# Probability Plot

## Summary

Provides a graphical and statistical (goodness-of-fit test) method for checking distribution assumptions when using various statistical tools. For example, many tools assume that the data are at least reasonably normal. A common way to check this assumption is to use the "fat pencil" test. The basis of this test is that if you laid a fat pencil over the plot, most of the plot points would be covered. If that is true, the distribution provides a reasonable fit for the data, which is usually all that is required.

• Does the chosen distribution model my data reasonably well?
When to Use Purpose
Start of project Checks the assumption of reasonable normality for some of the statistics generated in a baseline capability analysis.
Mid-project Checks the assumption of reasonable normality for many of the statistical tools used to determine whether an input has a significant effect on the output.
End of project Checks the assumption of reasonable normality for some of the statistics generated in the improved process capability analysis.

Continuous data.

## How-To

1. Enter the data in a single column.
2. Select the distribution. You can create a probability plot for the normal distribution or one of the 13 other available distributions.

## Guidelines

• The probability plot includes the Anderson-Darling goodness-of-fit test, which is stricter than the "fat pencil" test. The p-value for the Anderson-Darling test if often small, indicating a statistically poor fit, even though the "fat pencil" test indicates a reasonably good fit. In most cases, if the two tests do not agree, use the "fat pencil" test – a reasonably good fit is usually adequate.
• When you use a probability plot to determine whether a distribution (usually normal) provides a reasonable fit to your data, you should base part of that decision on what you are going to use your data for. Many statistical tests assume normality. Some tests are extremely robust to nonnormal data. For these cases, reasonably normal is sufficient.
• Always check the robustness of a particular test before you determine whether you can use it based on what you see in a probability plot.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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