Assuming that your two sample groups have roughly the same number of observations, it does appear that they are indeed different just by looking at the histograms alone. How to interpret the ks_2samp with alternative ='less' or alternative ='greater' Ask Question Asked 4 years, 6 months ago Modified 4 years, 6 months ago Viewed 150 times 1 I have two sets of data: A = df ['Users_A'].values B = df ['Users_B'].values I am using this scipy function: to check whether the p-values are likely a sample from the uniform distribution. As I said before, the same result could be obtained by using the scipy.stats.ks_1samp() function: The two-sample KS test allows us to compare any two given samples and check whether they came from the same distribution. of the latter. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Is it a bug? * specifically for its level to be correct, you need this assumption when the null hypothesis is true. If you preorder a special airline meal (e.g. Assuming that one uses the default assumption of identical variances, the second test seems to be testing for identical distribution as well. That's meant to test whether two populations have the same distribution (independent from, I estimate the variables (for the three different gaussians) using, I've said it, and say it again: The sum of two independent gaussian random variables, How to interpret the results of a 2 sample KS-test, We've added a "Necessary cookies only" option to the cookie consent popup. To learn more, see our tips on writing great answers. scipy.stats.ks_1samp. Fitting distributions, goodness of fit, p-value. Perhaps this is an unavoidable shortcoming of the KS test. This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Suppose we have the following sample data: #make this example reproducible seed (0) #generate dataset of 100 values that follow a Poisson distribution with mean=5 data <- rpois (n=20, lambda=5) Related: A Guide to dpois, ppois, qpois, and rpois in R. The following code shows how to perform a . Use the KS test (again!) The Kolmogorov-Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. Are there tables of wastage rates for different fruit and veg? Can airtags be tracked from an iMac desktop, with no iPhone? This means that (under the null) you can have the samples drawn from any continuous distribution, as long as it's the same one for both samples. It only takes a minute to sign up. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. When txt = TRUE, then the output takes the form < .01, < .005, > .2 or > .1. So, CASE 1 refers to the first galaxy cluster, let's say, etc. Basically, D-crit critical value is the value of two-samples K-S inverse survival function (ISF) at alpha with N=(n*m)/(n+m), is that correct? [4] Scipy Api Reference. It differs from the 1-sample test in three main aspects: It is easy to adapt the previous code for the 2-sample KS test: And we can evaluate all possible pairs of samples: As expected, only samples norm_a and norm_b can be sampled from the same distribution for a 5% significance. How do I read CSV data into a record array in NumPy? Connect and share knowledge within a single location that is structured and easy to search. If the the assumptions are true, the t-test is good at picking up a difference in the population means. Connect and share knowledge within a single location that is structured and easy to search. Since the choice of bins is arbitrary, how does the KS2TEST function know how to bin the data ? A Medium publication sharing concepts, ideas and codes. Can airtags be tracked from an iMac desktop, with no iPhone? I have some data which I want to analyze by fitting a function to it. 1 st sample : 0.135 0.271 0.271 0.18 0.09 0.053 scipy.stats. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. In Python, scipy.stats.kstwo just provides the ISF; computed D-crit is slightly different from yours, but maybe its due to different implementations of K-S ISF. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? 2nd sample: 0.106 0.217 0.276 0.217 0.106 0.078 To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Can I still use K-S or not? What is the correct way to screw wall and ceiling drywalls? Finally, we can use the following array function to perform the test. I have a similar situation where it's clear visually (and when I test by drawing from the same population) that the distributions are very very similar but the slight differences are exacerbated by the large sample size. vegan) just to try it, does this inconvenience the caterers and staff? The values of c()are also the numerators of the last entries in the Kolmogorov-Smirnov Table. The p value is evidence as pointed in the comments against the null hypothesis. rev2023.3.3.43278. identical. The region and polygon don't match. A place where magic is studied and practiced? What hypothesis are you trying to test? Making statements based on opinion; back them up with references or personal experience. If method='auto', an exact p-value computation is attempted if both However the t-test is somewhat level robust to the distributional assumption (that is, its significance level is not heavily impacted by moderator deviations from the assumption of normality), particularly in large samples. Ah. As seen in the ECDF plots, x2 (brown) stochastically dominates Do you think this is the best way? Suppose that the first sample has size m with an observed cumulative distribution function of F(x) and that the second sample has size n with an observed cumulative distribution function of G(x). When I compare their histograms, they look like they are coming from the same distribution. