Example of Fully Nested ANOVA
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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° 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 for four operators over four different shifts. You take three batch measurements during each shift. Because your design is fully nested, you use Fully Nested ANOVA to analyze your data.

1    Open the worksheet FURNTEMP.MTW.

2    Choose Stat > ANOVA > Fully Nested ANOVA.

3    In Responses, enter Temp.

4    In Factors, enter Plant - Batch. Click OK.

Session window output

Nested ANOVA: Temp versus Plant, Operator, Shift, Batch

 

 

Analysis of Variance for Temp

 

Source     DF         SS        MS      F      P

Plant       3   731.5156  243.8385  5.854  0.011

Operator   12   499.8125   41.6510  1.303  0.248

Shift      48  1534.9167   31.9774  2.578  0.000

Batch     128  1588.0000   12.4062

Total     191  4354.2448

 

 

Variance Components

 

                      % of

Source    Var Comp.  Total  StDev

Plant         4.212  17.59  2.052

Operator      0.806   3.37  0.898

Shift         6.524  27.24  2.554

Batch        12.406  51.80  3.522

Total        23.948         4.894

 

 

Expected Mean Squares

 

1  Plant       1.00(4) +  3.00(3) + 12.00(2) + 48.00(1)

2  Operator    1.00(4) +  3.00(3) + 12.00(2)

3  Shift       1.00(4) +  3.00(3)

4  Batch       1.00(4)

Interpreting the results

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 main effects at a = 0.05 (F-test p-values < 0.05). There is no significant evidence for an operator effect. The variance component estimates indicate 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.