6西格玛黑带培训-分析阶段.ppt

Analysis Of Covariance (Analyze Phase) Scope of Module Analysis Of Covariance Covariates Assumptions of ANACOVA Analysis Of Covariance Analysis Of Covariance (ANACOVA) is a technique that combines features of ANOVA and regression. It can be used for either observational studies or designed experiments. Covariates ANACOVA augments ANOVA (which deals only with factor effects) by allowing the inclusion of one or more additional quantitative variables that are related to the response. Each quantitative variable added to the ANOVA model is called a concomitant variable or covariate. A covariate should be observed before the study. If it is observed during the study, it should not be influenced by the other treatments in any way. Assumptions of ANACOVA Independence of Error Normality of Error Homoscedasticity of Error Example 1 A study was performed to determine if there is a difference in the strength of a monofilament fibre produced by 3 different machines. The data is in C1-C2 of Analysis of Covariance.MTW. Example 1 Stat ? ANOVA ? General Linear Model Example 1 Example 1 Session Window General Linear Model: Strength versus Machine Factor Type Levels Values Machine fixed 3 1 2 3 Analysis of Variance for Strength, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Machine 2 140.40 140.40 70.20 4.09 0.044 Error 12 206.00 206.00 17.17 Total 14 346.40 Example 1 Example 2 The engineer reckons that the fibre’s diameter may have a significant noise effect on the response. A correlation of the fibre’s diameter is made against strength. The fibre’s diameter can be found in C2 of the same file. Example 2 Stat ? Regression ? Fitted Line Example 2 Example 2 Example 3 The engineer decides to assess the results using ANACOVA, where Machine is a factor Diameter is a covariate Example 3 Stat ? ANOVA ? General Linear Model Example 3 Example 3 Session Window General Lin