Analysis of variance

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Analysis of variance is 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. Fixed effects models assume 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.)

• SS_Total = SS_Error + SS_Treatments

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.

• df_Total = df_Error + df_Treatments

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Dick Beldin