# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 15

# Transform Data

## Overview

Transform Data can be used to transform the data from a non-normal distribution to a normal distribution. For continuous data, two types of transformations can be used to transform the data into normal - Box-Cox transformation and Johnson Transformation. For discrete data, the software performs a Freeman-Tukey transformation. This transformation can be applied to both defects (Poisson distribution) and defectives (Binomial distribution).

This tool can be added to your active workbook by clicking on Stats and then selecting Normality > Transform Data.

## Inputs

Click on Analysis Setup to open the menu options for this tool.

### Setup

A sample screenshot of the setup menu is shown below.
1
Data Type: Specify the type of data for this analysis. The available options are:
OptionDescription
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example 34.53 deg centigrade).
DefectsDefect refers to failing to meet what the customer/client wants or fails to achieve the customer/client CTQ. Depending on the product we are working with, a product may have N number of defects.
DefectivesDefective means the failing of the entire product/service to meet the required criterion. A defective product may have one or more defects but not all defects make a product defective. A product or service can either be defective or not-defective.
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Input Type: Specify the format for input data. This selection is not enabled since there is only one format available.
3
Algorithm: Specify the algorithm to use to transform the data to normal. The available options are:
OptionDescription
Box-CoxCan be performed for continuous data. Uses a parameter lambda to transform the inputs into outputs. For example, the input values are raised to the power of lambda to get the output values.
JohnsonUses a complex transformation function to transform the inputs into outputs. There are three types of transformation functions for unbounded data, bounded data, and partially bounded data.
Freeman-TukeyCan be used for discrete data (both defects and defectives).
4
Parameter Value: For the Box-Cox transformation, determine how the software should determine the value of the transformation parameter (lambda). It can either estimate this value from your data set or you can type a value of lambda that it should use for the analysis. For the Johnson transformation, determine how the software should determine the type of distribution. It can either estimate this value from your data set or you can type the name of the distribution (Su, Sl, and Sb).
5
View Data: Click on this button to view the data you have selected for this analysis. You can view both the raw data as well as a graphical summary of the data.
6
Help Button: Click on this button to open the help file for this topic.
7
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
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OK Button: Click on this button to save all changes and compute the outputs for this analysis.
If your data is continuous, then enter the data for which you want to transform into the data column. If the data is discrete, then for Discrete - Defects transformation only the data column is required. For Discrete - Defectives, both the subgroup size and data columns are required. After the transformation, the transformed data is stored in the Trans. Data column.

### Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis.
1
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
2
Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
3
Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
4
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
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Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6
Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.

The data you specify for this analysis depends on the options you have specified in the Setup tab.
CaseDescription
1If your data type is Continuous, then you can specify that column that you want to transform under Analysis Variable. The Subgroup Size variable is disabled.
2If your data type is Defects, then you can specify the column that contains defects data under Analysis Variable. The Subgroup Size variable is disabled.
3If your data type is Defectives, then you would need to specify the data column that contains the defectives under Analysis Variable and the data column that contains the number of data points within each subgroup under Subgroup Size.
7
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

### Charts

If you click on the Charts button, you will see the following dialog box.

### Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

## Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The transformed data is stored in the worksheet along with a P-value for the transformed data set. If the P-value is more than alpha (default: 0.05) then the transformed data is normal.

### Reference

For the Box-Cox transformation, the values of lambda indicate the type of transformation applied to the data. The following table illustrates the type of transformation for specific values of lambda.

Lambda Transformation
-1 Reciprocal
0 Logarithmic
0.5 Square root
1 No Transformation
2 Square
For the Johnson transformation, there are three different types of transformation applied to the data. The following table illustrates the distributions available under Johnson transformation.
Distribution Transformation
Su Unbounded Transformation
Sl Logarithmic
Sb Bounded Transformation

## Notes

Here are a few pointers regarding this analysis:
• The Box-Cox transformation is always not successful in transforming a non-normal data to a normal data set. You would need to use a different transformation. The Johnson transformation is more successful in transforming the data to a normal distribution. However, this transformation is more complex and in some cases, the Johnson transformation may also not be successful in transforming the data to a normal distribution.
• The parameters for the Johnson distribution are estimated based on the method of Percentiles as proposed by Slifker and Shapiro.

## Examples

Following examples can be found in the Examples folder.
• Transform the data set given in the file to a normal distribution (Non Normal Data 1.xlsm).