## Single Factor ANOVA Example

The null hypothesis in single factor ANOVA is that the means of the various samples are equal.

Each of the following
four columns (stored in the waves f_{1}to f_{4}) represents instrument recording of
some arbitrary property consisting of 6 samples.

Sample | f_{1} | f_{2} | f_{3} | f_{4} |

1 | 19 | 22 | 20 | 21 |

2 | 21 | 21 | 22 | 19 |

3 | 19 | 20 | 20 | 22 |

4 | 20 | 22 | 22 | 19 |

5 | 19 | 22 | 21 | 20 |

6 | 18 | 19 | 20 | 18 |

H_{0}: there is no difference in the values recorded by the four instruments.

H_{a}: there is sufficient difference in the values recorded by the four instruments.

To run the test, execute the following command:

StatsAnova1Test/T=1/Q/W/BF f1,f2,f3,f4

The results are displayed in three tables. Straight ANOVA results are in the table "ANOVA1 Results":

DF | SS | MS | F | Fc | P | ||

Groups | 3 | 11.5 | 3.83333 | ||||

Error | 20 | 29 | 1.45 | ||||

Total | 23 | 40.5 | 1.76087 | 2.64368 | 3.09839 | 0.077207 |

Here the critical value F_{c}>F so H_{0} can't be rejected. Note also that P>alpha which is set by
default to 0.05.

The second table titled "Welch Test" contains the following results:

N1 | 3 |

N2 | 8 |

Fp | 0.45153 |

Fpc | 4.06618 |

Pp | 0.723258 |

Here F_{p} is the Welch test statistic associated with degrees of freedom N1 and N2, F_{pc} is the critical
value and P_{p} is the P-value.

The third table "Brown and Forsythe Test" contains the following results:

N1 | 3 |

N2 | 18 |

Fp | 2.64368 |

Fpc | 3.15991 |

Pp | 0.0805162 |

Here again F_{p} is the test statistic associated with degrees of freedom N1 and N2, F_{pc} is the critical
value and P_{p} is the P-value.