Select the method or formula of your choice.

The notation is critical to understanding ANOVA models. Listed below is the notation used for one-way analysis of variance.

Term | Description |
---|---|

r | number of levels of the factor, i = 1 ...r |

i | a given factor level |

j | a given case for a particular factor level, j = 1 ...n _{ i } |

y _{ij} | j ^{th} observation of the response for the i ^{th} factor level |

n _{i } | number of observations for the i ^{th} factor level |

n _{T} | total number of cases |

μ _{i} | true mean of observations at the i ^{th} factor level |

y _{i.} | total of the observations at the i ^{th} factor level |

mean of the response for the i^{th} factor |

The one-way analysis of variance model can be specified in several ways. The cell means model is:

All observations for the factor level have the same expectation, *μ* _{ i }. Because *μ _{i} * is a constant, all observations have the same variance, regardless of factor level.

In analysis of variance, least squares estimation is used to fit the model and provide estimates for the parameters, *μ _{i} *.

The hypothesis test for one-way analysis of variance is:

H_{0}: *μ* _{1} = *μ* _{2}= … = *μ* _{r}

H_{1}: At least one mean is not equal to the others

Term | Description |
---|---|

μ _{i } | parameters or the true mean of observations at the i ^{th} factor level |

ε _{ ij } | error that is independently and normally distributed with mean 0 and constant variance σ ^{2} |