Help Manual

Contents






Sigma Magic Help Version 17

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 are plotted on the X axis and the quantiles of the specified distribution are 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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Confidence Interval: Specify if you want to overlay the confidence intervals on the probability plot. The following options are available. Note that this option only applies to the probability plot, not the P-P or Q-Q plots.
OptionDescription
NoneNo confidence interval is superimposed on the probability plot.
PointwiseA pointwise confidence interval is superimposed on the probability plot. Note that these confidence intervals are calculated for individual percentiles and should be used with caution - they should not be used to assess the distribution as a whole.
BootsrapBootstrapping approach is used to superimpose the confidence interval on the probability plot. These confidence intervals are estimated by performing a Monte Carlo simulation of 1000 data sets, and the variation is used to estimate the confidence intervals.
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Confidence Level: Specify the confidence level to use for the confidence interval plot. The default value is 95%. However, you can pick any value between 0 and 100%.
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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: If possible, click this button to save any changes and compute the analysis outputs.

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.
6a
Analysis Variables: This list box contains the data used to create the probability plot. This list box is mandatory; at least one column must be specified. Note that the values specified in this column must be numeric. If multiple columns are specified, the probability plot is created using the data in each column.
6b
Categorical Variables: This list box contains the categories to use to create the probability plot. It is not mandatory and can contain either numeric or text data. Note that we can specify up to two categories. Suppose data has been selected for this list box. In that case, the groups specified here are used to split the analysis variables into multiple data sets, and a probability plot is created for each group. All the groups identified here will be plotted on the same chart.
6c
By Variable: This list box contains the categories to use to create the probability plot. It is not mandatory and can contain either numeric or text data. Note that we can specify up to one column here. Suppose data has been selected for this list box. In that case, the groups specified here are used to split the analysis variables into multiple data sets, and a probability plot is created for each group. All the groups identified here will be plotted on separate charts.
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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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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.
3
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.
5
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 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 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, the y-axis increment is set at 2. Note that this input is currently disabled, and you cannot change this setting.
7
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 a green checkmark. 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. 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 OK to perform the calculations. outputs
>
Notes: The notes section summarizes the inputs - specifically the number of data points, distinct groups, and the fit. The analysis results contain the group's name and the distribution's fit.
>
Graphs: The graph section contains the probability plot, a 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, 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 and P-P plots, the straight line is a 45-degree line passing through the origin. In the example above, the data points are far 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 - a fat pencil test to determine if the data points are close enough to the straight line.

Examples

The following examples are in the Examples folder.
  • Determine if the data in the following file follows a log-normal distribution (Probability Plot 1.xlsx).



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