XLSTAT: Running a Johnson Transformation

Many statistical methods assume that either the original data or some outputs are normally distributed. While some phenomena naturally follow a normal distribution, most of the time this is not the case.

This can become a real problem if a decision based on statistical information is of high impact. In such cases, a transformation is required. In this example, we will use the Johnson transformation.

 

Dataset for Example

The (attached) dataset contains the measurements of waste in production for 47 batches.

We would like to perform a regression with several process variables, but the hypothesis of Normality of the variable Level of waste is violated.

This can be verified using the Normality test and the Histogram XLSTAT functions. The results are displayed below.

We need to make a transformation of this variable before attempting a linear regression.

 

Setting Up

• Open XLSTAT.

• Click on the Preparing data menu and select the Variables transformation feature.

In the General tab:

• Select the variables you wish to transform in the Data field. In this example, we select the variable Level of waste in column B.

• Click on Other .

• Select the option Johnson transformation.

• Set the alpha equal to 0.05 and select the Shapiro-Wilk test.

• Select the Shapiro-Wilk test. (N.B.: While the authors use the Shapiro-Wilk test to assess the normality, XLSTAT allows you to use this same test or the Anderson-Darling test.)

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

In the result sheet called Variables transformation , you will find the Transformed data table and the formula used to transform this variable.

Let's check now the Normality tests and the histograms on the transformed data.

The p-value of all four normality tests are higher than 0.05 thus we cannot reject the null hypothesis that the variable from which the sample was extracted follows a Normal distribution.

The histogram also indicates that the transformed variable Level of waste follows a Normal distribution.