Select the method or formula of your choice.

*A*^{2} measures the area between the fitted line (which is based on the chosen distribution) and the nonparametric step function (which is based on the plot points). The statistic is a squared distance that is weighted more heavily in the tails of the distribution. A small Anderson-Darling value indicates that the distribution fits the data better.

The Anderson-Darling normality test is defined as:

H_{0}: The data follow a normal distribution

H_{1}: The data do not follow a normal distribution

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

F(Y_{i}) | , which is the cumulative distribution function of the standard normal distribution |

Y_{i} | ordered data |

A commonly used measure of the center of a batch of numbers. The mean is also called the average. It is the sum of all observations divided by the number of (nonmissing) observations.

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

x_{i} | i^{th} observation |

N | number of nonmissing observations |

Minitab displays the number of nonmissing observations in a sample.

Another quantitative measure for reporting the result of the normality test is the p-value. A small p-value is an indication that the null hypothesis is false.

If you know A^{2} you can calculate the p-value. Let:

Depending on A'^{2}, you will calculate p with the following equations:

- If 13 > A'
^{2}> 0.600 then p = exp(1.2937 - 5.709 * A'^{2}+ 0.0186(A'^{2})^{2}) - If 0.600 > A'
^{2}> 0.340 then p = exp(0.9177 - 4.279 * A'^{2}– 1.38(A'^{2})^{2}) - If 0.340 > A'
^{2}> 0.200 then p = 1 – exp(–8.318 + 42.796 * A'^{2}– 59.938(A'^{2})^{2}) - If A'
^{2}<0.200 then p = 1 – exp(–13.436 + 101.14 * A'^{2}– 223.73(A'^{2})^{2})

In general, the closer the points fall to the fitted line, the better the fit. Minitab provides two goodness-of-fit measures to help assess how the distribution fits your data.

The table below shows how the middle line is constructed:

Distribution | x coordinate | y coordinate |
---|---|---|

Normal | x | Φ^{–1} _{norm} |

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

Φ^{–1} _{norm} | value returned for p by the inverse cdf for the standard normal distribution |

The input data are plotted as the x-values. Minitab calculates the probability of occurrence without assuming a distribution. The Y-scale on the graph resembles the Y scale found on normal probability paper where the probabilities plot as a straight line, as if the data are from a normal distribution.

The sample standard deviation provides a measure of the spread of your data. It is equal to the square root of the sample variance.

If the column contains *x* _{1}, *x* _{2},..., *x* _{N}, with mean , then the standard deviation of the sample is:

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

x _{i} | i ^{th} observation |

mean of the observations | |

N | number of nonmissing observations |