# Questions tagged [kolmogorov-smirnov-test]

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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1answer
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### Test of difference: 2 KS tests or one?

I have two unrelated groups and am looking to perform a test for difference. Before I can do that, I need to perform a Kolmogorov–Smirnov (KS) test for normal distribution so I can decide whether to ...
0answers
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### How to compare different levels of discrete variable?

I have a discrete variable that $P(X_{n, m}) \sim \operatorname{Pois}(\lambda)$ where $n$ and $m$ are the minimum and maximum values that it can takes respectively. I want to analyse ...
2answers
36 views

### Issue with Kolmogorov - Smirnov test implementation in Matlab?

I observed a strange behavior of the 2 sample Kolmogorov - Smirnov test in Matlab and I'm not sure if I missing the obvious or if there is indeed an issue with implementation of the test? Below is a ...
0answers
25 views

### Can I use K-S statistic to determine best fit even when the null hypothesis is rejected?

I'm comparing data from two different models, I also have the real data. I want to demonstrate that one model fits the real data distribution better than the other model. Unfortunately none of the ...
1answer
32 views

### Comparisons of distributions: How to deal with discrepancies between visual impression and statistical tests (K-S, ranksum)?

I'm having some doubts how to properly compare my data (because of visual discrepancies), represented as histograms. Here's an minimal and representative example, illustrating the data: I measure BMI ...
2answers
44 views

### How to match the distribution of one dataset when subsampling from another?

I have two datasets that measure the same variable under different conditions. The first dataset (d1) is much larger (9,000 observations) than the second dataset (d2; 900 observations). A histogram of ...
0answers
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### Test goodness of fit of a multivariate distribution via testing GOF of linear combinations of components

I am modeling a continuous bivariate distribution of a random vector $(X_1,X_2)$ using a copula. I would like to assess how well I am doing. Given a data sample, I could probably do a bivariate ...
0answers
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### Calculating the sample cumulative distribution function for a Kolmogrov-Simulation test to examine the goodness of fit with given data [duplicate]

I have sample data for 'Times between successive crashes of a computer system' which is for a 6 month period and the data is given in hours. The data in brief is : 1,10,20,30,40,52..... I need to use ...
0answers
11 views

### Comparing CDFs, Kolmogorov-Smirnov, Max/Average?

I'm in the process of building a python group of classes that will calculate many CDFs for a large number of samples. I then want to compare the CDFs of all the samples to see if any two samples could ...
0answers
19 views

### Kolmogorov-Smirnov (KS) test two-sample eCDFs and Dmax

I am running the two sample KS test to see whether two models are similar or not. Now the KS test does give me the answer to my question. But I have a question regarding the eCDFs and Dmax computed by ...
1answer
39 views

### How to interpret KS statistic and p-value form scipy.ks_2samp?

I just performed a KS 2 sample test on my distributions, and I obtained the following results: CASE 1: statistic=0.06956521739130435, pvalue=0.9451291140844246; CASE 2: statistic=0.07692307692307693, ...
0answers
12 views

### Comparing Feature's Distribution in Logistic Regression

I was running Logistic Regression on some data. After some RFE, correlation testing and so on, I was expecting some features to play a determining factor. However, seeing at the coefficients given ...
0answers
21 views

### Quantifying if two datasets are from the same distribution, if I only have distances

Let's say that I have two datasets. The target dataset is 1K instances, the "predicted" dataset is 1M instances (but I could downsample). I can compute the distance between instances. How do ...
0answers
18 views

### Appropriate exponential goodness of fit test for unknown parameter

I have a set of univariate data (n=1000) that I believe to be exponentially distributed. I also have a separate, but inexact, prior estimation for the mean or parameter of the distribution I expect ...
0answers
7 views

### What statistical tests or procedures should I conduct for analyzing a repeated measures design experiment?

I have conducted a repeated measures design experiment on Paivio 1971's dual coding experiment, but my two conditions are Dual-Coding (visual + auditory) and Auditory on Animal Sounds. There are two ...
1answer
45 views

### Normality assumption: how deal with them? [duplicate]

I would like to ask whether there's a way to decide which test is the strongest in accomplishing the normality condition. Let's take this example, using a dataset I'm working on: ...
1answer
88 views

### Can I simulate a two-sample K-S test when I can't perform a one-sample test because a distribution parameter is unknown?

