Special Topics - Residuals Analysis
Basic Idea
Extended residuals analysis is available in the Experimental Design module as an option when analyzing 2(k-p) (two-level factorial) designs, 2-level screening designs, 2(k-p) maximally unconfounded and minimum aberration designs, 3(k-p) and Box Behnken designs, Mixed 2 and 3 level designs, central composite designs, and mixture designs. The options and selections available from the Residual statistics dialog provide for extensive residuals analyses, allowing you to use a variety of diagnostic tools in inspecting different residual and predicted values, and thus to examine the adequacy of the prediction model, the need for transformations of the variables in the model, and the existence of outliers in the data.
Residuals are the deviations of the observed values on the dependent variable from the predicted values, given the current model. The ANOVA models used in analyzing responses on the dependent variable in the programs in the Experimental Design module listed above make certain assumptions about the distributions of residual (but not predicted) values on the dependent variable. These assumptions can be summarized by saying that the ANOVA model assumes normality, linearity, homoscedasticity, and independence of residuals. All of these properties of the residuals for a dependent variable can be inspected using the options and selections available from the Residual statistics dialog.
Further details on residuals analysis can be found in the descriptions of the specific options for the Residual statistics dialog. Descriptions of the procedures for examining residuals, and performing power transformations of the dependent variable when necessary, can be found in the Example: Residuals Analysis and the Example: Box-Cox Transformation of a Dependent Variable. See also the Special Topic in Experimental Design - Box-Cox Transformations of Dependent Variables.