Anderson-Darling+Goodness-of-Fit+Test

Anderson-Darling Goodness-of-Fit Test (Goodness-of-Fit) (Regression Analysis)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

"In statistics, the **Anderson–Darling test**," ... "is a statistical test of whether there is evidence that a given sample of data did not arise from a given probability distribution. ..." - [|Wikipedia]

"In its application as a test that the normal distribution adequately describes a set of data, it is one of the most powerful statistics for detecting most departures from normality." - [|Wikipedia]

“ The Anderson-Darling test measures how well the data follow a particular distribution. The better the distribution fits the data, the smaller this statistic will be.” - Minitab (Help) While there does not seem to be a specific value for this test (like 2 for the Durbin-Watson test), in choosing between two distributions, pick the one with the smaller AD value. Just use the p-value to determine if the data is described by the distribution or not. - Van Dorp

**//Plot in Minitab.//** "The AD value is the statistic value of the Anderson-Darling goodness-of-fit test (similar in spirit as the Chi-squared-test). Large values of the AD-statistic indicate a larger deviation from the fitted theoretical distribution.

"The larger the P-value the larger the support for the theoretical distribution.

"If the theoretical distribution is a perfect fit of the data all data point should form a straight line.  "Deviations from the straight line show deviations from the fitted theoretical distribution.

"When can a data point be considered an outlier? Answer: when a data point is outside the boundaries that are drawn. ... " - EMSE 271, Spring 2009 ( Slide 106 or 107) - Belongs elsewhere.


 * Minitab Help**

Anderson-Darling statistic
Measures how well the data follow a particular distribution. The better the distribution fits the data, the smaller this statistic will be. Use the Anderson-Darling statistic to compare the fit of several distributions to see which one is best or to test whether a sample of data comes from a population with a specified distribution. For example, you can use the Anderson-Darling statistic to choose between the Weibull and lognormal distributions for a reliability data analysis or to test whether data meets the assumption of normality for a t-test. The hypotheses for the Anderson-Darling test are: H 0 : The data follow a specified distribution H 1 : The data do not follow a specified distribution If the p-value (when available) for the Anderson-Darling test is lower than the chosen significance level (usually 0.05 or 0.10), conclude that the data do not follow the specified distribution. Minitab does not always display a p-value for the Anderson-Darling test because it does not mathematically exist for certain cases. If you are trying to determine which distribution the data follow and you have multiple Anderson-Darling statistics, it is generally correct to compare them. The distribution with the smallest Anderson-Darling statistic has the closest fit to the data. If distributions have similar Anderson-Darling statistics, choose one based on practical knowledge. Some commands generate an adjusted Anderson-Darling, or AD*, statistic. The non-adjusted Anderson-Darling statistic uses the nonparametric step function based on the Kaplan-Meier method of calculating plot points, while the adjusted Anderson-Darling statistic uses other methods to calculate the plot points.

TBR - Check Slide 106 to see if anything else needs to be added.

**Sources:**

 * EMSE 271, Fall 2009
 * Anderson–Darling test. (2009, September 9). In //Wikipedia, The Free Encyclopedia//. Retrieved 16:11, September 9, 2009, from []
 * Van Dorp,
 * Minitab 15.1.30.0. (c) 2007, Minitab Inc.