The Kolmogorov-Smirnov test is a test for goodness of fit of data to a distribution. It is often used to test whether a variable is normally distributed.

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What is the two-sample CDF of of $D^{+}$ and $D^{-}$ from the one-sided Kolmogorov-Smirnov Test?

I am trying to understand how to obtain $p$-values for the one-sided Kolmogorov-Smirnov test, and am struggling to find CDFs for $D^{+}_{n_{1},n_{2}}$ and $D^{-}_{n_{1},n_{2}}$ in the two-sample case. ...
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Does it make sense to perform a one-tailed Kolmogorov-Smirnov test?

Is it meaningful and possible to perform a one-tailed KS test? What would the null hypothesis of such a test be? Or is the KS test inherently a two-tailed test? I would benefit from an answer that ...
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Where can I find the limiting distribution of the Kolmogorov-Smirnov distance in R? [migrated]

While doing an experiment on importance sampling, I simulate values of Kolmogorov-Smirnov distances $$ D_n = \max_x |\hat{F}_n(x)-F(x)| $$ where $n$ is the size of the original importance sample and ...
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29 views

two-sample Kolmogorov-Smirnov test in R p-value confusion

I'm confused about the appropriate interpretation of p-values returned by the two-sample Kolmogorov-Smirnov test (ks.test) in R. In slide 23 of this presentation about non-parametric two-sample ...
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28 views

Kolmogorov-Smirnov of two heart rate samples

I'm accumulating a lot of vital signs from emergency department patients, and would like to assess if different features yield significantly different distributions. Eg. for heart rate I have 888.424 ...
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75 views

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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20 views

Kolmogorov–Smirnov “with perturbation”

Let $F$ be known continuous CDF of a continuous R.V. and $F_n$ represent the empirical CDF for sample of size $n$, hypothesized to be drawn from $F$. The Kolmogorov–Smirnov statistic is $D_n :=sup ...
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71 views

Q-Q plot and KS test

I have a question regarding the QQ plot and KS test. I have a sample which is some positions on genome, and I calculated the distance between these positions. And I generated the null distribution ...
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847 views

My distribution is normal; Kolmogorov-Smirnov test doesn't agree

I have a problem with the normality of some data I have: I've done a Kolmogorov test which says it isn't normal with p=.0000, I don't understand: the skewness of my distribution =-.497, and the ...
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1answer
80 views

Statistical description of how two distributions are different

I am have a collection of events recorded in two separate conditions, and I have measured the duration of each one of them. I would like to know two things: 1) are the distributions of durations ...
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27 views

How to compare two independent KS tests?

I have two vectors of observed data obs1 and obs2, and two vectors of expected data exp1 and ...
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175 views

Why can't one generalize the Kolmogorov-Smirnov test to 2 or more dimensions?

The question says it all. I've read both that one can't generalize KS to a dimension equal or larger than two, and that famous implementations like that in Numerical Recipes are simply wrong. Could ...
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21 views

What is the best test to compare pattern similarity in different condition?

I have several subjects, for each subject I have two measure (pre and post treatment) of several parameters, I have calculated a multivariate similarity measure (Mahalanobis distance) between each ...
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2answers
97 views

Is there a simple equivalence test version of the Kolmogorov–Smirnov test?

Has two one-sided tests for equivalence (TOST) been framed for the Kolmogorov–Smirnov test to test the negativist null hypothesis that two distributions differ by at least some researcher-specified ...
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57 views

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 ...
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5answers
158 views

Kolmogorov-Smirnov test - reliability

Description I want to use Kolmogorov-Smirnov test to check how given clusters of 1D points differs from normal distribution (original question here: How to test which data match model at best). I am ...
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3answers
150 views

Testing if two non-normal distributions are significantly different (K-S or Wilcoxon or both?)

The Big Question I'm trying to decide between K-S and Wilcoxon (or something I haven't thought of yet) for two data sets I want to prove are significantly/insignificantly different from one another ...
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68 views

how to interpret KS test or Shapiro wilk test for ordinal criterion variable?

