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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 ...
Édio Renato Fávaro's user avatar
2 votes
3 answers
60 views

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 ...
Kώστας Κούδας's user avatar
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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 ...
DevD's user avatar
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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 ...
user391733's user avatar
3 votes
1 answer
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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 ...
Richard Hardy's user avatar
14 votes
2 answers
740 views

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 ...
Number's user avatar
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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 ...
Ewout's user avatar
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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 ...
aishik roy chaudhury's user avatar
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1 answer
92 views

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 ...
jojorabbit's user avatar
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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 ...
sc_zuko's user avatar
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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 ...
Waqas's user avatar
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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 ...
lazarea's user avatar
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1 vote
3 answers
138 views

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 ...
MathNewb's user avatar
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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 ...
Statistical scientist's user avatar
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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 ...
rockstone435's user avatar
1 vote
1 answer
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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 ...
rockstone435's user avatar
1 vote
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140 views

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/...
Omkar Salunke's user avatar
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1 answer
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How to show (algebraically) the C-vM statistic is a special case of general form of Anderson-Darling

Anderson and Darling proposed the GoF $n\int_{-\infty}^{\infty}[F_{emp}(x)-F(x)]^2 \phi (F(x)) \; dF(x)$ where $\phi (F(x))$ is a weight function. How can I obtain Cramer-von Mises statistic $CM=\frac{...
M.Ramana's user avatar
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1 answer
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Non-normal data, non-parametric tests for normality, and determination of statistical parameters

I have a database with more than 50000 observations. For the determination of normality by means of statistical contrasts, since the Shapiro-Wilk test cannot be used due to the large number of ...
Daaviid's user avatar
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How do I calculate effect size for Anderson-Darling test?

I'm looking at the list of tests and effect sizes on https://cran.r-project.org/web/packages/statsExpressions/vignettes/stats_details.html, but I can find any way to calculate effect size for Anderson-...
user1828605's user avatar
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0 answers
263 views

Anderson-Darling test: p-value reliability when testing fitted distribution

I have a question regarding the A-D test, and perhaps goodness-of-fit tests altogether. I fitted a dataset to a long list of distributions. According to A-D, a Wakeby distribution provides the closest ...
Stefan's user avatar
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2 votes
0 answers
97 views

Can you use a test statistic like Anderson–Darling for parameter estimation?

I was looking at the Wikipedia article for maximum spacing estimation and this got me thinking. The idea behind this method is that if you know the true distribution of the data, then its CDF should ...
Sjoerd Smit's user avatar
2 votes
1 answer
565 views

Two-sample Kolmogorov-Smirnov, Anderson-Darling, and after?

I am trying to investigate the differences between two datasets. Each one is composed of 20 000 elements obtained from a Monte-Carlo method whose implementation slightly differs in both cases. I'd ...
Clej's user avatar
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P value calculation for Anderson Darling normality

For p-value calculation I use (in c++) following equations I found on the internet ...
vlad's user avatar
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0 answers
157 views

Highly fluctuating value of test statistic in Anderson Darling test

I am trying to verify whether my sampled data is from a population with a Gamma density function. My plan is to do this by means of the Anderson-Darling test. Before doing so, I thought it would be ...
Rutger Mauritz's user avatar
2 votes
1 answer
475 views

Hypothesis test for arbitrary distribution

Given a sample of $N$ observed values I'd like to test the null hypothesis that they arose from an arbitrary PDF (for which I have the analytical form). There are tests in place that can handle some ...
Gabriel's user avatar
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6 votes
1 answer
2k views

Normality test for discrete values of a continuous variable

I have a dataset with several hundred pH measurements from a factory line. This dataset will be used to infer process capability using Minitab. On a physical basis, pH is a continuous scale (being ...
Markos Strofyllas's user avatar
1 vote
0 answers
1k views

testing for continuous uniform distribution in python

I'm setting up a statistical experiment. I am investigating whether a list of real values follows a continuous uniform distribution. In scipy, there is kstest to do it, I find it not robust after ...
pedro colombino's user avatar
0 votes
1 answer
145 views

Checking the normality of a large sample?

