Page 297 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 277

4. Some tests additionally require equal variance, which can be tested using
the F test for equality of variance (see “Hypothesis Test for Two-Sample
Variances: Two-Sided Example”). If the populations do not have equal
variances, then the data can be transformed (see “Transformation”). In
some cases, an equivalent test assuming unequal variance may be applied
(as shown below for the two-sample mean test).

Analyze Stage
• To compare the calculated mean of a sample to a desired mean value or
to a calculated mean from another data set

Improve Stage
• To compare process averages after improvements versus baseline esti-
mates

Methodology

1. State the null hypothesis H . For example, H : µ = 25. The null hypothesis
0
0
is often stated as what you would like to assert by the test. Sometimes,
however, it is better to state what you’d like to disprove because the test
provides only two possible conclusions: Reject the null hypothesis or fail
to reject it. In other words, we can’t prove the null hypothesis, but we can
disprove it or fail to disprove it based on the statistical evidence.
2. Specify the alternative hypothesis H . Most authors recommend that the
1
alternative hypothesis cover all the remaining options. For example, a null

hypothesis that the mean is less than or equal to a certain value would
have an alternative hypothesis that the mean is greater than that same
value. Minitab does not follow these conventions; its null hypothesis al-
ways uses the “equal to” designation so that your selection of an alternative
hypothesis determines the test criteria.
3. Choose a significance level (α) or define the p value. The significance level α,
or type 1 error, is the probability of rejecting a hypothesis that is true. A
significance of 0.05 is often used. Historically, an α error was assigned in
advance of the hypothesis test, much the same way a confidence interval
is constructed using an assigned significance. In this way, a hypothesis test
can be directly analogous to (and provide the same result as) a confidence
interval. The calculated statistic is compared with a tabulated value of the