Here Rank is my dependent variable from level (Strongly disagree to strongly agree) and Pre_Sales_support is one of the independent variable. Due to smaller sample size of 15, I am taking ...
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233 views

Plot Pareto tails in QQ-plot for log-normal distributions

I'm working on samples that I'm trying to fit into log-normal distributions. In some cases, Kolmogorov-Smirnov test statistics is something like D = 0.0056 with an associated p-value of 0. Hence, my ...
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28 views

Finding the probability of normality via Anderson-Darling, Shapiro-Wilk , and Kolomogrov-Smirov

I have quite a few distributions that were generated by some system, and I am trying to find the probability of accordance to normality for these distributions. So, the probability of accordance to ...
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217 views

Which test is better suited to compare averaged versus single data sets

I have a light curve, that is photon count rate versus time, of an astronomical object. These data are periodic, since the source signal is periodic. I can fold the data with the period and obtain an ...
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Generalization of one-sample Kolmogorov-Smirnov test for non identically distributed data?

Is there a standard approach for testing goodness-of-fit to a probability distribution when the samples are independent but not identically distributed? In other words, given the data $\{\{x_1, y_1\}, ...
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53 views

how do normality check in ks test assess for equivalence or difference in data sets?

I have a series of data of photon counts versus time. These data are periodic, then I can fold them and obtain an average profile of the data. Nonetheless, some variations appear sometime in the ...
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Mann-Whitney U and KS tests in R are not producing significant results [duplicate]

I wish to compare two test data sets using the Mann-Whitney U and KS tests in R. As a start, I thought to compare two similar sets (an A/A test) expecting to see a highly significant indication of ...
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49 views

PIT on a sample with m bins, and KS test used to estimate a good value for m

I know about PIT, but this works only when you know the distribution, or at least have a strong hint. What I am trying to achieve is to transform a given sample into an equivalent sample with ...
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28 views

In testing random numbers, what other tests should I use to complement the Kolmogorov-Smirnov? [duplicate]

I'm using the Kolmogorov-Smirnov test to test a random number generator. I'm wondering if there are other tests that I should implement as well. So far, I've looked at the equidistribution and serial ...
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56 views

Kolmogorov-Smirnov test for large sample [duplicate]

I am investigating if an exponential distribution is a good fit for a large sample of data (200) I have. I have already looked at a histogram but was wanting to investigate further. I was going to use ...
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92 views

How to guess a curve distribution from count data

I have a sample composed by 2500 count data values. I've plotted in R the corresponding histogram and ecdf. I've run the One-Sample Kolmogorov-Smirnov test to check if the distribution is either ...
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55 views

goodness of fit for censored data

How to estimate the goodness of fit of a sample containing censored values? There is some older work on the matter (here), but i'd like to know if there is anything more modern. I think a reasonable ...
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1answer
20 views

How to test if a value is over-represented in one sample vs another

I have two multinomial data samples that both have N discrete categories. I know that a Kolmogorov-Smirnov test will let me know if the distributions of the two ...
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41 views

Kolmogorov-Smirnov with parameter estimates

Can someone explain in as clear a (formalish mathematical) way as possible why the KS test in original form with parameter estimates is unreliable?
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106 views

Test for difference between 2 empirical discrete distributions

I have test data where I have several large samples from discrete distributions which I am using as empirical distributions. I am wanting to test whether the distributions are actually different and ...
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32 views

Is it meaningful to use Kolmogorov-Smirnov test in small sub sample?

I have a data set with around 14,000 observations. This is a sample data set not the population. I have fitted a model (based on fuzzy logic) based on this data. I have 27 actual values(from 14,000 ...
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51 views

Convergence of Empirical cumulative distribution functions?

I am exploring the cumulative distribution function of two samples. I am comparing the distribution of observations in which a focal animal was disturbed with the distribution of observations in which ...
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242 views

Kolmogorov-Smirnov test?

