Name: anderson-darling test for goodness of fit
Uploaded: 2025-01-09T15:14:08.000Z
Duration: 1 min 16 s
Channel: JoVE

In many cases, the distribution of the population from where the random samples are drawn is often unknown or difficult to determine.
In these cases, the Anderson-Darling test can aid in determining if such data and samples are drawn from a particular distribution, such as standard normal or uniform distribution.
When testing for normality, the null hypothesis states that the data follow a normal distribution, and the alternative hypothesis is that the data do not follow a normal distribution.
The test statistic A2 is calculated using the following equation to test for the normality of samples and compared with the critical value obtained from the theoretical standard normal distribution.
When this test statistic is greater than the critical value at a pre-decided significance level, the null hypothesis that the sample is from a normal distribution is rejected.
The data from laboratory experiments or even from natural observations are often assumed to be normally distributed.
The Anderson-Darling test can be applied to decide the appropriate parametric or nonparametric test for the analysis.

the anderson-darling test

The Anderson-Darling Test

The Anderson-Darling test is a statistical method used to determine whether a data sample is likely drawn from a specific theoretical distribution. Unlike parametric tests, it does not require assumptions about specific parameters of the distribution. Instead, it compares the sample&#39;s empirical cumulative distribution function (ECDF) with the cumulative distribution function (CDF) of the hypothesized distribution. Critical values for the test are specific to the chosen distribution rather than universal, making it adaptable to various distributions.
Developed by Theodore Wilbur Anderson and Donald Allan Darling in 1952, the test is widely used to check for normality, though it is a common misconception that it applies only to normal distributions. In fact, it can also test goodness-of-fit for distributions like exponential, Weibull, or logistic, as long as the relevant CDF is known.
A key consideration when using the Anderson-Darling test is whether a parametric or nonparametric approach is appropriate, depending on the information about the population distribution. Although it is frequently employed to test for normality, the test can assess fit across a broad range of distributions. It is considered an improvement over the Kolmogorov-Smirnov (K-S) test due to its greater sensitivity to deviations in the tails of the distribution, making it more effective for detecting outliers and extreme values. Finally, while calculating the Anderson-Darling test statistic manually can be complex, computer-based tools and software packages have simplified the process, providing both the test statistic and the critical values needed to interpret results efficiently.

In many cases, the distribution of the population from where the random samples are drawn is often unknown or difficult to determine.
In these cases, the ...

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Nonparametric Statistics

KEY TERMS AND CONCEPTS

anderson-darling test for goodness of fit

The Anderson-Darling test checks whether a data sample fits a specific theoretical distribution. It compares the sample’s empirical cumulative distribution function, or ECDF, with the cumulative distribution function, or CDF, of the distribution being tested. This makes it a useful goodness-of-fit method when the population distribution is uncertain.

Unlike parametric tests, the Anderson-Darling test does not require assumptions about specific distribution parameters. Its critical values depend on the chosen distribution, not on one universal cutoff. The test is often used to check for normality, but it is not limited to normal data.

The same method can also test other distributions, such as exponential, Weibull, or logistic, as long as the correct CDF is known. A key choice is whether a parametric or nonparametric approach fits the available information about the population. The test is considered an improvement over the Kolmogorov-Smirnov test because it is more sensitive to differences in the tails of the distribution.

That extra sensitivity helps it detect outliers and extreme values more effectively. Theodore Wilbur Anderson and Donald Allan Darling developed the test in 1952. Although the statistic can be hard to calculate by hand, computer tools now provide the test statistic and the critical values needed to interpret the result.

Anderson-Darling Test for Goodness of Fit

anderson-darling-test-for-goodness-of-fit

introduction to nonparametric statistics

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sign-test-for-median-of-single-population

Single-Population Sign Test for a Median

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wilcoxon signed-ranks test for matched pairs

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wilcoxon signed-ranks test for median of single population

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Wilcoxon Signed-Rank Test Using Ranked Differences

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Comparing Two Groups with Rank Sums

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The Anderson-Darling test checks whether a data sample fits a specific theoretical distribution. It compares the sample’s empirical cumulative distribution function, or ECDF, with the cumulative distribution function, or CDF, of the distribution being tested. This makes it a useful goodness-of-fit method when the population distribution is uncertain. Unlike parametric tests, the Anderson-Darling test does not require assumptions about specific distribution parameters. Its critical values...

spearman's rank correlation test

Using Ranks to Measure Correlation

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Kendall Tau for Rank Correlation

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wald-wolfowitz runs test ii

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Friedman Rank Test for Repeated Measures

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Ranking Agreement with Kendall's W

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key terms and concepts

Learn how the Anderson-Darling test compares a sample to a theoretical distribution and why it is useful for normality, outliers, and goodness of fit.

Anderson-Darling Test for Goodness of Fit | JoVE K12

statistics

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Anderson-Darling Test for Goodness of Fit

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