The Anderson-Darling test is available in some statistical software. To illustrate, here's statistical software output for the example on IQ and physical characteristics from Lesson 5 (), where we've fit a model with PIQ as the response and Brain and Height as the predictors:
The Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, and the Cramér-von Mises statistic are based on the empirical distribution function (EDF). However, some EDF tests are not supported when certain combinations of the parameters of a specified distribution are estimated. See for a list of the EDF tests available. You determine whether to reject the null hypothesis by examining the -value that is associated with a goodness-of-fit statistic. When the -value is less than the predetermined critical value (), you reject the null hypothesis and conclude that the data did not come from the specified distribution.
Other alternatives include Ryan-Joiner or ..
The Kolmogorov-Smirnov test is available in some statistical software. For the IQ and physical characteristics model with PIQ as the response and Brain and Height as the predictors, the value of the test statistic is 0.097 with an associated p-value of 0.490, which leads to the same conclusion as for the Anderson-Darling test.
Norm Test | Statistical Hypothesis Testing | P Value
The Ryan-Joiner test provides a correlation coefficient, which indicates the correlation between your data and the normal scores of your data. If the correlation coefficient is near 1, your data falls close to the normal probability plot. If it is less than the appropriate critical value, you will reject the null hypothesis of normality.
The common null hypothesis for these three tests is H0: ..
The Ryan-Joiner test is available in some statistical software. For the IQ and physical characteristics model with PIQ as the response and Brain and Height as the predictors, the value of the test statistic is 0.988 with an associated p-value > 0.1, which leads to the same conclusion as for the Anderson-Darling test.
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Each statistical test has its assumptions about the data being supplied for testing. The Anderson-Darling test fails when goes up in steps. I encountered an example of this when lab data was being reported to 2 digits when the 3rd was significant. The data failed the Anderson-Darling normality test. It can do so even when the data passes the “10 bucket” rule!!