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 to estimate ratio of variances?

Suppose we have two time series generated by \begin{align} x_t &= \sigma_t\,e_t \\ y_t &= c\,\sigma_t\, f_t \end{align} where $e_t$ and $f_t$ are IIDs with mean zero and unit variance. We ...
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Two-sample Kolmogorov–Smirnov test with weights

I have to compare two datasets. The first is real data, while the second is a simulation. I want to look just to one variable in the datasets, and testing if it is compatibile between data and ...
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Can K-S goodness-of-fit be used on estimated models? [duplicate]

For example, for a dataset generated from lognormal distribution, I estimate a normal distribution from that data (using maximaum-likelyhood or whatever methods). Then, can I perform K-S test to ...
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How to check for the distribution stability?

I need for verifying that the training set I'm using to build a model is equally distributed to the test set. The model is for prediction purposes and I think it is necessary the 2 samples are ...
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Comparing two (or more) discrete distributions

I would like to know what the most powerful way of comparing two (or more) discrete distributions is. I know that the Kolmogorov-Smirnov test could be used (if corrected for the discrete ecdfs), ...
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Goodness of fit test for bivariate distribution?

I have a dataset which is x-y distributed, and I fitted a model for it. (see below, left and right) How can I test the goodness of fit for the model I fitted? ...
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Comparing two ECDFs using Kolmogorov-Smirnov test (alternative hypothesis)

I am taking measurements of a computer system performance over time and I'd like to understand if the performance is degrading or improving as time passes.. After doing some research, I picked the KS ...
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How to perform a Kolmogorov–Smirnov test for a Poisson distribution in Stata?

I have a sample with count variables, i.e. overdispersed data. My data looks like it is distributed as either a negative binomial distribution or a Poisson distribution. I want to test these two ...
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52 views

Check if distribution is bell-shaped

I am not necessarily interested in testing normality, but at least ensure that: The mean is near 0 There is single mode Tails are thinning out as you go further from the mean Any ideas?
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53 views

Normality test with large data set

I think I am dealing with this issue http://www.r-bloggers.com/normality-tests-don%E2%80%99t-do-what-you-think-they-do/ I have large data set(10k data points) that slightly diverges from normal, and ...
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2 sample KS test for time series data - portion vs. whole

I have time series data and I want to know whether preserving only a limited portion (say first 300 seconds) and discarding the rest would still leave me with a good estimate of the shape and spread ...
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Why would the Critical Values increase as you decrease the Level of Significance for the Kolmogorov-Smirnov Goodness of Fit Test?

This same exact (similar) question is posted on this thread: Why does the critical value varies inversely with the level of significance in hypothesis testing? However, that question and its answer ...
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Multiple sampling problem

I have a question about multiple sampling. I estimated parameters of lognormal distribution for some dataset. Then I generate 1000 samples of size 1000 from this dataset and test with ...
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KS-Test in R comparing several distributions

I have the following situation: A plot consisting of 4 sub-plots(A-D), each have N trees on it with the diameter d. My aim was to test if the diameter distributions are the same in the 4 subplots and ...
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58 views

Two-sample Kolmogorov-Smirnov test with errors on data points

Short version I want to test if two samples, which follow a skewed distribution, can be distinguished from each other. A Kolmogorov-Smirnov statistic for two samples would be sufficient if there was ...
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61 views

Kolmogorov-Smirnov test with dependent data

Let's say, I have 100 students, each of them have 2 scores: reading score and writing score, so basically I will have 2 vectors with the length of each is 100. I want to test the distribution of ...
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Probability that sample distribution of nominal variables came from the population

I received a list of approximately 500 social security numbers that I noticed tended to start with a certain number. I plotted the distribution of the numbers over the population of several million it ...
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Interpretation of Kolmogorov-Smirnov test result

How do I interpret the following output of the Kolmogorov-Smirnov [KS] test? [shown below, with reproducible example in R] Also: Can the KS test be used for predictive model diagnostics? ...
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Kolmogorov-Smirnov vs simple area difference estimation to compare two statistical models

Could anyone explain, or point some references that I can locate this, how KS compares to the relative area estimation method? It is known that Kolmogorov-Smirnov, among other famous similar ...
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When using Kolmogorov-Smirnov equivalence test approach, does a large number of samples invalidate the test?

I've been using the Kolmogorov--Smirnov test to test for equivalence between two sets of data. I have around 150 samples in each dataset. Following the process for Two One-Sided Tests in this ...
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Can you use the Kolmogorov-Smirnov test to directly test for equivalence of two distributions?

