Analysis of an Experiment with Three-Level Factors - Box-Cox Tab

Analyzing the 3(k-p) Design

Select the Box-Cox tab in the Analysis of an Experiment with Three-Level Factors dialog to access the options described here.

Box-Cox transformation
Use the options in the Box-Cox transformation group box to produce a diagnostic graph and spreadsheet for estimating Lambda for a Box-Cox transformation. Note that these results are for the currently specified model. You can specify a new model on the Model tab.
Box-Cox Transformation
Click this button to produce a diagnostic graph with accompanying spreadsheets for estimating Lambda for the Box-Cox transformation of the Dependent Variable.

The Box-Cox transformation graph shows the Residual sum of squares, given the model, as a function of different computed estimates of Lambda, and shows the maximum likelihood estimate of Lambda, which is the estimated value of Lambda for which the Residual sum of squares is a minimum.

The accompanying Box-Cox transformation spreadsheet lists the Observed values and Residuals for the dependent variable, and corresponding Transformed observed values and Transformed residuals, using the Box-Cox transformation with the maximum likelihood estimate of Lambda.

The Final statistics spreadsheet lists the maximum likelihood estimate of Lambda, the SSE(1), the maximum likelihood Chi-square(1), and its associated probability, p. The SSE(1) is the Residual sum of squares, given the model and using a single parameter, Lambda, to transform the dependent variable, and the Chi-square(1) is the appropriate statistic for testing the reduction in the Residual sum of squares produced by the Box-Cox transformation with the maximum likelihood Residual statistics estimate of Lambda (see Maddala, 1977). Several options are available on this tab for specifying the search for the maximum likelihood estimate of Lambda.

Max. iterations.
The value in the Max. iterations box specifies a limit for the number of iterations in the search. Typically, the search will converge in a few dozen iterations.
Min./Max. lambda.
lambda. The values in the Min. lambda and Max. lambda boxes specify the range of values from which to search for the maximum likelihood estimate of Lambda. The default values are -2 and +2, respectively.
Delta (converg)
The value in the Delta (converg.) box specifies the target difference in successive estimates of Lambda that will terminate the search. The default value is .00001.

For additional information regarding the power family of transformations, see Box and Cox (1964), Box and Draper (1987), and Maddala (1977). See also the Special Topic in Experimental Design - Box-Cox Transformations of Dependent Variables.

Note: in addition to the Box-Cox transformation based on the maximum likelihood estimate of Lambda available from this tab, Statistica also contains the related Statistica Visual Basic programs Boxcox.svb, Boxcoxp.svb, and Boxtid.svb. These programs provide additional methods for selecting transformation of the variables in an ANOVA. For descriptions of these programs, see Notes and Technical Information: Box-Cox Plots for Selecting Transformations.