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. I wouldn't call that truncated at all. We can now evaluate the KS and ROC AUC for each case: The good (or should I say perfect) classifier got a perfect score in both metrics. Using K-S test statistic, D max can I test the comparability of the above two sets of probabilities? null and alternative hypotheses. How to interpret KS statistic and p-value form scipy.ks_2samp? The two-sided exact computation computes the complementary probability By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. As stated on this webpage, the critical values are c()*SQRT((m+n)/(m*n)) To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It's testing whether the samples come from the same distribution (Be careful it doesn't have to be normal distribution). alternative. Hypothesis Testing: Permutation Testing Justification, How to interpret results of two-sample, one-tailed t-test in Scipy, How do you get out of a corner when plotting yourself into a corner. How do I align things in the following tabular environment? Then we can calculate the p-value with KS distribution for n = len(sample) by using the Survival Function of the KS distribution scipy.stats.kstwo.sf[3]: The samples norm_a and norm_b come from a normal distribution and are really similar. Using Scipy's stats.kstest module for goodness-of-fit testing says, "first value is the test statistics, and second value is the p-value. The single-sample (normality) test can be performed by using the scipy.stats.ks_1samp function and the two-sample test can be done by using the scipy.stats.ks_2samp function. This is explained on this webpage. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. When both samples are drawn from the same distribution, we expect the data We can do that by using the OvO and the OvR strategies. KS Test is also rather useful to evaluate classification models, and I will write a future article showing how can we do that. You may as well assume that p-value = 0, which is a significant result. There is also a pre-print paper [1] that claims KS is simpler to calculate. you cannot reject the null hypothesis that the distributions are the same). If method='asymp', the asymptotic Kolmogorov-Smirnov distribution is The codes for this are available on my github, so feel free to skip this part. Column E contains the cumulative distribution for Men (based on column B), column F contains the cumulative distribution for Women, and column G contains the absolute value of the differences. If your bins are derived from your raw data, and each bin has 0 or 1 members, this assumption will almost certainly be false. less: The null hypothesis is that F(x) >= G(x) for all x; the Charles. In the figure I showed I've got 1043 entries, roughly between $-300$ and $300$. https://ocw.mit.edu/courses/18-443-statistics-for-applications-fall-2006/pages/lecture-notes/, Wessel, P. (2014)Critical values for the two-sample Kolmogorov-Smirnov test(2-sided), University Hawaii at Manoa (SOEST) [1] Adeodato, P. J. L., Melo, S. M. On the equivalence between Kolmogorov-Smirnov and ROC curve metrics for binary classification. Really, the test compares the empirical CDF (ECDF) vs the CDF of you candidate distribution (which again, you derived from fitting your data to that distribution), and the test statistic is the maximum difference. Accordingly, I got the following 2 sets of probabilities: Poisson approach : 0.135 0.271 0.271 0.18 0.09 0.053 makes way more sense now. You reject the null hypothesis that the two samples were drawn from the same distribution if the p-value is less than your significance level. The two-sample t-test assumes that the samples are drawn from Normal distributions with identical variances*, and is a test for whether the population means differ. can I use K-S test here? Is there a single-word adjective for "having exceptionally strong moral principles"? Does a barbarian benefit from the fast movement ability while wearing medium armor? Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? The result of both tests are that the KS-statistic is $0.15$, and the P-value is $0.476635$. Why do small African island nations perform better than African continental nations, considering democracy and human development? Is it suspicious or odd to stand by the gate of a GA airport watching the planes? Both examples in this tutorial put the data in frequency tables (using the manual approach). x1 tend to be less than those in x2. Would the results be the same ? The test only really lets you speak of your confidence that the distributions are different, not the same, since the test is designed to find alpha, the probability of Type I error. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Am I interpreting this incorrectly? . Do you have some references? Finally, the formulas =SUM(N4:N10) and =SUM(O4:O10) are inserted in cells N11 and O11. Charles. The two sample Kolmogorov-Smirnov test is a nonparametric test that compares the cumulative distributions of two data sets(1,2). KS-statistic decile seperation - significance? So i've got two question: Why is the P-value and KS-statistic the same? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. There are three options for the null and corresponding alternative On the x-axis we have the probability of an observation being classified as positive and on the y-axis the count of observations in each bin of the histogram: The good example (left) has a perfect separation, as expected. Perform the Kolmogorov-Smirnov test for goodness of fit. but the Wilcox test does find a difference between the two samples. Master in Deep Learning for CV | Data Scientist @ Banco Santander | Generative AI Researcher | http://viniciustrevisan.com/, print("Positive class with 50% of the data:"), print("Positive class with 10% of the data:"). See Notes for a description of the available its population shown for reference. If method='asymp', the asymptotic Kolmogorov-Smirnov distribution is used to compute an approximate p-value. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Confidence intervals would also assume it under the alternative. Find centralized, trusted content and collaborate around the technologies you use most. It seems like you have listed data for two samples, in which case, you could use the two K-S test, but Computes the Kolmogorov-Smirnov statistic on 2 samples. I have Two samples that I want to test (using python) if they are drawn from the same distribution. how to select best fit continuous distribution from two Goodness-to-fit tests? ks_2samp interpretation. Hi Charles, thank you so much for these complete tutorials about Kolmogorov-Smirnov tests. Let me re frame my problem. expect the null hypothesis to be rejected with alternative='less': and indeed, with p-value smaller than our threshold, we reject the null What is the point of Thrower's Bandolier? Newbie Kolmogorov-Smirnov question. The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A place where magic is studied and practiced? Hi Charles, Max, Charle. There is a benefit for this approach: the ROC AUC score goes from 0.5 to 1.0, while KS statistics range from 0.0 to 1.0. After some research, I am honestly a little confused about how to interpret the results. Am I interpreting the test incorrectly? Do new devs get fired if they can't solve a certain bug? Suppose we wish to test the null hypothesis that two samples were drawn ks_2samp (data1, data2) Computes the Kolmogorov-Smirnof statistic on 2 samples. 2. @O.rka Honestly, I think you would be better off asking these sorts of questions about your approach to model generation and evalutation at. (this might be a programming question). The medium one got a ROC AUC of 0.908 which sounds almost perfect, but the KS score was 0.678, which reflects better the fact that the classes are not almost perfectly separable. thanks again for your help and explanations. Check it out! It does not assume that data are sampled from Gaussian distributions (or any other defined distributions). finds that the median of x2 to be larger than the median of x1, Is a PhD visitor considered as a visiting scholar? Sure, table for converting D stat to p-value: @CrossValidatedTrading: Your link to the D-stat-to-p-value table is now 404. famous for their good power, but with $n=1000$ observations from each sample, Mail us for help: info@monterrosatax.com 14541 Sylvan St, Van nuys CA 91411 How to interpret p-value of Kolmogorov-Smirnov test (python)? document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 2023 REAL STATISTICS USING EXCEL - Charles Zaiontz, The two-sample Kolmogorov-Smirnov test is used to test whether two samples come from the same distribution. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Notes This tests whether 2 samples are drawn from the same distribution. Excel does not allow me to write like you showed: =KSINV(A1, B1, C1). The best answers are voted up and rise to the top, Not the answer you're looking for? Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. KDE overlaps? Why does using KS2TEST give me a different D-stat value than using =MAX(difference column) for the test statistic? If I have only probability distributions for two samples (not sample values) like Note that the values for in the table of critical values range from .01 to .2 (for tails = 2) and .005 to .1 (for tails = 1). (If the distribution is heavy tailed, the t-test may have low power compared to other possible tests for a location-difference.). distribution functions of the samples. Can I tell police to wait and call a lawyer when served with a search warrant? scipy.stats.ks_2samp.
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