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Contents






Sigma Magic Help Version 17

Normality Analysis

Overview

Normality Analysis can be used to determine if the input data is normal. It analyzes the Anderson-Darling statistic to determine if the data is normal.

This template can be added to your active workbook by clicking on Stats and then selecting Normality > Normality Analysis.

Inputs

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

Setup

A sample screenshot of the setup menu is shown below.
inputs
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Selected Test: Specify the methodology to use to check if the data is normal. The following options are available:
OptionDescription
Anderson-DarlingIs much more sensitive to the tails of the distribution. Critical values use information about the distribution. This is the default method for checking normality.
Kolmogorov-SmirnovIs much more sensitive to the center of the distribution. Critical values are independent of the distribution.
Shapiro-WilkUses the W statistic to test whether the distribution is normal. This test has done well compared to other methods.
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Confidence Level: Specify the level of confidence (1 - alpha) for this test. The default value is 95%.
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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.

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 the search for 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 up the Data Editor dialog box, where you can import more data into your workbook or 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.
OptionDescription
1If you want to analyze a single column of data, you can specify that column under Analysis Variables and leave the Grouping Variable blank.
2If you want to analyze multiple columns of data, you can specify the multiple columns under Analysis Variables and leave the Grouping Variable blank.
3If you are working with grouped data, then you enter the variable data under the Analysis Variables and the column that contains grouping information under Grouping Variables. Note that you can have up to two grouping variables.
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View Selection: Click on this button to view the data 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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Pick Charts: Select the charts you would like to display for this analysis.
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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 specify 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 optional.
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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 specify 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-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. 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 results on the worksheet. A sample screenshot of the worksheet is shown below. outputs The Normality analysis will output the Anderson-Darling statistic and the P-value if you have selected the AD test; otherwise, it will output the Kolmogorov-Smirnov statistic and the associated P-value(s). A normal probability plot of the data is plotted along with the confidence intervals. Finally, a histogram of the data and the normal fit curve are also displayed. If the P-value of the Normality test is less than the alpha, we conclude that the data is NOT normal. Otherwise, the data is normal. You can also view the figure to determine if the data points are sufficiently close to the normal line (shown in red) and within the confidence level bounds.

Notes

Here are a few pointers regarding this analysis:
  • Sigma Magic computes the Anderson-Darling estimate (AD) based on the data you enter as the default. This value is then converted to a P-value. If the P-value is less than alpha, then the data is reported as being not normal. You can change the alpha value in the Options menu. The default value of alpha is 0.05.
  • The Rough guideline is that we need at least 30 data points to get a good idea of whether the data is normally distributed.
  • If you have too many data points, the tests become very sensitive for minor departures from normality. Hence, even though the data may be considered normally distributed for all practical purposes, the P-value may show that the data is not normal.
  • Note that for the Shapiro-Wilk test, you need to have greater than 3 data points and less than 5000 data points.

Examples

The following examples are in the Examples folder.
  • For the data in the file, determine if the data set is normal (Normality 1.xlsx).


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