# Analyzing Fully Nested design

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.

# Dialog box items

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.

# Minitab Commends:

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.