Perform a fully nested ANOVA

Use Fully Nested ANOVA to determine whether the means of two or more groups differ when all the factors are nested. For example, compare the production rates of two machines that each have unique operators. To perform ANOVA with nested factors in Minitab you can use either Fully Nested ANOVA or General Linear Model. Fully Nested ANOVA does not display F and p values when the data are unbalanced while General Linear Model does.

The following options show how to perform fully nested ANOVA using both methods using an example. Suppose you want to understand the sources of variability in the manufacture of glass jars. You do an experiment and measure furnace temperature three times during a work shift for each of four operators from each plant on four different shifts. Using the Minitab sample data set FurnaceTemperature.MTW where Temp is the response and the four nested factors are Plant, Operator, Shift and Batch.

Option 1: Use Fully Nested ANOVA

  1. Choose Stat > ANOVA > Fully Nested ANOVA.
  2. In Responses, enter Temp.
  3. In Factors, enter Plant Operator Shift Batch. Click OK.

    In step 3, the factors are listed in hierarchical order.

Option 2: Use General Linear Model

  1. Choose Stat > ANOVA > General Linear Model > Fit General Linear Model.
  2. In Responses, enter Temp.
  3. In Factors, enter Plant Operator Shift Batch.
  4. Click Random/Nest.
  5. Under Nesting, complete the table as follows.
    Factor/Covariate Nested in specified factors
    Operator Plant
    Shift Operator
    Batch Shift
  6. Under Factor type, change all the factors to Random.
  7. Click OK in each dialog box.
    The general linear model output will not be identical to the fully nested ANOVA output.
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