Let's say I have a signal which I want to test for normality. I know that the mean from the theoretical distribution is zero, but it has an undetermined (unknown) variance. If I knew mean and variance ...
1answer
62 views

### Trade-off among statistical tests

I was reading up on the KS test and I got a doubt why is it not okay to check with this test when there is a statistically significant difference between the two samples: Sample 1, taken from t=1 to ...
0answers
21 views

### Whitney Mann U test vs Kolmogorov Smirnov for a highly skewed continuous variable

I would like to compare task time to completion distributions (measured in minutes) across two groups. The distributions are highly skewed (the means are 300 to 400 times larger than the medians) and ...
0answers
23 views

### How to test if the influence of changing a parameter is larger than the influence of random noise?

I have an algorithm under test that generates a vector of results, influenced by an underlying RNG. I want to test whether, when I change parameter a, the results change 'more' then when changing the ...
1answer
47 views

### Distribution of p-values from scipy ks-test

I wast trying to understand how kstest works using scipy. I generated chi2 random variables and then checked if the values follow the chi2 distribution. The codes are shown below. ...
1answer
25 views

### Probability of sample distribution being different from population distribution

I have a population distribution I know is exponential, with mean $\mu_1$. I also have a sample of the population (of size $n$) that appears to be exponential with mean $\mu_2$. I have all the $n$ ...
1answer
61 views

### Kolmogorov-Smirnov test returning a p-value of 1

I have two datasets data1 and data2 with different sample sizes: over 50,000 and around 8,000, respectively. These data consist ...
1answer
26 views

### Is the set of distribution $\{ X | \max_t |f_X(t) - f_Y(t)| \leq \epsilon \}$ convex, where f is the cdf or inverse cdf?

I'm trying to figure out if the set is convex, where the maximum difference between cdf(or inverse cdf) of X and a reference distribution Y is smaller than $\epsilon$. 1. Let $f_X(t)$ denote the cdf ...
0answers
56 views

### Testing uniform distribution of a discrete function derived from a random number generator

(Forewarning: I'm a programmer, not a statistician, so I apologize in advance for any misuse of terminology!) I'm testing a known random number generator that implements the PCG algorithm. This RNG ...
0answers
47 views

### Is KS statstic (in classification) from ROC Curve same as K-S from cum Gain curve or PR Curve?

This is related to classification problems (specifically binary classification problems covered in scoring) where curves referenced below are used. I understand each of these curves for a classifier ...
0answers
14 views

### Comparison of medians in data with multimodal distributions

I'm comparing continuous data obtained at two different time periods with the distributions seen below. They appear fairly similar, but they're clearly non-normal. The ideal hypothesis is that the ...
0answers
35 views

### I wanna know how to compare the distribution similarity of two d-dimensional sample sets

I wanna know how to compare the distribution similarity of two d-dimensional sample sets, I know Kolmogorov-Smirnov, but this algorithm can only be used in one dimension, right? I also know the KL ...
1answer
53 views

### How to differentiate statistically between two numerical continuous datasets?

Sample from: Green - Gamma(45, 1); Red - Normal(375, 19) These two samples clearly come from two different distributions. Is it possible to verify that these two samples come from two different ...
0answers
23 views

### different results between the published paper and my code to calculate the p-value of Kolmogorov–Smirnov (K–S) test using R

I want to know if the following distributions fit the given data well or not. I used the Kolmogorov–Smirnov (K–S) statistic for the following two distributions but, i obtained different p-value of k-s ...
1answer
65 views

### Kolmogorov-Smirnov two-sample test p-value evaluation

I'm using python's scpipy implementation of the Kolmogorov-Smirnov two-sample test (ks_2samp). Q1: Why are my p-values in the examples below so low, specifically on the first example? Q2: Can I ...
0answers
48 views

### Why are people using KS statistic to choose cutoff for binary predictions?

I've seen that people are sometimes using Kolmogorov-Smirnov statistic to determine a cutoff in a binary classification models, such as logistic regression. However, i do not fully understand why and ...
0answers
24 views

### Statistical power of the Lilliefors test: how to compare results for samples of different sizes?

The power of the Lilliefors test (LT) strongly depends on the sample size. I need to apply LT to a discrete distribution to find the minimum value m_min above which it is exponential. I need to do it ...
0answers
27 views

