with repeated measures on only one factor both factors Split plot designs Completely randomized split plot designs Randomized complete block split plot designs Three basic questions How to design