# Questions tagged [kolmogorov-smirnov]

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 determine which distribution fits my data best?

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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### Kullback–Leibler vs Kolmogorov-Smirnov distance

I can see that there are a lot of formal differences between Kullback–Leibler vs Kolmogorov-Smirnov distance measures. However, both are used to measure the distance between distributions. Is there a ...
2k views

### Intuitive explanation of Kolmogorov Smirnov Test

What is the cleanest, easiest way to explain someone the concept of Kolmogorov Smirnov Test? What does it intuitively mean? It's a concept that I have difficulty in articulating - especially when ...
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### Is Kolmogorov-Smirnov test valid with discrete distributions?

I'm comparing a sample and checking whether it distributes as some, discrete, distribution. However, I'm not enterily sure that Kolmogorov-Smirnov applies. Wikipedia seems to imply it does not. If it ...
113k views

### What is the difference between the Shapiro-Wilk test of normality and the Kolmogorov-Smirnov test of normality?

What is the difference between the Shapiro-Wilk test of normality and the Kolmogorov-Smirnov test of normality? When will results from these two methods differ?
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### Is it meaningful to test for normality with a very small sample size (e.g., n = 6)?

I have a sample size of 6. In such a case, does it make sense to test for normality using the Kolmogorov-Smirnov test? I used SPSS. I have a very small sample size because it takes time to get each. ...
4k views

### Why does the Kolmogorov-Smirnov test work?

In reading about the 2-sample KS test, I understand exactly what it is doing but I don't understand why it works. In other words, I can follow all the steps to compute the empirical distribution ...
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### Kolmogorov-Smirnov with discrete data: What is proper use of dgof::ks.test in R?

Beginner questions: I want to test whether two discrete data sets come from the same distribution. A Kolmogorov-Smirnov test was suggested to me. Conover (Practical Nonparametric Statistics, 3d) ...
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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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### 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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### Can I use Kolmogorov-Smirnov to compare two empirical distributions?

Is it OK to use the Kolmogorov-Smirnov goodness-of-fit test to compare two empirical distributions to determine whether they appear to have come from the same underlying distribution, rather than to ...
74k views

### Understanding Kolmogorov-Smirnov test in R

I'm trying to understand the output of the Kolmogorov-Smirnov test function (two samples, two sided). Here is a simple test. ...
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### Test for IID sampling

How would you test or check that sampling is IID (Independent and Identically Distributed)? Note that I do not mean Gaussian and Identically Distributed, just IID. And idea that comes to my mind is ...
5k 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 ...
6k views

### 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 ...
25k 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 ...
5k views

### Can I use Kolmogorov-Smirnov test and estimate distribution parameters?

I've read that Kolmogorov-Smirnov test should not be used to test the goodness of fit of a distribution whose parameters have been estimated from the sample. Does make sense to split my sample in two ...
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### 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 ...
15k views

### Is there a multiple-sample version or alternative to the Kolmogorov-Smirnov Test?

I am comparing the size distribution of trees in six pairs of plots where one plot received a treatment and the other a control. Using a Kolmogorov-Smirnov test on each pair of plots I find that $p$ ...
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### Is there an alternative to the Kolmogorov-Smirnov test for tied data with correction?

I've got a bunch of data from two samples (control and treated), each containing several thousand values which are to undergo significance testing in R. Theoretically, the values should be continuous, ...
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### 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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### Two-dimensional Kolmogorov-Smirnov

I would like to run some two dimensional Kolmogorov-Smironov tests to determine whether a two-dimensional distribution fits with a reference. Is there any package or application that I could I use in ...
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### Clustering probability distributions - methods & metrics?

I have some data points, each containing 5 vectors of agglomerated discrete results, each vector's results generated by a different distribution, (the specific kind of which I am not sure, my best ...
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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. ...
22k views

### “Ties should not be present” in one-sample Kolmgorov-Smirnov test in R

I am going to use the Kolmogorov-Smirnov test to test normality of MYDATA in R. This is an example of what I do ks.test(MYDATA,"pnorm",mean(MYDATA),sd(MYDATA)) ...
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### Correlation between dichotomous and continuous variable

I am trying to find the correlation between a dichotomous and a continuous variable. From my ground work on this I found that I have to use independent t-test and the precondition for it is that the ...
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### Book for non parametric statistics

What would be a good book for non-parametric statistics. Not just the introduction but advanced level. Also I am looking at something I can use for learn and not for reference. In particular I am ...
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### 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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### Is there a multivariate two-sample Kolmogorov-Smirnov test?

Is there a multivariate alternative to two-sample Kolmogorov-Smirnov test? What I mean is a test that can be used to check whenever two underlying multidimensional distributions differ.
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### 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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### Measuring goodness-of-fit in a model that combines two distributions

I have data with a double peak that I'm trying to model, and there's enough overlap between the peaks that I can't treat them independently. A histogram of the data might look something like this: I'...
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### Kolmogorov-Smirnov two-sample $p$-values

I am using the Kolmogorov–Smirnov two-sample test to compare distributions, and I noticed a $p$-value is frequently reported as the test statistic. How is this $p$-value determined? I know it's ...
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### ks.test and ks.boot - exact p-values and ties

I am confused by the behaviour of ks.test (package stat) a) in the presence of ties and b) if one-sided while doing a two-sample test. Documentation: "Exact p-values are not available for the two-...
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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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### Using Kolmogorov–Smirnov test

A newbie question (please provide detailed answers): I am trying to use the Kolmogorov–Smirnov test. I managed to calculate the difference between the empirical points and the theoretical distribution ...
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### 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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### Kolmogorov Smirnov Z vs Mann Whitney U small sample size n= 15?

I have a small sample size of 15. I want to see if there is a difference in the nutrient intakes between two independent variables, group 1 n = 11, group 2 n= 4. The data is not normally distributed. ...
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### 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 ...
939 views

### Why “supremum”, not “maximum” in Kolmogorov-Smirnov test?

Why the test function in Kolmogorov-Smirnov test takes the supremum of the set of differences, not maximum? When maximum (greatest element) of a set does not exist then supremum may exist, but if ...
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### Inconsistent normality tests: Kolmogorov-Smirnov vs Shapiro-Wilk

I'm currently looking into some data that was produced by an MC simulation I wrote - I expect the values to be normally distributed. Naturally I plotted a histogram and it looks reasonable (I guess?): ...
15k views

### two-sample Kolmogorov-Smirnov test p-value in R 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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### 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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### 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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### A naive question about the Kolmogorov Smirnov test

I would like to test if they are distributed according to an exponential distribution. I can apply the Kolmogorov-Smirnov in python using ...
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### How can the F-test reject the null hypothesis while the KS test does not?

Suppose I have two datasets, $\mathbf{a}$ and $\mathbf{b}$. I want to test whether the two datasets are different in a statistically significant way. To compute the F-test, I take the ratio of the ...
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### Is the Kolmogorov-Smirnov-Test too strict if the sample size is large?

I often hear the statement that the KS-Test (for comparing two distributions described by two samples) is too strict if the sample size is rather large, meaning that the 0-hypothesis of equal ...
721 views

### Kolmogorov Smirnov conflicts with visual data

I recorded the length of 197 nursing care episodes. My normalised data $(x-\mu)/\sigma$ looks like this: Kolmogorov-Smirnov gives me a p-value of 0.14. Can't be right surely?! Am I misinterpreting my ...
7k views

### 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), and/...