The Six Sigma ANOVA Method
Analysis of variance, or ANOVA, is a statistical method used to compare data from multiple groups to determine whether differences exist. In Six Sigma, ANOVA provides information about differences in process performance among work groups and time periods. It is typically used during the Analyze and Improve phases of a process improvement project using the DMAIC (Define-Measure-Analyze-Improve-Control) framework.
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Theory
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The ANOVA test is determines differences among group averages. It compares the amount of variance within each group to the amount of variance among the different groups. When it is used for only two groups, the method and results are identical to those for the t-test, a simpler test that is helpful when the user wants to compare only two groups.
Calculation
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While it is possible to conduct an ANOVA using manual calculations, most Six Sigma project teams rely on a software program. The Black Belt or other knowledgeable team member enters the data and runs the ANOVA test. The test calculates an F-score, which represents that ratio between the between-group variation and the within-group variation. The test also provides a p-value which specifies that likelihood that you would obtain that value for F given no real difference. Note that it is not necessary for project team members to understand these details so long as members understand what the results mean.
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Data Assumptions
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In order to use an ANOVA test you must have data that is normally distributed for each group and the groups must have equal variances. The data for a group should be a representative sample, and the process itself must be stable. A stable process does not show trends or other special causes but instead displays only random variation due to factors inherent in the process itself.
Use in Measure Phase
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During the Measure phase ANOVA helps the project team members clarify the current situation. They can compare data for different situations to determine when or under what circumstances the problem under investigation occurs. If a suspected difference is verified using ANOVA, the team can conclude that something about the two groups is different and is affecting process variance. This information can help the team focus its problem statement.
Use in Analyze Phase
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In Analyze, teams use ANOVA to verify suspected root causes by testing whether changing the causal factor results in the expected change in process performance. If a difference is verified, the factor is a confirmed cause that the team may want to address in implementing solutions during Improve. If a significant difference does not exist, the team should explore other potential root causes.
Use in Improve Phase
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During Improve, ANOVA provides confirmation that the implemented solutions did in fact result in improvement, by comparing the before and after data. If a statistically significant improvement occurred and the amount of improvement meets project goals, the team can complete the rollout and move on to the Control phase.
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