**
By Lloyd S. Nelson
**

DIFFERENCES among several means from normally distributed populations can be examined using the analysis of variance or the analysis of means. Differences among several variances from normally distributed populations can be examined using Bartlett's test (Dixon and Massey (1983) or an analysis of means type test (Wludyka and Nelson (1997)). In what follows, the problem of testing normally distributed data simultaneously for differences among either means or variances or both is illustrated. This is referred to as a general test of homogeneity. It has the advantage of involving a single significance level.

**Problem Illustration:** Batches
of items are purchased from a company that manufactures them.
Prior experience indicates that the characteristic of interest
meets the requirement of normality. You wish to test whether
the mean and/or the variance have changed over time. Time
constraints and economics dictate the batch size, which must
be constant, and the frequency of sampling from the supplier
s process.

**Solution:** Imagine that it
is feasible to obtain a constant number *n* = 4 observations
taken each week for *k* = 6 weeks. Table 1 shows an example.

The null hypothesis to be tested
is H_{0}: Neither the mean nor the variance has changed
over the time of sampling. The alternative hypothesis is H_{1}:
Either the mean or the variance or both have changed over
the time of sampling. The required statistic is

where

Key Words: *Monte Carlo Simulation,
Significance Test*.

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