Help Manual

Contents






Sigma Magic Help Version 17

Probability Calculations

Overview

The Probability calculations worksheet can be used to determine the probability and inverse probability values for a given distribution. For example, if you want to calculate the Sigma level manually or if you want to perform some calculations that are not available in Sigma Magic, then you can use this worksheet

This tool can be added to your active workbook by clicking on Stats and then selecting Distribution > Probability Calculations.

Inputs

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

Setup

A sample screenshot of the setup menu is shown below.
inputs
1
Data Type: Specify the data type for this analysis. The available options are:
OptionDescription
DiscreteDiscrete data is like count data that has only a finite set of values (like the number of defects in a product example 20, 30, 43).
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example, 34.53 degrees centigrade).
2
Distribution Name: Specify the name of the distribution you want to use for this analysis. The available distributions shown in this dropdown box depend on the data type you selected in Step 3. The available options are:
OptionTypeParameters
BetaContinuousNu, Omega, Min, Max
CauchyContinuousLocation, Scale
Chi-SquaredContinuousDOF
ErlangContinuousScale, Shape
Extreme ValueContinuousLocation, Scale
ExponentialContinuousScale
FContinuousNu, Omega
GammaContinuousShape, Scale
LaplaceContinuousLocation, Scale
Log NormalContinuousMu, Sigma
LogisticContinuousLocation, Scale
Log LogisticContinuousAlpha, Beta
NormalContinuousMu, Sigma
ParetoContinuousLocation, Scale
PertContinuousMin, Max, Most Likely
PowerContinuousMax, Shape
RayleighContinuousScale
T DistributionContinuousDOF
TriangularContinuousMin, Max, Mode
UniformContinuousMin, Max
WeibullContinuousEta, Beta
BernoulliDiscreteProbability
BinomialDiscreteNum Trials, Probability
Discrete UniformDiscreteMin, Max
GeometricDiscreteProbability
Hyper GeometricDiscretePopulation Size, Num Success, Sample Size
Negative BinomialDiscreteXth Success, Probability
PoissonDiscreteLambda
3
Distribution Parameters: Specify the values for the distribution parameters. Note that some distributions may have only one parameter, some may have 2, some may have 3, etc.
4
Calculate: Specify the type of analysis you want to perform. The available options are:
OptionDescription
Probability at XCalculate probability at x = X
Probability to the left of XCalculate probability at x <= X
Probability to the right of XCalculate probability at x > X
Probability between X1 and X2Calculate probability for X1 < x <= X2
Probability P on the leftCalculate X such that Prob (x <= X) = P
Probability P on the rightCalculate X such that Prob (x > X) = P
Probability P on the insideCalculate X1 and X2 such that Prob (X1 < x <= X2) = P
Probability P on the outsideCalculate X1 and X2 such that Prob (x <= X1) + Prob (x > X2) = P
5
Help Button: Click on this button to open the help file for this topic.
6
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
7
OK Button: Click on this button to save all changes and compute the outputs for this analysis.
The software will open a real-time viewer window if you click the Real-Time Viewer button. An example screenshot of the viewer is shown in the figure below. inputs
1
Distribution Details: Ensure that you are viewing the right distribution here. It contains the name of the distribution and the distribution parameters.
2
Help Button: Open the help file for this topic.
3
X Axis Values: Specify the X Left and X Right values. These values will be updated on the chart. All data points that fall to the left to the X Left value and to the right of the X Right value will be highlighted in red, and the corresponding values will be shown both on the chart and the Probability Values textboxes.
4
Probability Values: Specify the P Left, Middle, and P Right values. The software will determine the corresponding X Left and X Right values based on this data, and all data points that fall to the left to the X Left value and the right of the X Right value will be highlighted in red.
5
Fit Percent: Shows the value of the percentage of the graph that falls in each region.
6
Basic Statistics: Shows the basic descriptive statistics for the selected distribution.
7
PDF: Shows the probability density function for the given distribution.
8
OK Button: Click on the OK or Cancel Button to close this dialog box. No changes made in the dialog box are saved, and the real-time viewer has updated no charts on the worksheet.

Charts

You will see the following dialog box if you click the Charts button. Charts
1
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.
2
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.
4
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 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 optional.
6
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.
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.
8
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, and finally, any checks that are required to be performed by the user are shown as blue info icons.
1
Item: The left-hand side shows the major tabs and the items checked within each section
2
Status: The right-hand side shows the status of the checks.
3
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 The probability or the X values are displayed in the output text box and the Conclusion box.

Notes

Here are a few pointers regarding this analysis:
  • Note that for a continuous distribution, the probability at X is the value of the probability density function and not the probability at a given value, which is always 0 for a continuous case.
  • You can control the number of decimal places of the display result in the Options menu.

Examples

The following examples are in the Examples folder.
  • Determine the probability to the right of X = 30 for a normally distributed data with Mean = 25 and Stdev = 2.


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