Page 296 - Six Sigma Demystified

276 Six SigMa DemystifieD

for the process represented by the bottom set of control charts because the
process is out of control. By definition, then, the data are from multiple process
distributions.
Thus, if the process is out of control, then, by definition, a single distribution
cannot be fit to the data. Therefore, always use a control chart to determine
statistical control before attempting to fit a distribution (or determine capabil-
ity) for the data. Once statistical control is established, use goodness-of-fit tests
(described earlier) to determine if an assumed distribution provides a reason-
able approximation. Remember that a histogram provides only part of the pic-
ture and can never be used to assess process stability.

Hypothesis Testing

Hypothesis testing refers to a general class of problems where we seek to com-
pare, at a stated degree of confidence, a sample statistic against a standard value
or a statistic from another sample. Hypothesis testing is used in regression anal-
ysis and designed experiments to determine if factors included in the analysis
contribute to the variation observed in the data (as discussed under “Regression
Analysis” below). Hypothesis testing is a tool of statistical inference, where we
use sample statistics (such as a sample average X or a sample standard devia-
tion s) to infer properties of a population (such as its mean µ or standard devia-
tion σ).
When to Use

Key assumptions include

1. The population is both constant (it does not change over time) and homo-
geneous (a given sample is representative of the sample as a whole).
2. Samples are randomly collected from the population and representative
of the population under investigation. In surveys, low response rates typi-
cally would provide extreme value estimates (i.e., the subpopulation of
people who have strong opinions one way or the other).
3. The hypothesis tests shown below and their associated α and β risks, de-
pend on the normality of the population. If the population is significantly
nonnormal, then the tests are not meaningful, and nonparametric tests
should be used. Goodness-of-fit tests are used to test this assumption. Non-
parametric tests can be used if the populations are significantly nonnormal.