### Feature selection using LASSO and KS tests

I have derived a binary classification model using LASSO-based feature selection and got a list of 10 features that gave an overall AUROC 0f 0.83. Now I wanted to check whether there exist any class-...
1answer
42 views

### KS Test for Hawkes Process

I am analyzing some data by applying 1d-Hawkes processes. To evaluate the fit of the model itself (and particularly the chosen kernel, i.e. exponential), I am performing a KS test. However, it is not ...
1answer
41 views

### Is the following approach a reasonable way of defining $p$-value thresholds?

I have many small sets of data (each sample containing 8 to 64 individual points) which I would like to test for normality. I want to do this with two main tests: Shapiro-Wilk Kolmogorov–Smirnov ...
1answer
10 views

### Comparing species size distribution across multiple habitats

I am looking at one species' size distribution across three primary habitats, we'll call them Habitat A, B, and C for simplicity. I have taken multiple samples (seine tows) within each habitat (n ...
1answer
25 views

### two-sample Kolmogorov-Smirnov test suggest that sample with the same data generating process from different populations

I have two different samples I need to test if they are drawn from the same population distribution. The two samples are of the volatility of an asset that I simulated. Since the data is simulated I ...
1answer
43 views

### Intepretation of $p$-values for a Kolmogorov-Smirnov test

I'm using a Kolmogorov-Smirnov test to examine how normal (or Gaussian) some data sets I have are. I am having trouble with interpreting the $p$-values (surprise surprise). My present understanding is ...
2answers
183 views

### Kolmogorov-Smirnov and AIC giving opposite goodness-of-fit results. Is this possible/surprising/normal?

I have some data on the duration of several activities (rounded to the nearest half hour). I'm trying to add up these random variables (one per activity) so that I can calculate the total duration of ...
0answers
35 views

### comparing gene expression distributions with replicates

I have gene expression data for single cells (hundreds per sample) in two conditions that I would like to compare. For each condition I have 4 replicates. So in essence I need to compare 4 ...
0answers
72 views

### Is it accurate to take the maximum distance between CDF and ECDF only at the edges? (Kolmogorov-Smirnov Test)

I have two samples, one obtained empirically and the other is the result of a simulation. I want to tune the simulation so that the result resembles the reality, for that I will minimize the KS ...
0answers
24 views

### KS two sample test, p-value equal to 1

I have done a KS two sample test with the following samples: I have received a P-value of 1, I was expecting a high p-value but I thought this value can never reach 1 unless both samples are exactly ...
1answer
67 views

### Appropiate test for comparing integer distance distributions

I am trying to determine if wildfires occur closer to forests or not. For this, I have two matrices with the same shape: A matrix of ones and zeros where each value represents whether a fire is ...
0answers
15 views

### Significant change over NxM distributions

I have 100 sets of data, each of which consists of ~ 15 distributions along time, I've attached a figure of 1 of these sets to hopefully clear up what I mean. The plot shows the 95% confidence ...
1answer
55 views

### Distribution Selection based on Kolmogorov Smirnov Test

I am trying to model the distribution of some non normal data, to do so i am fitting many different distributions(Student, Pareto...) to the data. When computing the Kolmogorov Smirnov Statistic for ...
0answers
35 views

### What distribution could the data stem from?

From checking the histogram of the distribution I had the intuition that the data could follow a Poisson or an exponential distribtuion. However, Lilliefors test that the data is exponentially ...
0answers
31 views

### Why do I have different KS test results?

I have been using scipython ks2samp to apply a two sided , sample KS test to some data. import scipy.stats as ss import numpy as np All_smirnoff = ss.ks_2samp(X, Y) where X and Y are two 1D numpy ...
1answer
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### goodness-of-fit and bootstrap

Assume one has two data samples: $X = \{ x_{1}, \dots, x_{n} \}$ and $Y = \{y_{1}, \dots, y_{m}\}$. Next, we aim to check if the data $Y$ was generated by the same data generating process (DGP) as $X$ ...
0answers
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### Unexpected behaviour of Anderson Darling test for normality for low sample size

I’m testing the power of the Anderson Darling test to detect deviations from standard normal distributions. I’m calibrating the AD test statistic numerically using python and I noticed an unexpected ...