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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Kolmogorov–Smirnov test vs. t-test

I'm having some difficulty in understanding the interpretation of the 2 sample KS test, and how it is different from a regular t test between 2 groups. Lets say I have males and females doing some ...
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Pool data from two different points of time with different attendants

I have two samples (each nurses) one from 2008 and the other drawn 2013. Both got the same questionaire to fill out. Now I would like to pool the data but do not know if I just can do it. My idea was ...
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“Less Than”/“Greater Than” k-Sample Anderson-Darling

I want to compare two ECDFs using the Anderson-Darling test. Specifically, I think one ECDF is less than the other akin to a one-tailed test. I know that you can do this with the Kolmogorov-Smirnov ...
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How to compare binned CDFs?

We want to compare binned CDFs from sampled data. Each CDF is 101 numbers representing percentiles, i.e., $P(x<a_k)=k/100$ where $k=0..100$. The sample size is 1-3k (unknown at comparison time ...
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Compare between median/IQR and reference mean/SD

I have a small set of non-normally distributed measurement data (Kolmogorov-Smirnov rejected similarity to a normal distribution) and a reference value from a large population (n=120) of healthy ...
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Comparing count groups/hisotgrams with different bins

I'm looking at clustering techinques for which I have a ground truth. From the ground truth I can extract the cardinality (size) of clusters and I would like to test how well different methods can ...
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Seemingly random results from kstest2 function in MATLAB

I'm trying to understand the kstest2 function in MATLAB so I can use it to check if output samples from two models are from the same distribution. The first thing I did was run a test to make sure ...
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13 views

Method to justify claim that two samples come from the same distribution

I know of ways to test "whether" two data sets come from the same distribution, in the sense that I can treat the hypothesis that they are from the same distribution as the null hypothesis. However, ...
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37 views

Interpreting Kolmogorov Smirnoff Test

I have two sets of data and I want to determine whether they come from similar distributions or not so I am using the Kolmogorov-Smirnoff Test. So I understand that if I get a p-value of less than ...
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25 views

Variable that discriminates but performance metrics don't improve

I have a score adjusted by a logistic regression done with variables let's say X1 to X5. I'm not including a variable X6 to be chosen. Now, if I let the algorithm (stepAIC from R) choose among all of ...
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How do you do power analysis with a non-parametric approach?

How can we determine the sample size needed (aka do Power Analysis) for non-parametric approaches like the Mann Whitney U test or the Kolmogorov Smirnov Test?
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Test if the distribution of a discret sample came from a known distribution [duplicate]

Hello I have a sample and I want to test if it is drawn from a discrete distribution (Binomal for example), I read that the KS test is more used, but as you know, the KS test can only be used for ...
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30 views

Kolmogorov-Smirnov test between two distributions - R

I've two distributions computed on the same grid (that is, for each point of the grid I know the value of each CDF at that point). I want to check whether the two distributions are the same. I can't ...
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2answers
86 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, ...
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21 views

Test for Divergence in Two Large Vectors Non-Normally Distributed

I have very large sets of biological data, ca. 5,000,000 points, which are the proportion of methylation throughout the genome. Data is therefore on 0-1 scale. I am looking at testing distribution ...
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17 views

Area Based Kolmogorov Smirnov

I have several sets to two ECDFs that I want to compare. I know I can use the Kolmogorov-Smirnov test (and I have) but one set of ECDF is returning statistically significant when I suspect the ECDFs ...
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26 views

KS test with estimating parameters in t-Student case

I have some doubt: practically my dataset, graphically speaking, seem generated from t-student o similar distribution. If I estimate Normal on the data, also graphically, the fit is no good and ...
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42 views

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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1answer
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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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77 views

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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190 views

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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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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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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36 views

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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52 views

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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88 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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90 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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115 views

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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40 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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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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232 views

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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42 views

compare multiple size frequency distributions

I have a dataframe with annual size frequency distributions: ...
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72 views

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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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 ...