Page 327 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 307

The Mann-Whitney test may be used for testing the equality of two medians.
It assumes that the distributions of the two populations have the same shape
and spread. If the distributions are approximately normal, the test is 95 percent
as efficient as a standard t test for large samples. Regardless of the distribution,
the test is always at least 86 percent as efficient as a t test.
These tests may be performed in Minitab (use Stat\Nonparametrics) or other
statistical software.

Interpretation

The result of the test is to compare the calculated statistics with a test statistic.
For example, if the calculated statistic exceeds the critical value of the test statis-
tic (based on the α level chosen), then we reject the null hypothesis. If not, then
we fail to reject the null hypothesis. Rejecting the null hypothesis is known as a
strong conclusion: We have disproven that the medians are equal. When we fail to
reject the null hypothesis, then the medians may be equal or may not be; we re-
ally can’t tell based on the data. This is considered a weak conclusion for obvious
reasons. We may want to collect larger samples to further test the hypothesis.

Np Chart

An Np chart is one of a set of control charts specifically designed for attributes
data. The Np chart monitors the number of times a condition occurs, relative to
a constant sample size, when each sample can either have this condition or not
have this condition. For example, we could sample a set number of transactions
each month from all the transactions that occurred and from this sample count

the number of transactions that had one or more errors. We then would track on
the Np control chart the number of transactions with errors each month.

When to Use

Measure Stage

• To estimate, using attributes data, the process baseline (Generally, we
would greatly prefer to use a variables control chart for this purpose.)

Improve Stage
• Since the number of errors tends to be quite small (for even very large
samples), the use of attribute charts is limited in the improve stage.