# Questions tagged [anderson-darling-test]

The A-D test assess the fit of an empirical (observed) distribution to a theoretical one. It is an especially powerful option when the theoretical distribution is the normal. The A-D test can also be used to see if several empirical distributions come from the same population.

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### How Anderson Darling hypothesis test is set up?

I'd like to know what is the hypothesis test behind Anderson Darling test. I know that H0 is for data follows the distribution and H1 is for data doesn't follow the distribution. But how is it written ...
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### Testing the Anderson–Darling and Central Limit Theorem

I was trying to simulate the Central Limit Theorem in R. Unfortunately, even in large samples (e.g., 80), the Anderson–Darling test could not recognize normality. Therefore, I wrote the following code ...
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### How Anderson-Darling test with Braun's method works in R?

I generally work with skewed and heavy-tailed lifetime distributions, so I need to check the goodness-of-fit of certain data to such distributions. After some exploration, I came to know that the AD ...
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### Relation between the sample size with the powers of Kolmogorov Smirnov, Cramer Von Mises and Anderson Darling?

I want to know the mathematical relation between the sample size with the powers of 1. Kolmogorov Smirnov, 2. Cramer Von Mises, and 3. Anderson Darling. I have seen many posts and other websites ...
52 views

### Does the null distribution matter when choosing between goodness-of-fit tests?

There are multiple goodness of fit tests such as Kolmogorov-Smirnov, Cramer-von Mises, Anderson-Darling, and Kuiper's. Which one shall one use? There are threads (e.g. 1, 2, 3) and a nice textbook ...
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### What are the advantages (if any) of the Kolmogorov-Smirnov test over other tests?

Given a reference distribution and an unknown sample, we need some statistical test to determine if the unknown sample came from the reference (one-sample test), or given two samples to determine ...
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### Looking for a goodness-of-fit measure for fitting a model to an image

I am trying to fit a model to a noisy image. After fitting, I would like to have some way of assessing the quality of the fit (i.e. whether there are any systematic deviations of the model from the ...
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### How to compare two empirical CDFs obtained from current status data

I have failure time information of a product in the form of current status data, which looks something like this. Observed Time($t_i$) failed ? ($y_i$) 5 hrs 1 6 hrs 0 5 hrs 0 7 hrs 1 ...
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### What is the distribution of the test statistics for Shapiro Wilk, Anderson-Darling, and Lilliefors (KS) tests for normality under null?

Have been researching tests for normality, and have some idea of how some of these tests work from Wikipedia. However, they leave out explaining the distributions of the test statistics under the null ...
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### Why does Anderson-Darling statistic increase as Frequency is increased for my data?

I have been carrying out sieve analysis to estimate the median particle size of a powder. I wanted to check if the data so far followed a normal or lognormal distribution, as I have come across ...
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### Anderson darling test results are similar for multiple variables

I performed the Anderson darling test from scipy.stats on multiple different variables but the test is outputting similar critical values for all the varaibles. Only the test statistics values are ...
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### Kolmogorov-Smirnov inconsistency with increasing dataset sizes

I want to compare two arbitrary distributions and know that Kolmogorov-Smirnov is one such test that can handle any non-normal distribution. I noticed however, that p-values returned by the KS test ...
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1 vote
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### Statistical Test for Randomness

just wanted to ask if it's possible to check whether a given sample of data is drawn from a random distribution? If so, can I use some statistical test like the Anderson-Darling test or Chi-squared ...
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### A-D test for normality

I would like to ask about the critical value for A-D test for normality, I use R to compute the statistic test by this code ad.test(rnorm(10,1,1)) level of significance is 0.05, which critical value ...
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### Comparing P-Values of two tests doing the same task

There are two statistical tests which do the same thing. For instance, they both tell if two samples are generated from same distribution. KS Test (2 samples) and Anderson Darling Test (K Samples). I ...
1 vote
459 views

### Multi-variate two-sample Anderson-Darling test

Suppose we receive a reading of samples taken from a sensor system with multiple variables, which may be assumed as continuous real values. After few days, we receive another reading of samples from ...
1 vote
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### Kolmogorov-Smirnov test results Interpretation-significance

I want to use Kolmogorov-Smirnov test to check how these two distribution at each bin are matching. I took implementation of KS-TEST from here https://docs.scipy.org/doc/scipy/reference/generated/...
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### Why do I get different results of goodness of fit test using AD tests from different R libraries?

I am trying to find the best method for goodness of fit while testing my data with different models of distributions. I need to use AD test. So I have compared results using two different ...
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The Anderson-Darling test statistic is $$A^2 := n \int_{-\infty}^{\infty} \frac{(F_n(x)-F(x))^2}{F(x)(1-F(x))} \, \mathrm{d}F(x)$$ We know that the samples  Z(x) := \frac{\sqrt{n}(F_{n}(x) - F(x))}...
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### Comparing two-sample statistical test results: Kolmogorov-Smirnov and Anderson-Darling

I am not sure how to interpret a given Anderson-Darling criterion as computed from SciPy. Suppose, for example, I have a Kolmogorov-Smirnov (KS) statistic of 0.60 and an Anderson-Darling (AD) ...
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### Kolmogorov Smirnov test vs. Anderson Darling test

I learned that Kolmogorov Smirnov loses sensitivity (power) in the tails, thus it is not adequate for testing goodness-of-fit of fat tailed distributions. However, Anderson Darling test is more ...
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### Why do two implementations of the Anderson-Darling test produce such different p-values?

I want to check the normality assumption of my series I am trying to figure out the way is computed the p-value of the Anderson Darling in R packages, goftest and <...
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### Alternatives to 2-sample Kolmogorov-Smirnov Test?

I have 2 samples with numerous repeating numbers like this: Sample 1: 1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,... Sample 2: 1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,... and I would like to ...
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### Using Anderson Darling test statistic vs p value to infer Goodness of Fit

I have been reading articles recently that discourage the use of p value for hypothesis testing (https://www.sciencenews.org/blog/context/experts-issue-warning-problems-p-values) Rather than using a ...
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When I run ...
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