Editing Analysis of variance (section)

===Textbook analysis using a normal distribution===
The analysis of variance can be presented in terms of a [[linear model]], which makes the following assumptions about the [[probability distribution]] of the responses:<ref>{{cite book |title = Statistical Methods
| last1 = Snedecor | first1 = George W. 
| last2 = Cochran | first2 = William G.
| year = 1967 | edition = 6th | page = 321
}}</ref><ref>Cochran & Cox (1992, p 48)</ref><ref>Howell (2002, p 323)</ref><ref>
{{cite book | last1 = Anderson | first1 = David R.
| last2 = Sweeney | first2 = Dennis J.
| last3 = Williams | first3 = Thomas A.
| title = Statistics for business and economics 
| publisher = West Pub. Co | location = Minneapolis/St. Paul 
| year = 1996 | edition = 6th| isbn = 978-0-314-06378-6 | pages = 452–453}}
</ref>
* [[Statistical independence|Independence]] of observations – this is an assumption of the model that simplifies the statistical analysis.
* [[normal distribution|Normality]] – the distributions of the [[Residual (statistics)|residuals]] are [[Normal distribution|normal]].
* Equality (or "homogeneity") of variances, called [[homoscedasticity]]—the variance of data in groups should be the same.

The separate assumptions of the textbook model imply that the [[errors and residuals in statistics|errors]] are independently, identically, and normally distributed for fixed effects models, that is, that the errors (<math>\varepsilon</math>) are independent and
<math display="block">\varepsilon \thicksim N(0, \sigma^2).</math>