Data considerations for Fully Nested ANOVA

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The data should include only categorical factors that are random and nested

If your design contains covariates, fixed factors, or crossed factors, use Fit General Linear Model.

For more information on factors, go to Factors and factor levels, What are factors, crossed factors, and nested factors?, and What is the difference between fixed and random factors?.

The design must be fully nested

Minitab fits a hierarchically fully nested model with the nesting performed according to the order of factors in the Factors box. If you enter factors A B C, the model terms will be:

• A
• B nested in A
• C nested in B, nested in A

You do not need to specify the nesting as you would for Balanced ANOVA or GLM.

Nesting does not need to be balanced. A nested factor must have at least 2 levels at some level of the nesting factor. If factor B is nested within factor A, there can be unequal levels of B within each level of A. In addition, the subscripts used to identify the B levels can differ within each level of A. However, if your fully nested design is not balanced, Minitab cannot calculate the F and p-values.

Minitab uses sequential (Type I) sums of squares for all calculations in Fully Nested ANOVA. If you want to use adjusted sums of squares, use Fit General Linear Model.

If your design is not fully nested, use Fit General Linear Model.

The response variable should be continuous

If the response variable is categorical, your model is less likely to meet the assumptions of the analysis, to accurately describe your data, or to make useful predictions.

• If your response variable has two categories, such as pass and fail, use Fit Binary Logistic Model.
• If your response variable contains three or more categories that have a natural order, such as strongly disagree, disagree, neutral, agree, and strongly agree, use Ordinal Logistic Regression.
• If your response variable contains three or more categories that do not have a natural order, such as scratch, dent, and tear, use Nominal Logistic Regression.
• If your response variable counts occurrences, such as the number of defects, use Fit Poisson Model.

Each observation should be independent from all other observations

If your observations are dependent, your results might not be valid. Consider the following points to determine whether your observations are independent:

• If an observation provides no information about the value of another observation, the observations are independent.
• If an observation provides information about another observation, the observations are dependent.

The sample data should be selected randomly

Random samples are used to make generalizations, or inferences, about a population. If your data were not collected randomly, your results might not represent the population.

Collect data using best practices

To ensure that your results are valid, consider the following guidelines:

• Make certain that the data represent the population of interest.
• Collect enough data to provide the necessary precision.
• Measure variables as accurately and precisely as possible.
• Record the data in the order it is collected.

The model should provide a good fit to the data

If the model does not fit the data, the results can be misleading. In the output, use residual plots to determine how well the model fits the data.