Editing Analysis of variance (section)

===Summary of assumptions===
{{See also|Shapiro–Wilk test|Bartlett's test|Levene's test}}
The normal-model based ANOVA analysis assumes the independence, normality, and homogeneity of variances of the residuals. The randomization-based analysis assumes only the homogeneity of the variances of the residuals (as a consequence of unit-treatment additivity) and uses the randomization procedure of the experiment. Both these analyses require [[homoscedasticity]], as an assumption for the normal-model analysis and as a consequence of randomization and additivity for the randomization-based analysis.

However, studies of processes that change variances rather than means (called dispersion effects) have been successfully conducted using ANOVA.<ref>Montgomery (2001, Section 3.8: Discovering dispersion effects)</ref> There are ''no'' necessary assumptions for ANOVA in its full generality, but the ''F''-test used for ANOVA hypothesis testing has assumptions and practical 
limitations which are of continuing interest.

Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. 
The property of unit-treatment additivity is not invariant under a "change of scale", so statisticians often use transformations to achieve unit-treatment additivity. If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance.<ref>Hinkelmann and Kempthorne (2008, Volume 1, Section 6.10: Completely randomized design; Transformations)</ref> Also, a statistician may specify that logarithmic transforms be applied to the responses which are believed to follow a multiplicative model.<ref name="Cox" /><ref>Bailey (2008)</ref>
According to Cauchy's [[functional equation]] theorem, the [[logarithm]] is the only continuous transformation that transforms real multiplication to addition.{{citation needed|date=October 2013}}