Help Manual

Contents






Sigma Magic Help Version 17

Transform Data

Overview

Transform Data can be used to transform 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 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.
Transform Input Dialog Box
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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 failing to achieve the customer/client CTQ. Depending on the product we are working with, a product may have N defects.
DefectivesDefective means the failure 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.
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Algorithm: Specify the algorithm to use to transform the data to normal. The available options are:
OptionDescription
Box-CoxCan be performed for continuous data. It 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: unbounded data, bounded data, and partially bounded data.
Freeman-TukeyCan be used for discrete data (both defects and defectives).
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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 lambda value that it should use for the analysis. For the Johnson transformation, determine how the software should determine the type of distribution. It can estimate this value from your data set, or you can type the distribution name (Su, Sl, and Sb).
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Help Button: Click on this button to open the help file for this topic.
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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, enter the data you want to transform into the data column. If the data is discrete, only the data column is required for discrete defect transformation. For Discrete-Defectives, both the subgroup size and data columns are needed. After the transformation, the transformed data is stored in the Trans—data column.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. Data
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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 speed up finding the right data 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.
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Available Data: The available data box contains the list of data available for analysis. If your workbook has no 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 crucial that you not only specify the column name but also the table name.
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Add or View Data: Click on this button to add more data to 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 the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
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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, you must select only numeric columns. If the code begins with a T, you can select 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, you must select a minimum of 2 columns of data and a maximum of 4 columns 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 choose 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 choose the data is to double-click on the columns in the list of Available Data. Finally, you can 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.
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Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in 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 in the Setup tab.
CaseDescription
1If your data type is Continuous, then you can specify the 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.
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View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

Charts

You will see the following dialog box if you click the Charts button. Charts
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Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
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Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
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X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
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Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
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X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is currently disabled, and you cannot change this setting.
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Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10, and the maximum y-axis is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
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Horizontal Lines: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
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Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. Verify The software checks 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, they are shown as green checkmarks. If the verification checks fail, they are shown as a red cross. If the verification checks result in a warning, they are shown in the orange exclamation mark, and finally, any checks that are required to be performed by the user are shown as blue info icons.
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Item: The left-hand side shows the major tabs and the items checked within each section
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Status: The right-hand side shows the status of the checks.
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Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

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

Reference

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

Lambda Transformation
-1 Reciprocal
0 Logarithmic
0.5 Square root
1 No Transformation
2 Square
Three different types of transformation are applied to the data for the Johnson transformation. The following table illustrates the distributions available under Johnson's 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 not always successful in transforming non-normal data into 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; in some cases, the Johnson transformation may not successfully transform 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

The following examples are in the Examples folder.
  • Transform the data set given in the file to a normal distribution (Non-Normal Data 1.xlsx).



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