Editing Analysis of variance (section)

==Cautions==
Balanced experiments (those with an equal sample size for each treatment) are relatively easy to interpret; unbalanced experiments offer more complexity. For single-factor (one-way) ANOVA, the adjustment for unbalanced data is easy, but the unbalanced analysis lacks both robustness and power.<ref>Montgomery (2001, Section 3-3.4: Unbalanced data)</ref> For more complex designs the lack of balance leads to further complications. "The orthogonality property of main effects and interactions present in balanced data does not carry over to the unbalanced case. This means that the usual analysis of variance techniques do not apply. Consequently, the analysis of unbalanced factorials is much more difficult than that for balanced designs."<ref>Montgomery (2001, Section 14-2: Unbalanced data in factorial design)</ref> In the general case, "The analysis of variance can also be applied to unbalanced data, but then the sums of squares, mean squares, and ''F''-ratios will depend on the order in which the sources of variation are considered."<ref name="Gelman" />

ANOVA is (in part) a test of statistical significance. The American Psychological Association (and many other organisations) holds the view that simply reporting statistical significance is insufficient and that reporting confidence bounds is preferred.<ref name="Wilkinson" />