There has been talk on other questions of how one might use the Two One-Sided Tests (TOST) approach for the Kolmogorov-Smirnov (KS) test, but I was wondering whether it was possible to directly use ...
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37 views

Test for very large sample

I have a cellphone income data. and i want to compare 2 groups. First group is the treated group, who got a promotion campaign. The second is a control group. I use Wilcoxon and Kolmogorov-Smirnov ...
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25 views

compute p-value for test conditions vs baseline conditions

Generally: I am interested in seeing if there is a statistically significant difference between baseline and the test conditions, given the null hypothesis that my test conditions are changing due to ...
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Suggest a (nonparametric?) test for the difference between two strictly-positive distributions

$\mathbf{X}$ is a $n\times p$ matrix of data. I'm treating $\mathbf{X}$ as having a multivariate normal distribution with some arbitrary covariance structure. $\mathbf{Y}$ is a $(m<n)\times p$ ...
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Matlab: check if normal distributed

I have some matlab code given from my advisor at university to check if my data is normal distributed: ...
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Comparing accuracy of two non-parametric predictors

I have a quantity x_i that I have n measurements for. I also have for every point two separate non-parametric and non-symmetric distributions A_i and B_i that are supposed to predict the quantity ...
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Gibbs Sampling Parallel convergence

I have a Gibbs Sampler. I am running 1000 parallel walks of the sampler. For any given walk I use the 2 value Kolmogorov Smirnov test to determine if convergence is reached within that instance. I ...
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compare multiple size frequency distributions

I have a dataframe with annual size frequency distributions: ...
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Help me understand a step of the procedure for KS test with estimated parameters

I read the following procedure to perform KS test with estimated parameters Testing whether data follows T-Distribution At first I couldn't make head or tails of it, partly because I mistaked the ...
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Kolmogorov-Smirnov vs. Kuiper test

I would like to compare two 2D distributions with quantitative variables, illustrated here: For each "x", they are several measures "y". I can't assume these distributions are parametric. A ...
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148 views

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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KS test for normality on residuals from OLS vs. MLE

This is a conceptual issue. Suppose, one wants to test the residuals $e_t$ from the regression for normality. So, he runs the regression, obtains the estimates of error variance $\sigma^2$, and forms ...
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Distribution analysis “too uniform” - need help understanding my result

I have $n>1000$ vectors of size $k=20$, sampled from an unknown source that I would like to find their distribution. They appear uniform, so I run the KS test with $\alpha=0.1$ to check. If this ...
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Two sample one-sided Kuiper Test and KS-statistic

With the KS-Test it is possible to conduct a two sample one-sided test between two different random samples $A$ and $B$ to test whether one CDF is larger or smaller than the other, i.e. is $CDF_A$ ...
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How can I test variance explained by the factor group if each subject in the group comprises a different number of measurements?

The data structure I have 2 groups with 30 subjects each. Each subject has a different number of fibers (approximately 46000 +/- 3000) of different length (see histogram). My goal is to determine how ...
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Splitting dataset at intersection of 2 ECDF before ks.boot analyses

This is my follow-up to an earlier post Help with understanding the ks.boot test results. I have an example pair of datasets: http://pastebin.com/s6ATRLDC and http://pastebin.com/hEc7Mqhp. I want to ...
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Help with understanding the ks.boot test results

I am trying to perform the ks.boot analysis to compare two numerical dstributions for 2 different phenomena. Those 2 numerical lists are at http://pastebin.com/s6ATRLDC and ...
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1answer
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What is the best way to find change points in empirical power law distributions?

I'm looking at some data that conform reasonably well to a continuous power law distribution, according to a Kolmogorov-Smirnov test that compares the estimated power-law fit to the data (per Clauset, ...
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Goodness of fit in R

I need to check for goodness of fit using K-S test in R. I have a dataset (containing 50 data points) and a non-standard continuous probability distribution. Should I peform a one-sample or two-sample ...
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Difference between the two way of performing Kolmogorov-Smirnov normality test [duplicate]

There are 2 ways to perform Kolmogorov-Smirnov test in SPSS: Analyze; Nonparametric Tests; 1-Sample K-S Analyze; Descriptive Statistics; Explore; Plots; Normality plots with tests What is the ...
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generating discrete distribution comparison score

I have constructed a distribution of some data that I am analyzing, so it is discrete, and I would like to be able to compare it to other distributions in order to generate a score or rank so that I ...
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69 views

Similarity between two small datasets

I have gone through several test's (Kolmogorov-Smirnov, t-test, u-test etc..) but I am not sure which one to use when it comes to comparing two small data sets, lets say of size 10 each. ...
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Comparing two estimated distributions

I estimated the density function (adaptive kde) from two samples and the cdf using approxfun() and integrate(). Now, I would implement a ks test to know if the two distributions are similar. I guess I ...
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1answer
108 views

KS Test and Wilcoxon Rank Sum Test, large differences in p values

I am relatively new to non-parametric tests. I wrote the following R code to test 2 sample tests using the KS test and the Wilcoxon Rank Sum test. Drawing 2 samples of various sizes from unit Normal ...
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Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
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Fitting Data with Ties Using unique() Walk-Around and ks.test

I'm looking for a distribution that best fits my data. Looking at the frequency plot, seems like the distribution could follow a Gamma or Weibull distribution. With that in mind, I use the ...
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114 views

KS, RMSE tests in R

I have a set of yearly peak river flows and I am trying to use the KS test to conclude if the data is coming from a generalized extreme value (GEV) distribution. I am also trying to calculate a root ...
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Using KS test to evaluate differences

There are two different empirical CDFs which I have and I would like to evaluate how different they are. The place at which I started was Kolmogorov-Smirnov test - the result in my case looks like ...
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Efficient statistical test to compare two multivariate distributions

I am looking for a test to assert the "equality" of two multivariate discrete distributions, $\mathbf{A}=\{A_1,\dots,A_k\}$ and $\mathbf{B}=\{B_1,\dots,B_k\}$ for which I do observe two samples ...