Box-Cox Transformation

The Box-Cox transformation is one of the possibel ways to solve the problem of data that don't obey the assumptions of variance analysis, as data normality.

Example:  For specific analysis it is necessary for the data to follow a normal distribution. One study found that the following 11 measures of pieces weights (in pounds), do not follow this distribution. Thus, it is necessary to use some transformation to solve this problem. The obtained data are presented in the following

^{click here to download the data}

To use the tool Box-Cox Transformation the user must follow these steps:

1. Access the menu:

Action → Basic Statistics → Box-Cox Transformation 

2. The following window will appear;

3. With the cursor in the field Data Set select the column (table or row, without selecting the variable name, if there is one) that contains the data, which must be numeric. Use the mouse to select;

4. In the boared Show Results, we have to select between Current Cell or New Sheet. We suggest the option New Sheet, because Action does not have the undo command;

REMARK: When choosing the option Current Cell, the results will be printed from the cell where the cursor is. In this case, the user must put the cursor in an appropriate position previously (before step 1);

5. To finish, click Ok.

Results and Interpretation

Once the process is finished, the following results will be shown:

The graphic shows that the maximum value of the function is about λ = 2.5.

Once you know the value of λ, the next step is to obtain the transformed data and then redo the analysis using the new data. The relationship between the transformed data and the original ones Y is expressed by the equation .