The Anderson-Darling statistic is a measure of how far the plot points fall from the fitted line in a probability plot. The statistic is a weighted squared distance from the plot points to the fitted line with larger weights in the tails of the distribution. Minitab uses an adjusted Anderson-Darling statistic, because the statistic changes when a different plot point method is used.

Minitab provides an Anderson-Darling statistic for the maximum likelihood and least squares estimation methods.

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

n | number of plotted points |

A_{i} | |

B_{i} | |

C_{i} | |

z_{i} | fitted estimate of the cumulative distribution function for the i^{th} point |

F_{n}(z_{i}) | the point plotted for the i^{th} data point |

z_{0} | equals 0 |

F_{n}(z_{0}) | equals 0 |

ln_{n}(z_{0}) | equals 0 |

z_{n+1} |

For least squares estimation, Minitab calculates a Pearson correlation coefficient. If the distribution fits the data well, then the plot points on a probability plot will fall on a straight line. The correlation, usually signified by *r* (rho), measures the strength of the linear relationship between the X and Y variables on a probability plot.