Page 261 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 241

When to Use

Analyze Stage and Improve Stage
• To test observed data used in an ANOVA

• To test residuals in a regression analysis

Methodology

A statistical test for the equality of the variance at a experimental condi-
tions is provided by Bartlett. Minitab offers this test, as well as the Levene
test, which is preferred if nonnormality is suspected. We would generally
expect the regression residuals to follow a normal distribution, and ANOVA
requires normality of the parameters, so Bartlett’s test is adequate in these
cases.
The Bartlett test tests the equality of the treatment variances against the
alternative that at least one variance is unequal to the others. The null hypoth-
esis is that of equal variances for the subsets:

2
2
H : σ = σ = σ = . . . 2
2
0 1 1 2 = σ a
The alternative is that at least one of the subsets has an unequal variance.
The equality of variance test requires multiple samples from each test condition
to evaluate the variance at each condition. For example, the replicated experi-

mental data presented in the “Factorial Design” topic may be analyzed for
equality of variance. In the original design, there are six factors (A through F)
estimated using eight unique design conditions, replicated for a total of sixteen
total experimental trials. In this original model of six factors, there would be
two samples available to estimate variance at each of the eight unique design
conditions. We could instead evaluate the equality of variance for the final rec-
ommended model, where four of the six factors have been removed for being
statistically insignificant. This two factor model provides four samples to esti-
mate the variance at each of the final four design conditions, summarized
shown in Table T.5. It should be clear the test for equality of variance will nec-
essarily differ for a given set of data depending on the model chosen for
analysis.