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:
- The fixed effects model assumes that the data come from normal populations which differ in their means.
- Random effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy.
- 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
- dfTotal = dfError + dfTreatments
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