In statistics, normality tests are used to assess whether a data set is well-modelled by a normal distribution. There are a variety of normality tests, but in this blog post, we’ll focus on the Anderson Darling test. Keep reading to learn more about this test and how to interpret the results.
What is the Anderson Darling Test?
The Anderson Darling test is a statistical test that can be used to assess whether a data set follows a normal distribution. The test is based on the idea that if a data set is normally distributed, then the maximum difference between the cumulative distribution function of the data and the normal distribution should be minimized. This difference is quantified using the Anderson-Darling test statistic.
The Anderson Darling test is one of the most powerful normality tests because it is less sensitive to outliers than other tests. However, this power comes at a cost; the Anderson Darling test also has a higher Type I error rate than other normality tests.
Understanding the Anderson-Darling Statistic
The Anderson-Darling statistic is used to evaluate the goodness of fit for statistical models. It measures how well the data aligns with a specified distribution, making it a crucial metric in validating distributional assumptions.
Understanding the Anderson-Darling Statistic
The Anderson-Darling statistic is a measure of how well a dataset follows a specified distribution. It is a non-parametric test, meaning it does not require any specific distribution to be assumed. The statistic is calculated based on the cumulative distribution function (CDF) of the specified distribution and the ordered data. A smaller Anderson-Darling statistic indicates a better fit between the distribution and the data. This statistic is particularly useful for testing the assumption of normality for a t-test and can also be used to compare the fit of several distributions to determine which one best matches the data.
Hypotheses and Test Procedure
The Anderson-Darling test has two hypotheses:
Null hypothesis (H0): The data come from a specified distribution.
Alternative hypothesis (H1): The data do not come from a specified distribution.
The test procedure involves calculating the Anderson-Darling statistic and determining the p-value. The p-value is used to test the null hypothesis, with a p-value less than a chosen alpha (usually 0.05 or 0.10) indicating rejection of the null hypothesis. The test can be performed using various software packages, including Minitab, which may not display a p-value for the Anderson-Darling test in certain cases.
How to Interpret the Results of the Test
There are two main things you need to look at when interpreting the results of an Anderson Darling normality test:
– The p-value: This is the probability that you would observe a test statistic as extreme as or more extreme than the one you actually observed, given that the null hypothesis is true. A small p-value (generally anything below 0.05) means that you can reject the null hypothesis and conclude that the data is not normally distributed.
– The critical values: These are percentage points of the distribution under the null hypothesis. If your test statistic is greater than or equal to one of these values, you can reject the null hypothesis and conclude that the data is not normally distributed.
Applying the Test to the Data
To apply the Anderson-Darling test to the data, the following steps can be followed:
Choose a specified distribution to test against, such as a normal distribution.
Calculate the Anderson-Darling statistic using the CDF of the specified distribution and the ordered data.
Determine the p-value using the Anderson-Darling statistic and the sample size.
Compare the p-value to the chosen alpha level.
If the p-value is less than the alpha level, reject the null hypothesis and conclude that the data do not come from the specified distribution.
If the p-value is greater than the alpha level, fail to reject the null hypothesis and conclude that the data may come from the specified distribution.
Note: The Anderson-Darling test is a powerful tool for detecting departures from normality, but it is not foolproof. Additional criteria, such as probability plots, should be used to choose between distributions when the statistics are close together.
Conclusion:
In conclusion, The Anderson Darling Normality Test is a statistical tool used to evaluate whether a Normal Distribution can reasonably model a dataset. The Test accepts or rejects this assumption by identifying outliers in the dataset that deviate from what would be expected under a Normal Distribution. This information can help researchers better understand their data and determine which type of Statistical Analysis would best suit their study moving forward.
The Anderson Darlington Normality Test is covered as part of our Lean Six Sigma Black Belt Course and a shorter introduction within our Green Belt Course
