Help Manual

Contents






Sigma Magic Help Version 15

Probability Plot

Application

The Probability Plot worksheet can be used to determine if a data set follows a given distribution.

This tool can be added to your active workbook by clicking on Graph and then selecting Probability Plot.

Inputs

Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below. inputs
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Chart Type: Specify the type of probability plot to create. The available options are:
OptionDescription
Probability PlotCreate a probability plot with the data plotted on the X axis and the probability values on the Y axis. This is the default setting.
P-P PlotPlot the data using a probability-probability plot where the CDF of your data is plotted on the X axis and the CDF of the specified distribution is plotted on the Y axis.
Q-Q PlotPlot the data using a quantile-quantile plot where the quantiles of your data is plotted on the X axis and the quantiles of the specified distribution is plotted on the Y axis.
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Fit Distribution: Specify the distribution you want to use for the probability plot.
OptionDescription
Distribution NameFit the selected distribution to the histogram. The default is to fit a Normal distribution to the selected data.
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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 discard any changes and close the dialog box.
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OK Button: Click on this button to save any changes and compute the analysis outputs if possible.

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. 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 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.
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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.
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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.
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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, 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.
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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.
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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 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. Charts
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Title: The system will automatically pick a title for your chart. However, if you would like to override that with your own 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 would like to override that with your own subtitle you can 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 own 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 own 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 then 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 will not be able to 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 specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum y-axis scale is set at 10 and the maximum y-axis scale is set at 20. If you specify 10;2;20, then, the y-axis increment is set at 2. Note that this input is currently disabled and you will not be able to change this setting.
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Horizontal Lines: If you want to add a few extra horizontal reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
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Vertical Lines: If you want to add a few extra vertical reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5 then two vertical lines are plotted at X = 2 and X = 5 respectively. Note that this input is optional.

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. Verify 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 OK to perform the calculations. outputs
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Notes: The notes section contains the summary of the inputs - specifically the number of data points, number of distinct groups and the fit. The analysis results contain the name of the group and the fit of the distribution.
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Graphs: The graph section contains the probability plot, Quantile-Quantile plot, and a Probability-Probability plot. The straight line contains the best fit distribution. If the data points closely follow the straight line, then the data follows the given distribution. For the probability plot, the straight line is computed by joining the first and third quartiles and extending the straight line to either end. For the Q-Q plot and the P-P plot, the straight line is a 45-degree line passing through the origin. In the example given above, the data points are far away from the line, hence we would conclude that this data set does not fit the log-normal distribution.

Notes

Here are a few pointers regarding this analysis:
  • To determine if the data points are close to the line, we need to perform a visual test - perform a fat pencil test to determine if the data points are close enough to the straight line.

Examples

Following examples can be found in the Examples folder.
  • Determine if the data in the following file follows a log-normal distribution (Probability Plot 1.xlsm).