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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How can I express $D_{m,n}$ as a distribution free statistic in terms of $d_l$

Consider 2-sample problem with m and n observations from the mutually independent, absolutely continuous populations $F_X$ and $F_Y$, respectively, define 2-sided kolmogorov-smirnov statistics ...
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Do Dvoretzky–Kiefer–Wolfowitz bounds and Kolmogorov-Smirnov test different hypotheses?

This question is related to my previous question that was answered excellently by Matt Krause. I am trying to compare two data vectors to find out if they come from the same distribution. I computed ...
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53 views

Computing Dvoretzky–Kiefer–Wolfowitz bounds in MATLAB

When I run the Kolmogorov-Smirnov test (kstest2 function in MATLAB) on two given data vectors, I get the value of KS Statistic. How should I compute Dvoretzky–Kiefer–Wolfowitz (DKW) bound using this ...
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Statistical test to check if mean of two groups are “significantly” same [duplicate]

Is there a statistical test, to check mean of two group is "sigificantly" same. Something opposite to Wilcoxon test. I was thinking may be running Wilcox test and if it not significant, then check the ...
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Reference request: Using randomized interpolation to apply KS-Test to discrete distributions

I'm dealing with $n$ samples $X_1,\ldots,X_n$ from $n$ different (but related) distributions with CDFs $F_n$. If all the distributions were continuous, I could use the transformation $U_i := ...
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Comparing distributions from a factorial design

I have the following experimental design: I have six animals, where three received treatment and the other three were used as control (so treatment and control animals are not paired). From each of ...
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136 views

Can you calculate the power of a Kolmogorov-Smirnov test in R?

Is it possible to do a power analysis for a 2-sided Kolmogorov Smirnov test in R? I am testing whether two empirical distributions differ using ks.test(), and am looking to add a power analysis. I ...
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Proof of Kolmogorov-Smirnov test

Could someone provide me a reference, preferably a book, where I can find detailed proofs and explanations of the Kolmogorov-Smirnov test (including the two-sample variant) and the derivation of the ...
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250 views

Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed?

I'd like to check if distribution of my data is significantly different from a uniform distribution. I know that the K-S test is used for checking the normality of data, but I wonder if it can be ...
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Interpretation P value one sample KS test

I have some difficulties with understanding the output of the KS test in R. Suppose I want to test whether my data follows a exponential distribution with rate 1/117.5 with a significance level ...
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Comparing two distribution known by their deciles

I am trying to compare a travel time measuring device with a reference device. The assessed device only provide the decile (+min and max values) and not all the measured individual travel time. I am ...
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50 views

Does the position at which maximum distance occurs in a KS test make a difference?

From my understanding of the KS test, fromt the CDF of two datasets, it measures the distance between the two distributions at various points and and compares the 'maximum distance' to a predefined ...
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141 views

How do you interpret Kolmogorov-Smirnov Test results in R?

I'm using 50,000 values of data. I can't perform a K.Wallis test in R because my data amount is bigger than 5000. Therefore I considered to use Kolmogorov-Smirnov test. I guess that my data follows a ...
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2answers
67 views

Meaning of significance level and critical values for kolmogorov smirnov goodness of fit test

I'm new to using goodness of fit tests and am encountering what I guess is a beginners misunderstanding of how the tables for critical values and different significance levels have to be read. I have ...
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61 views

Low p-value in test of uniformity of uniformly distributed data?

First we generated 10 numbers from a $U(0,1)$ then performed a Kolmogorov Smirnov test for q uniform distribution. Why is the p-value small? ...
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When KL Divergence and KS test will show inconsistent results?

I know that Kullback–Leibler divergence and Kolmogorov–Smirnov test are differnt and should be used in different scenarios. But they are similar in many ways and given two distributions, we could ...
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153 views

Reproducibility of the two-sample Kolmogorov–Smirnov test

I am using the two-sample Kolmogorov–Smirnov test to check if two datasets have the same underlying distribution. I can regenerate those two datasets as many times as I want. When I apply the test, ...
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Kolmogorov-Smirnov test: horizontal variant?

The Kolmogorov Smirnov test is based on the maximum vertical distance between the ECDFs of two provided samples. Is there a variant that checks the maximum horizontal distance?
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31 views

Compare cumulative distribution functions of several function point counters

Function point counters are used to measure the size of software. However, they are believed not to deliver exact results. Different measurements sometimes produce different results. The performance ...
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31 views

Interpreting Two-sample Kolmogorov-Smirnov with jerzy

I am using the project jerzy to run a Two-sample Kolmogorov-Smirnov test in Javascript, regarding another question I asked on stats.SE: Timing attacks: When the time to complete two different tasks ...
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Compare two sets of correlations coefficients

I have two matrices, A and B, of the same size. Each row of A corresponds to a row of B. Theory predicts that some rows of A will negatively correlate with corresponding rows of B. I am interested in ...
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How to determine which distribution fits my data best (R)?

I have a dataset and would like to figure out which distribution fits my data best. I used the fitdistr() function to estimate the necessary parameters to ...
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Understanding multiple KS tests

I have read these two questions Why are p-values uniformly distributed under the null hypothesis? and Understanding scipy Kolmogorov-Smirnov test And this inspired me the following experiment. I ...
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If my histogram shows a bell-shaped curve, can I say my data is normally distributed?

I created a histogram for Respondent Age and managed to get a very nice bell-shaped curve, from which I concluded that the distribution is normal. Then I ran the normality test in SPSS, with n = 169. ...
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Do any statistical tests compare distributions when one has far fewer observations?

