Equal Variances Test

Summary

Analyzes observed differences in the process standard deviation at different levels (settings) of an input. To use the test for equal variances, you must collect a sample at each level of the input.

Answers the questions:
  • If I change an input from one level to another, does the variation in the process stay the same or does it change?
  • Is the process variation the same before and after a change has been made to the process?
When to Use Purpose
Mid-project Fixing an input at two or more different settings (levels) helps determine which inputs have significant influence on the variation in the output.
Mid-project Verify changes to inputs result in significant differences from the pre-project standard deviation.

Data

Continuous Y (output), usually a single X (input) at 2 or more levels.

How-To

  1. Verify the measurement systems for the Y data and the input X are 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. You can use one of three methods to enter the data in Minitab:
    • Enter data in two columns using one column for each factor level. Use Stat > Basic Statistics > 2 Variances for data set up this way, and then choose Samples in different columns.
    • Enter Y data in one column with factor level (X) in a second column. Use this method for three or more levels of X. Use either Stat > ANOVA > Test for Equal Variances or Stat > Basic Statistics > 2 Variances for data set up this way, then choose Samples in one column.
    • Use summarized data. This method applies only when you have two levels of X. Enter the sample sizes and variances directly into the dialog box for Stat > Basic Statistics > 2 Variances, and then choose Summarized data.
  4. Determine your hypotheses. The alternative hypothesis (Ha) is what you are trying to prove with your data. The alternative hypothesis for a test of equal variances test is whether at least one level has a significantly different variance than the other levels. The null hypothesis (Ho) is that the variances are the same at all levels.

Guidelines

  • Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
  • The output for all approaches is the same. The F-test (displayed when you have just two levels) and Bartlett’s test (displayed when you have more than two levels) assume reasonable normality; however, Levene’s Test only requires a continuous distribution. Minitab only tests the alternative hypothesis that at least one of the levels has a different standard deviation than at least one other level.
  • Note the F-test and Bartlett’s test are not robust to nonnormal data. You should use these tests only after you have verified the data in each sample is reasonably normal.
  • When you have more than one factor, use Stat > ANOVA > Test for Equal Variances to test for equality of the standard deviations of all combinations of levels of the factors.
  • 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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