Stat > ANOVA > Fully Nested
ANOVA

Use Fully Nested ANOVA to perform
fully nested (hierarchical) analysis of variance and to estimate variance
components for each response variable. All factors are implicitly assumed to be
random. Minitab uses sequential (Type I) sums of squares for all calculations.

You can analyze up to 50 response
variables with up to 9 factors at one time. If your design is not a
hierarchically nested one or if you have fixed factors, use either Balanced ANOVA
or GLM. Use GLM if you want to use adjusted sums of squares for a fully nested
model.

Responses: Enter the columns
containing your response variables

Factors: Enter the columns
containing the factors in hierarchical order

Example: You are an engineer trying to understand the sources of variability in
the manufacture of glass jars. The process of making the glass requires mixing
materials in small furnaces for which the temperature setting is to be 475
degrees F. Your company has a number of plants where the jars are made, so you
select four as a random sample. You conduct an experiment and measure furnace
temperature three times during a work shift for each of four operators from
each plant over four different shifts. Because your design is fully nested, you
use Fully Nested ANOVA to analyze your data.

1
Open the file FURNTEMP.MTW.

2
Choose Stat > ANOVA > Fully Nested
ANOVA.

3
In Responses, enter Temp.

4
In Factors, enter Plant - Batch.

5
Click OK.

Interpretation:

Minitab displays three tables of
output: 1) the ANOVA table, 2) the estimated variance components, and 3) the
expected means squares. There are four sequentially nested sources of
variability in this experiment: plant, operator, shift, and batch. The ANOVA
table indicates that there is significant evidence for plant and shift effects
at a = 0.05 because F-test p-values are less than 0.05. There is no significant
evidence for an operator effect. The variance component estimates indicates
that the variability attributable to batches, shifts, and plants was 52, 27,
and 18 percent, respectively, of the total variability.

If a variance component estimate
is less than zero, Minitab displays what the estimate is, but sets the estimate
to zero in calculating the percent of total variability.