If I want to analyze a large sample size (N = 50.000) of continuous data ($ revenue) from an A/B test, what would then be the best way to check for normality? Thanks in advance!
JohnE230's user avatar
2 votes
0 answers
209 views

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 ...
Runciter's user avatar
5 votes
1 answer
192 views

Confusion about Anderson-Darling test

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))}...
user14717's user avatar
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0 answers
114 views

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) ...
user258204's user avatar
7 votes
1 answer
2k views

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 ...
Master Shi's user avatar
5 votes
1 answer
3k views

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 <...
dangulo's user avatar
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4 votes
1 answer
2k views

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 ...
superasiantomtom95's user avatar
0 votes
0 answers
198 views

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 ...
Jonathan Dunne's user avatar
3 votes
0 answers
394 views

How to test for conditional independence with mix of categorical and continuous data

I wish to test for conditional independence between $X$ and $Y$ given $Z$. However $X$ is continuous, while $Y$ and $Z$ are categorical variables. My idea is to test if $P(X|Z = z) = P(X|Y = y, Z = z)...
Ben Lansdell's user avatar
2 votes
0 answers
415 views

Anderson-Darling test for any distribution with unknown parameters

I have been spending the last two days trying to construct a solid answer to the question: What is the distribution that best describes my sample? I did the following: Plot the histogram (nomalized ...
gioxc88's user avatar
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3 votes
1 answer
570 views

Is the Anderson-Darling test similar to the Kruskal-Wallis test to compare more than 2 groups?

I would like to compare more than 2 groups (their dependent variable is not distributed normally). Can I use the Anderson-Darling test like I would use the Kruskal-Wallis test? I have no specific ...
statisticianwannabe's user avatar
0 votes
0 answers
205 views

Is there an equivalent to the Anderson-Darling test for categorical data?

I have categorical data of the following form: |Total|Pos|Neg In | 6 | 4 | 2 Out | 11 | 4 | 5 There are two categories: In/Out and Positive/Negative. All ...
cosmosis's user avatar
1 vote
0 answers
78 views

Kolmogorov-Smirnov test with PDFs instead of data points?

I don't have a background in statistics, so I don't know exactly how to phrase my question, and I am likely misusing some of the statistic lingo. I have a model which I am fitting to 30 sets of data,...
Steven Stetzler's user avatar
1 vote
1 answer
95 views

Checking closeness of a mixture weibull and a mixture normal distribution to sample data

I have a sample data whose histogram shows a two peak distribution. So I generated two distributions which is the Mixture (average) of two (1) two weibull distributions (2) two normal distributions I ...
Honeybronzed's user avatar
2 votes
1 answer
478 views

Interpretation of the test statistics of ks.test, ad.test, and wilcox.test

I am currently writing my Master's Thesis and I have a question in regards to the Kolmogorov-Smirnov test (ks.test in R), Anderson-Darling test (ad.test in R), and Wilcox/Mann-Whitney U test (wilcox....
tiba14ab's user avatar
2 votes
1 answer
2k views

Can we compute P-value of Anderson Darling Test with AD statistic without using the tables given

I am fitting my experimental data with different distributions, I am computing Anderson Darling statistic for my data and theoretical distributions. I want to compute P value from Anderson Darling ...
user150427's user avatar
0 votes
1 answer
108 views

How to find the samples that contribute to the differences between two distributions?

I have two very large distributions, I did anderson-darling test on these two distributions and the result shows they're from different populations, significantly. Now I want to know which samples in ...
Yan's user avatar
  • 216
5 votes
1 answer
2k views

Distribution specificity of the Anderson-Darling test

When fitting a (gamma) distribution to a data sample and in-turn estimating its parameters (shape/scale), a Kolmogorov–Smirnov goodness-of-fit test is no longer applicable as the distribution being ...
AnnaSchumann's user avatar
5 votes
1 answer
2k views

R and SAS produce the same test-statistics but different p values for normality tests

I use Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests to examine the normality of residuals of an OLS regression. It puzzles me that R and SAS, despite giving the same test-statistics ...
Ye Tian's user avatar
  • 629
1 vote
0 answers
78 views

Maximizing the p-value associated with a goodness-of-fit test

Problem (concrete version): Let $p = p(T, \mathcal{D}, \mathbf{X})$ be the $p$-value associated with goodness-of-fit test $T$ (i.e. Kolmogorov-Smirnov, Anderson-Darling, Cramér–von Mises) on ...
Tom Chen's user avatar
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8 votes
1 answer
3k views

Why does scipy.stats.anderson_ksamp give a p-value of over a million for these data? [closed]

When I run ...
Esteemator's user avatar
26 votes
2 answers
23k views

2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises

I was wondering what are the criteria to use Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling when comparing 2 ECDFS. I know the mathematics of how each differ, but if I have some ECDF data, ...
Plinth's user avatar
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