I am studying disturbance caused by ship traffic to a small seabird. I observed focal animals for a set amount of time and record whether or not they fly from the water during the observation. This ...
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919 views

Which to believe: Kolmogorov-Smirnov test or Q-Q plot?

I'm trying to determine if my dataset of continuous data follows a gamma distribution with parameters shape $=$ 1.7 and rate $=$ 0.000063. The problem is when I use R to create a Q-Q plot of my ...
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361 views

Evaluating goodness of fit for distributions (e.g. LogNorm, Gamma, …) with estimated parameters using KS tests (and R)

Currently I am trying to find a well-known distribution that fits to my positive skewed dataset (n=70) the best. First I used the fitdistrplus R package to estimate ...
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63 views

Is it possible to calculate the probability that two samples are drawn from the same distribution?

Given $X_1$..$X_n$ and $Y_1$..$Y_n$ drawn from unknown distributions $F(x)$ and $G(x)$ respectively, statistical tests such as two-sample Kolomogorov-Smirnov, Cramer-von Mises, and Anderson-Darling ...
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122 views

Interpretation and usage of Kolmogorov-Smirnov Test in Python

I have a sample of data, and I want to know weather it is Gaussian-distributed or not. The mean of my data is not zero. To check weather I'm using the K-S test correct, I generated some ...
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30 views

Kolmogorov-Smirnov test using half the sample to estimate mean and variance and testing against the other half moments for normality

using a monte carlo simulation Im just trying to test the null hypothesis for normality in a sample that splits N values into 2, using the first N/2 values to estimate the sample mean and variance, ...
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220 views

Small sample sizes and the Kolmogorov-Smirnov test

I have split my data set into four categories but one of them only has four data points in it. I have run K-S normality tests on the other three categories which are each normal and when the data ...
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1answer
124 views

Is a p-value correction necessary for assessing pairwise location shifts on centered data?

I am currently assessing whether or not a location-shift can be assumed in non-parametric comparisons to be able to formulate the rejection of the null hypothesis in other terms than the probabilistic ...
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181 views

How to compare two samples of frequencies with categorical x values where one is subset of the other

I am trying to compare two arrays of frequencies. The second is a subset of the first. I want to know if the second is a representative of the first. The arrays are: ...
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91 views

Similarity between two sets of random values

I have two sets of random floats between [0,1], each one with a different number of elements: $$A = \{0.3637852, 0.2330702, 0.1683102, 0.2127219, 0.0152532, ..., N_A\}$$ $$B = \{0.4541056, 0.7521812, ...
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Determining which pair of empirical distributions is the most similar

I'm looking at three discrete (seven-option) survey questions that were asked on two different surveys (100 < N < 150 for each question). I've paired up the six answer distributions so that each ...
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107 views

Explain the meaning of $\alpha$ in a Kolmogorov-Smirnov two-sample test

The Wikipedia article on the two-sample Kolmogorov-Smirnov test states that: The Kolmogorov–Smirnov test may also be used to test whether two underlying one-dimensional probability distributions ...
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Calculating the Kolmogorov-Smirnov coefficient

I need to calculate the coefficient of the Kolmogorov-Smirnov test for any given null hypothesis rejection level. For example, have a look at the table in this wikipedia entry. It only gives ...
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297 views

Kolmogorov-Smirnov test strange output

I am trying to fit my data to the one of the continuous PDF (I suggest it to be gamma- or lognormal-distributed). The data consists of about 6000 positive floats. But the results of the ...
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491 views

What is the test statistic in Kolmogorov–Smirnov test?

I am reading the Wikipedia page on the Kolmogorov-Smirnov test, specifically the section titled Kolmogorov_distribution. $x$ is $D_\text{max}$ in the CDF $Pr(k\leq x)$? My question is the number of ...
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132 views

How can the Kolmogorov-Smirnov test be used/interpreted?

The test of Kolmogorov-Smirnov (K-S) is a traditional test of normality, although Shapiro-Wilk test (S-W) is applied more frequently than K-S (Arango, 2012). I am not an expert in statistics, so my ...