# 1 Variance Test

## Summary

Analyzes the difference between an observed process standard deviation (or variance) and a specified value.

• Is the variability of the process significantly different than a specified value (for example, a known standard or a previous known value of the process standard deviation)?
When to Use Purpose
Pre-project Verify the variability of the process is significantly different from expectations, validating the need for an improvement project.
Mid-project Test whether a significant change has occurred in the variability of the output when an input is controlled at a new setting or a previously uncontrolled setting is now controlled.
Mid-project Verify changes from the pre-project standard, throughout the course of making improvements.
End of project Verify the variability of the controlled improved process is different from the pre-project variability. Of course, this assumes that one of the goals of the project was to reduce the variability of the process.

### Data

Continuous Y (output).

## How-To

1. Verify the measurement system for the Y data is adequate.
2. Develop a data collection strategy (who should collect the data, as well as where and when; how many data values are needed; the preciseness of the data; how to record the data, and so on).
3. Collect process data, and enter the values into a single column in a Minitab worksheet.
4. Enter the standard or benchmark value of the standard deviation to compare the process data against. Note: although this is called a 1-variance test, Minitab tests the standard deviation (the square root of the variance) by default.
5. Determine your hypothesis. The alternative hypothesis (Ha) is often what you are trying to prove with the data. The alternative hypothesis for a 1-variance test can state that the process standard deviation is greater than, less than, or not equal to a benchmark value. The null hypothesis (Ho) is the opposite of the alternative hypothesis.
6. You can also perform the test without the actual data if you know the standard deviation and sample size.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• Use Minitab’s Power and Sample Size command to determine the sample size necessary to detect the smallest difference of interest with sufficient power.
• Minitab calculates results based on two methods: the standard and adjusted methods. The standard method is more powerful, but requires that the data are reasonably normal. The adjusted method is less powerful; therefore, it is used only for nonnormal data. If the data are reasonably normal, use the standard method. If the data are not reasonably normal, use the adjusted method.
• It is good practice to graph your data when you use a statistical test. For a 1-variance test, use the histogram or normal probability plots to evaluate normality. Use histograms to identify outliers.
• 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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