Page 326 - Six Sigma Demystified

306 Six SigMa DemystifieD

parametric test is one in which there are no distributional requirements, such
as normality, for the validity of the test. Typically, nonparametric tests require
larger sample sizes than parametric tests.

When to Use

Analyze Stage

• To compare the mean of samples from different conditions when normal-
ity cannot be assumed

Improve Stage

• To compare process averages after improvements versus baseline esti-
mates when normality cannot be assumed

Methodology

State the null hypothesis H using the same reasoning discussed under “Hy-
0
pothesis Testing on Mean of Two Samples” above. In this case, the null hypoth-
esis will be the median of population 1 equals the median of population 2.
Nonparametric tests typically will use the median rather than the mean be-
cause the median is a reliable estimate of the central tendency regardless of the
distribution. Recall that the average is not a reliable predictor for nonsymmet-
ric distributions.
Specify the alternative hypothesis H to cover the remaining options. In this
1
case, the alternative hypothesis would be the median of population 1 does not
equal the median of population 2.

Choose a significance level (α) or the p value. The significance level, or type
I error, is the probability of rejecting a hypothesis that is true. A value of 0.05
is typical.
Collect samples. As the sample size is increased, the type II error (β error:
the probability of accepting a false hypothesis) is decreased.
The simplest of the nonparametric tests for central tendency is the one-
sample sign test, which tests that approximately half the data are above the test
level.
An enhancement of this test, known as the Wilcoxen signed rank test, includes
the magnitude and sign of the difference from the median. It assumes a sym-
metric, continuous distribution, and it can be applied to differences between
paired observations as well.