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The average of the observations at a given factor level.

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

n _{i} | number of observations at factor level i |

y _{ij} | value of the j ^{th} observation at the i ^{th} factor level |

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

y _{ij} | observations at the i ^{th} factor level |

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

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

The common variance for all observations. The pooled variance is:

The pooled standard deviation is the square root of the above formula. An equivalent form follows:

The pooled standard deviation is equivalent to S, which is in the output and is equal to:

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

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

sample mean for factor level i | |

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

n _{T} | total number of observations |

s _{i} ^{2} | variance of observations |

r | number of levels of the factor |

MS | Mean Square |

The confidence intervals are calculated for each factor level mean using the pooled standard deviation. The formula is:

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

n_{T} | total number of observations |

r | number of factor levels |

S | pooled standard deviation |

inverse cumulative distribution function from the t distribution at 1− α/2 with n_{T} − r degrees of freedom |