I've been researching different methods to compare two distributions for equality, or inequality rather. I want to compare actual user performance against projected performance, after a particular ...
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Compare non-gaussian distributions and evaluate sampling process

I have a 150,000 datapoints (continuous values between 0 and 1) and I am running a process that averages groups of smaller samples based on some other data values and results in ~100,000 datapoints. ...
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what is the algorithm of getting maximum $D$ value in ks.test?

When I was writing R code to plot two empirical cumulative density curves, I came across ks.test in R. I looked into the code of ...
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Bootstrapping and Kolmogorov-Smirnov

Here is an experiment I did: I bootstrapped a sample $S$ and stored the results as empirical distribution under the name $S_1$. Then I bootstrapped $i=10000$ times in a row the same sample $S$ and ...
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Why did KS test give significant result?

I have two samples where I want to tell if their distributions are significantly different. I conducted a Kolmogorov-Smirnov test which rejected the null hypothesis (D=0.0983, p=2.14e-11) leading me ...
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345 views

Kolmogorov-Smirnov vs Mann-Whitney U When There Are Ties

I have a dataset consisting of rank data, some 100 cases and 2 groups. (The 2 groups contain about 1/3 and 2/3 of the cases.) I would like to test whether the two groups differ with respect to median ...
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comparing two CDFs with different x-ranges?

I was wondering what is an appropriate method to quantitatively compare two CDFs where the x-ranges are different. For example, lets say CDF1 has x values ranging from 0 0.5 and CDF2 has values ...
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225 views

Testing whether data follows T-Distribution

I am involved in a project where I need to check whether my data follows a T-distribution with N degrees of freedom for a given value of N. I know that Kolmogorov-Smirnoff can be used, but is there ...
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Can I use K-S test to distinguish distributions?

I am using the kolmogorov smirnov test to differentiate between distributions. My example is below where I am comparing DATA2 and DATA3 to DATA1. From the image, I was hoping to quantify that DATA1 ...
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Kolmogorov Smirnoff and Predictive Analytics

I am trying to interpret the Kolmogorof Smirnoff test in the case of predicitve analytics to compare three models: a neural network, a decision tree and a logistic regression. The target variable is ...
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157 views

Nonparametric bootstrap of one-sample Kolmogorov-Smirnov goodness of fit test

I'm fitting a Weibull distribution to some forestry data and I want to perform a test of whether or not there is sufficient evidence to indicate that the data does not come from a Weibull ...
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Kolmogorov-smirnov two-sample confidence level [duplicate]

I do not find information about how to calculate the $c(\alpha)$ "by hand" (see wikipedia article for two samples: http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) for the formula: $ ...
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Two sample Kolmogorov-Smirnov test for the stochastic dominance

I'm trying to use KS test to determine whether one group of data is scholastically dominates another. So I'm studying dataset regarding performance of companies, which are divided into 2 groups. ...
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62 views

How am I using KS test incorrectly in R?

Here are the codes I input into R: ...
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45 views

Difference between two data distributions

I have the following problem: I have two datasets: A and B. From each of the datasets, I extracted the same features. I also know the data labels. So, I would like to perform 10-fold CV to see how a ...
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90 views

Univariate Kolmogorov-Smirnov test instead of multivariate

Since it is not easy to apply a Multivariate Kolmogorov-Smirnov test for two samples, I thought: is it possible to compare the different statistics with the univariate KS? For example: Object 1: ...
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Testing if the mean of one data set is bigger than the mean of the other data set [duplicate]

I have two data sets, i.e., the number of flowers measured in field A and in field B. Each data set has about 40 samples. I want to do a test to check the hypothesis that field A has more flowers than ...
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42 views

Compare distributions of two ECDFs

I am investigating the achieved mark in a math test in grade 8 in two different cities. The plot shows the two Empirical Cumulative Distribution Functions (ECDF). How can I evaluate whether these ...
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Multivariate Kolmogorov-Smirnov for two samlpes

Let’s say we have data of some fruits and we want to consider different statistics for each fruit (there are various samples for each statistic). For example: Watermelon: Sugar: 50, 57, 36… Water: ...
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Evaluate goodness-of-fit of estimation of Pareto-like distribution

I would like to evaluate the goodness-of-fit of the following (Pareto-like) distribution: $$ f(r) = \sigma \centerdot r^{-\rho} $$ The function estimates the population of cities given the rank $r$ in ...
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Test identicality of discrete distributions

Is there a standard way to test whether two vectors were drawn with the same discrete distribution in R? Something like a Kolmogorov-Smirnov test, but for discrete distributions. I think two-sample ...
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1answer
168 views

Understanding scipy Kolmogorov-Smirnov test [duplicate]

I'm trying to understand the Kolmogorov-Smirnov test using a very simple example. I generate a set of random, uniform values between 0 and 1.0. I then test that these values are from a uniform ...
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How to justify a distribution fit is good

I've got 5 datasets to which I would like to fit a model distribution. I'd like to use the same distribution for each dataset but with different parameters. So I use MLE to compute the best parameters ...
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116 views

Can I use Kolmogorov–Smirnov test on my Data?

I am not good in statistics so I desperately need your help. So I have this dataset of distributions, and I want to know if I can use the KS-test on it. the Idea is saying that the feature's ...
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2 sampled ks test in r

I need to do a two-sample Kolmogorov-Smirnov (KS) test in R, only I don't understand the formulae and how it works when I look it up. I suspect this is because I ...
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comparing normal distributions using a two sample kolmogorov-smirnov test

I've been redirected here from another forum... I have used a two sample Kolmogorov-Smirnov test to compare the distributions of two sets of data. Basically I am comparing the error distributions ...