# Questions tagged [anderson-darling]

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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### 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 ...
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### 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 ...
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### Unexpected behaviour of Anderson Darling test for normality for low sample size

I’m testing the power of the Anderson Darling test to detect deviations from standard normal distributions. I’m calibrating the AD test statistic numerically using python and I noticed an unexpected ...
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### 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 ...
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### Sample Size Guidelines for KS-Test and AD-Test

so I've been looking into the Anderson Darling and Kologorov-Smirnov test because I have datasets with a large number of observations (~6000) and would like to fit distributions to them. They are ...
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### Issue with two-samples Anderson-Darling test with same dataset (scipy anderson_ksamp)

I am computing several two samples Anderson-Darling statistics using the Python scipy.stats.anderson_ksamp function (both samples have $N = 20000$ values), and I ...
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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 ...
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### Power of Anderson-Darling with known vs unknown parameters

I recently ran some AD tests for normality on some data. I ran AD in two modes: (i) With specified (mean, sd) of the normal (ii) With unspecified (mean,sd) These correspond to cases 0 and 3, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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,...
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### 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 ...
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### 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....
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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When I run ...
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### 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, ...
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### Calculating the confidence interval

I have a simple random sample of size 40 which talks about no. of newspapers being sold by a particular salesboy each day. Population standard deviation is not know. I did a normality test on this ...
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### Anderson Darling Test on student-T distribution

I would like to do an Anderson Darling test in R using ad.test() from the package “goftest”. My null hypothesis is H0: Data follows a student-t distribution with 2 degrees of freedom. I receive the ...
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### Anderson-Darling test for normality with estimated parameters

I have a set of measurements coming from a manufacturing processes. I want to test if the measurements come from a normal distribution. If I understadn correctly, it's wrong to use K-S test or A-D ...
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### Is it valid to rank goodness-of-fit based on the value of the Kolmogorov-Smirnov or Anderson-Darling test statistics?

When using Kolmogorov-Smirnov or Anderson-Darling goodness-of-fit tests, is it valid to claim that, because distribution X has a lower test statistic than distribution Y, distribution X is a better ...
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### Scipy.stats.anderson_ksamp negative return values for test statistic

Ok, so I've been trying to run this test on the the iris dataset to see if it flags the clusters within the data as samples that aren't from the same population. from sklearn import datasets iris = ...
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### sample size of Anderson-Darling test

Why must the sample size of the Anderson-Darling test for normality be greater than 7? The function ad.test in some packages in R enforce a sample size $n>7$. ...
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### Gaussian based clustering/partitioning, does it make sense with not much data?

I have a dataset about hourly aggregated mobile phone usage (#calls, #sms, #internetConnections) in one mobile cell. For example I have this data about activity at 8:00am: ...
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### Use of normality test to distinguish gamma from log-normal distribution

I have random population sample data that I would like to describe using a distribution. If I plot the estimated kernel density, the data appear positively skewed and using functions in R such as ...
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### Simulation of KS-test with estimated parameters

We know that the original KS-test has a limitation, requiring the Null hypothesis testing underlying distribution to be fully specified, rather than estimated. But in practice, we usually need to test ...
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### Multiple Sample Equality-of-Distributions Test For Panel Data

Suppose I have repeated time observations for 800 meter sprint for a group of athletes over the course of a season. I would like to test the hypothesis that all the times are drawn from the same ...
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### Anderson-Darling test in 2D time series

Suppose two time series (of light flux). The goal is to determine whether the series are from the same distribution. It is usual to use the Kolmogorov-Smirnov (KS) test in this situation. However, ...
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### Testing for membership in a distribution with one single value

I came across an interesting little quirk when I was coding up a hypothesis test in Python. I was wondering why very time I tested some values for normalcy using the Anderson–Darling test, I was ...
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### Anderson-Darling vs Kolmogorov-Smirnov (Many points in sample)

Previous question In my previous question (Kolmogorov-Smirnov test - reliability) I misused two-sample KS test for normality testing of one-sample data. I was given an advice that I should use one-...
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### Anderson-Darling test - what is adjustment good for

I am trying to understand and implement Anderson-Darling test for normal distribution in C++. I've found Octave/Matlab implementation of Anderson-Darling test here, but the critical values differ from ...