Box-Cox Transformation for ANOVA Model

Toxic Agents Example

Minitab homepage offers a macro that execute Box-Cox transformation in regression. It finds the MLE of λ on maximizing the log-likelihood of the joint distribution of the responses under such regression model. It's equivalent to minimizing the residual sum of squares as does the classnotes' procedure. The code can be found in http://support.minitab.com/en-us/minitab/17/macro-library/macro-files/quality-control-and-doe-macros/box-cox-transformation-for-regression-and-response-surface-models (with download instruction on the link). You can go on the MINITAB Homepage and click on Support and pull down to select Macro Library to go to the abovementioned page.
Now click ANOVA & Regression and select item 3 (Box-Cox ...). Then click code for download and click Documentation for a brief documentation.

Setup

The macro can be used for ANOVA context. We only need to create indicator variables for each factor involved.

Make Indicator Variables

Do CalcMake Indicator Variables. For factor poison:

(poisons08.png here)
Note that, for a factor of k levels, MINITAB requires k output columns. However, only k−1 indicator variables will be used. Here we will use C4 and C5 (named poison1 and poison2, respectively) and allow C6 be recycled for the indicator variables of factor treat:
(poisons09.png here)
Since factor treat has four levels, only indicator variables C6, C7, and C8 (named treatA, treatB, and treatC, respectively) will be used in regression. These indicator variables (C4 to C8) constitute the 5 = 2 + 3 degrees of freedom of the main effects. The following gives a (portion of) screeshot of the the worksheet:
(poisons10.png here)

Submit Macro Call

Do EditCommand Line Editor (or use Ctrl-L keyboard shortcut):
(poisons11.png here)

Session Output

Macro is running ... please wait
Box-Cox Power Transformation Analysis

Model Information
------------------------------
Response:       time

Predictor(s):   poison1 , poison2 , treatA , treatB , treatC
------------------------------

Estimated Lambda: -0.75

Approximate 95% CI for Lambda: (-1.13 , -0.36)

Box-Cox Power Transformation Analysis

(poisons12.png here)

It yielded the same λ as in the classnotes with comparable 95% confidence interval.