In a Six Sigma DMAIC project it is often necessary to compare data for different groups or conditions to determine if any differences exist. In the Analyze phase, we seek to validate root causes by verifying whether manipulating an input variable affects process performance or another outcome measure such as customer satisfaction. During the improve phase, we seek to confirm that implementing process improvements actually results in a change in one or more process metrics. Other projects that involve data measurement may also require a means of comparing group data.
To compare group data when the input variable is discrete and the output variable is continuous, use the ANOVA test. This test actually compares the variance within each group to the variance among all the groups to determine whether any differences among the groups exist. In other words, it determines whether differences among samples in different groups exist solely because of random variation affecting all groups or whether something specific about a condition itself creates a difference.
The ANOVA is based on calculation of the F-statistic, which is the result when you divide the variance between groups by the variance within groups. If there are no differences among groups, those two values are equal, resulting in an F value of 1. If F is significantly different from 1, as determined by consulting an F table, you would conclude that the null hypothesis does not hold and that there is at least one group that differs from at least one other group.
