In statistics,

**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. The initial techniques of the analysis of variance were pioneered by the statistician and geneticist Ronald Fisher in the 1920s and 1930s. There are three conceptual classes of such models:

- 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.

*df*) can be partitioned in a similar way and specifies the Chi-square distribution which describes the associated sums of squares.

Table of contents |

2 Random-effects model 3 Degrees of freedom 4 Tests of significance |

## Fixed-effects model

## Random-effects model

## Degrees of freedom

Degrees of freedom indicates the effective number of observations which contribute to the sum of squares in an ANOVA, the total number of observations minus the number of linear constraints in the data.

## Tests of significance

Analyses of variance lead to tests of statistical significance using Fisher's F-distribution.

See also: ANCOVA