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Introduction to Analysis-of-Variance Procedures |

When you design an experiment, you choose how many experimental
units to assign to each combination of levels (or cells) in the
classification. In order to achieve good statistical properties
and simplify the computations, you typically attempt to
assign the same number of units to every cell in the design.
Such designs are called *balanced designs*.

In SAS/STAT software, you can use the ANOVA procedure to perform
analysis of variance for balanced data. The ANOVA procedure performs
computations for analysis of variance that assume the balanced nature
of the data. These computations are simpler and more efficient than
the corresponding general computations performed by PROC GLM. Note
that PROC ANOVA can be applied to certain designs that are not
balanced in the strict sense of equal numbers of
observations for all cells. These additional designs include all
one-way models, regardless of how unbalanced the cell counts are, as
well as Latin squares, which do not have data in all cells. In
general, however, the ANOVA procedure is recommended only for balanced
data. **If you use ANOVA to analyze a design that is not balanced,
you must assume responsibility for the validity of the output.** You
are responsible for recognizing incorrect results, which may include
negative values reported for the sums of squares. If you are not
certain that your data fit into a balanced design, then you probably need
the framework of general linear models in the GLM procedure.

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