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Homogeneity of Variance

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Purpose

Homogeneity of variance is the statistical comparison to confirm that no significant difference exists between the variances of different subgroups.
Homogeneity of variance is a fundamental concept in statistics.


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Anatomy


Reference: Juran’s Quality Handbook

Terminology

A. Histogram of data from subgroup A, with standard deviation A.

B. Histogram of data from subgroup B, with standard deviation B.

C. Normal curve.

D. Normal curve Standard deviation.

Statistical tests requiring similar variances may be performed and they confirm that there is no process output variability change.

Homogeneity of Variance Tests


Purpose

Used to compare the variances of two or more populations on a continuous CT characteristic. Since you don't know the population variances, an analysis of samples of data is required.

This test is usually used to determine if there is a statistically significant change in the variance of a CT characteristic under two or more conditions introduced by one factor (see Concept Factor and Levels).

Anatomy


Reference: Minitab Reference Manual

Terminology

A. Null (H0) and alternative (Ha) hypotheses where the variances of the g levels of the factor are compared. There is only one alternative hypothesis: at least the variances of two levels are significantly different.

B. Minitab Session Window Output.

C. Minitab Graphical Output.

D. Confidence Intervals for standard deviations for each level.

E. Bartlett's Test Statistic and P-Value for normal distributions. The P-Value has to be compared with the alpha level and the following decision rule is used: if P < alpha, reject H0 and accept Ha with (1-P)100% confidence; if P > alpha, don't reject H0.

F. Levene's Test Statistic and P-Value for any continuous distribution. The P-Value has to be compared with the alpha level and the following decision rule is used: if P < alpha, reject H0 and accept Ha with (1-P)100% confidence; if P > alpha, don't reject H0.


Major Considerations

The Bartlett's test is not robust to data that is not normally distributed and may lead to wrong conclusions. Use the Levene's test when the data comes from a continuous, but not necessarily normal distribution.

Application Cookbook

1. Define problem and state the objective of the study.

2. State Null and Alternative Hypothesis.

3. Select random samples.

4. Measure the CT characteristic.

5. Analyze data with Minitab:

The data has to be stacked into one column and a second column to contain the level codes (subscripts). This can be done using the function under Manip > Stack/Unstack > Stack Columns.

Use the Function under Stat > ANOVA > Homogeneity of Variance.
Input the name of the column that contains the measurement of the CT characteristic into the 'Response' field, and the name of the column that contains the level codes into the 'Factor' field.

6. Make a Statistical decision from the session window output of Minitab. Either accept or reject H0. If H0 is rejected we can conclude that there is a significant difference between the variances of the levels.

7. Translate statistical conclusion into practical decision about the CT characteristic.

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