The Anderson-Darling normality test is one of the three general normality tests that can detect deviations from normality. Although it is often referred to as the strongest test, there are other tests that can be used. The other two tests have comparable power. Distribution Analyzer’s p-values for this test might differ from other software packages because they were corrected to be within 3 significant digits.
If the p-value is lower than or equal to 0.05, the test will reject the hypothesis of normality. You can fail the normality test and state with 95% confidence that the data doesn’t fit the normal distribution. The normality test is only valid if you can prove that there was no significant deviation from normal.
While the Anderson-Darling normality test is very theoretically sound, it has serious problems when applied to real-world data. Poor precision can severely affect the Anderson-Darling test. Anderson-Darling will reject data that contains significant ties, regardless of whether the data is within the normal distribution. Here is an example of data that was generated using the normal distribution, but was rounded to the nearest 0.50 to create ties.
Analyzing your data is often started by testing for normality. Normality is an assumption that many statistical tools may use. You may need to try a different statistical approach or tool if you fail this assumption. This article will explain what normality means for data and how to use the AD test to verify that your data meets the assumption of normality. We will also discuss the advantages of the AD test and provide some best practices to help you understand when and how to use it.
But what does this mean?
Normality is a statistical distribution known as a normal or the Gaussian distribution or bell-shaped curve. The normal distribution is a symmetrical continuous distribution by the mean or standard deviation of data.
The normal distribution is a hypothetical distribution. The AD test does not determine if your data conforms to a normal distribution. It only tests whether your data are close enough to normal so that your statistical tool can be used without any concern.