# Analysis of variance

(Redirected from ANOVA)

Analysis of variance (ANOVA) is a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts. There are three conceptual classes of such models:

1. The fixed effects model assumes that the data come from normal populations which differ in their means.
2. Random effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy.
3. Mixed models describe situations where both fixed and random effects are present.

The fundamental technique is a partitioning of the total sum of squares into components related to the effects in the model used. For example, we show the model for a simplified ANOVA with one type of treatment at different levels. (If the treatment levels are quantitative and the effects are linear, a linear regression analysis may be appropriate.)

• SSTotal = SSError + SSTreatments

The number of degrees of freedom (abbreviated 'df') can be partitioned in a similar way and specifies the Chi-squared distribution which describes the associated sums of squares.

• dfTotal = dfError + dfTreatments

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