# Normality test

Use a normality test to provide a graphical and statistical (goodness-of-fit test) method to determine if the normal distribution fits your data. A common way to check normality is to use what is called 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 normal distribution model my data reasonably well?
When to Use Purpose
Start of project Check the assumption of reasonable normality for some of the statistics generated in a baseline capability analysis.
Mid-project Check 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 Check the assumption of reasonable normality for some of the statistics generated in the improved process capability analysis.

## Data

Your data must be continuous values.

## Guidelines

• The normality test includes the Anderson-Darling, Ryan-Joiner, and Kolmogorov-Smirnov goodness-of-fit tests, which are more strict tests than the "fat pencil" test. The p-value for these tests is 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 covers a lot of ground.
• Always check the robustness of a particular test before you determine whether to 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.

## How-to

1. Collect data and enter them into Minitab in a single column.
2. Select which of three statistical tests you will use to measure the goodness of fit. Note that, while three different tests are available, the Anderson-Darling test is viewed by many as the standard normality test.