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. but KS2TEST is telling me it is 0.3728 even though this can be found nowhere in the data. alternative is that F(x) < G(x) for at least one x. During assessment of the model, I generated the below KS-statistic. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? Since D-stat =.229032 > .224317 = D-crit, we conclude there is a significant difference between the distributions for the samples. 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. If method='auto', an exact p-value computation is attempted if both If the sample sizes are very nearly equal it's pretty robust to even quite unequal variances. In fact, I know the meaning of the 2 values D and P-value but I can't see the relation between them. expect the null hypothesis to be rejected with alternative='less': and indeed, with p-value smaller than our threshold, we reject the null To subscribe to this RSS feed, copy and paste this URL into your RSS reader. two-sided: The null hypothesis is that the two distributions are identical, F (x)=G (x) for all x; the alternative is that they are not identical. For Example 1, the formula =KS2TEST(B4:C13,,TRUE) inserted in range F21:G25 generates the output shown in Figure 2. Note that the alternative hypotheses describe the CDFs of the The Kolmogorov-Smirnov test, however, goes one step further and allows us to compare two samples, and tells us the chance they both come from the same distribution. Is this correct? warning will be emitted, and the asymptotic p-value will be returned. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. I am curious that you don't seem to have considered the (Wilcoxon-)Mann-Whitney test in your comparison (scipy.stats.mannwhitneyu), which many people would tend to regard as the natural "competitor" to the t-test for suitability to similar kinds of problems. How to interpret `scipy.stats.kstest` and `ks_2samp` to evaluate `fit` of data to a distribution? The KS test (as will all statistical tests) will find differences from the null hypothesis no matter how small as being "statistically significant" given a sufficiently large amount of data (recall that most of statistics was developed during a time when data was scare, so a lot of tests seem silly when you are dealing with massive amounts of data). The result of both tests are that the KS-statistic is 0.15, and the P-value is 0.476635. Kolmogorov-Smirnov (KS) Statistics is one of the most important metrics used for validating predictive models. How can I make a dictionary (dict) from separate lists of keys and values? two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different. But who says that the p-value is high enough? How do you get out of a corner when plotting yourself into a corner. Main Menu. Making statements based on opinion; back them up with references or personal experience. 99% critical value (alpha = 0.01) for the K-S two sample test statistic. 1 st sample : 0.135 0.271 0.271 0.18 0.09 0.053 where c() = the inverse of the Kolmogorov distribution at , which can be calculated in Excel as. Using Scipy's stats.kstest module for goodness-of-fit testing. and then subtracts from 1. Is normality testing 'essentially useless'? After some research, I am honestly a little confused about how to interpret the results. Newbie Kolmogorov-Smirnov question. empirical CDFs (ECDFs) of the samples. Default is two-sided. Nevertheless, it can be a little hard on data some times. The scipy.stats library has a ks_1samp function that does that for us, but for learning purposes I will build a test from scratch. It is widely used in BFSI domain. Paul, The medium one (center) has a bit of an overlap, but most of the examples could be correctly classified. KS is really useful, and since it is embedded on scipy, is also easy to use. The values of c()are also the numerators of the last entries in the Kolmogorov-Smirnov Table. Time arrow with "current position" evolving with overlay number. I know the tested list are not the same, as you can clearly see they are not the same in the lower frames. What is the point of Thrower's Bandolier? It seems like you have listed data for two samples, in which case, you could use the two K-S test, but I should also note that the KS test tell us whether the two groups are statistically different with respect to their cumulative distribution functions (CDF), but this may be inappropriate for your given problem. In Python, scipy.stats.kstwo (K-S distribution for two-samples) needs N parameter to be an integer, so the value N=(n*m)/(n+m) needs to be rounded and both D-crit (value of K-S distribution Inverse Survival Function at significance level alpha) and p-value (value of K-S distribution Survival Function at D-stat) are approximations. Connect and share knowledge within a single location that is structured and easy to search. 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 quick answer is: you can use the 2 sample Kolmogorov-Smirnov (KS) test, and this article will walk you through this process. Are you trying to show that the samples come from the same distribution? In this case, OP, what do you mean your two distributions? Is there an Anderson-Darling implementation for python that returns p-value? ks_2samp interpretation. [5] Trevisan, V. Interpreting ROC Curve and ROC AUC for Classification Evaluation. In a simple way we can define the KS statistic for the 2-sample test as the greatest distance between the CDFs (Cumulative Distribution Function) of each sample. betanormal1000ks_2sampbetanorm p-value=4.7405805465370525e-1595%betanorm 3 APP "" 2 1.1W 9 12 to be consistent with the null hypothesis most of the time. The significance level of p value is usually set at 0.05. 2. exactly the same, some might say a two-sample Wilcoxon test is If your bins are derived from your raw data, and each bin has 0 or 1 members, this assumption will almost certainly be false. Why are trials on "Law & Order" in the New York Supreme Court? We then compare the KS statistic with the respective KS distribution to obtain the p-value of the test. makes way more sense now. of two independent samples. Hello Ramnath, alternative is that F(x) > G(x) for at least one x. Please clarify. As for the Kolmogorov-Smirnov test for normality, we reject the null hypothesis (at significance level ) if Dm,n > Dm,n, where Dm,n,is the critical value. A Medium publication sharing concepts, ideas and codes. Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2. numpy/scipy equivalent of R ecdf(x)(x) function? Imagine you have two sets of readings from a sensor, and you want to know if they come from the same kind of machine. The test statistic $D$ of the K-S test is the maximum vertical distance between the Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Define. Histogram overlap? It is a very efficient way to determine if two samples are significantly different from each other. Can you please clarify? The calculations dont assume that m and n are equal. What do you recommend the best way to determine which distribution best describes the data? Thank you for the nice article and good appropriate examples, especially that of frequency distribution. statistic value as extreme as the value computed from the data. Further, it is not heavily impacted by moderate differences in variance. The codes for this are available on my github, so feel free to skip this part. If method='asymp', the asymptotic Kolmogorov-Smirnov distribution is The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. Partner is not responding when their writing is needed in European project application, Short story taking place on a toroidal planet or moon involving flying, Topological invariance of rational Pontrjagin classes for non-compact spaces. It's testing whether the samples come from the same distribution (Be careful it doesn't have to be normal distribution). Is it possible to do this with Scipy (Python)? 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) Topological invariance of rational Pontrjagin classes for non-compact spaces. yea, I'm still not sure which questions are better suited for either platform sometimes. KS2TEST(R1, R2, lab, alpha, b, iter0, iter) is an array function that outputs a column vector with the values D-stat, p-value, D-crit, n1, n2 from the two-sample KS test for the samples in ranges R1 and R2, where alpha is the significance level (default = .05) and b, iter0, and iter are as in KSINV. Finally, note that if we use the table lookup, then we get KS2CRIT(8,7,.05) = .714 and KS2PROB(.357143,8,7) = 1 (i.e. where KINV is defined in Kolmogorov Distribution. There cannot be commas, excel just doesnt run this command. What is the point of Thrower's Bandolier? Learn more about Stack Overflow the company, and our products. @O.rka But, if you want my opinion, using this approach isn't entirely unreasonable. The best answers are voted up and rise to the top, Not the answer you're looking for? I explain this mechanism in another article, but the intuition is easy: if the model gives lower probability scores for the negative class, and higher scores for the positive class, we can say that this is a good model. The original, where the positive class has 100% of the original examples (500), A dataset where the positive class has 50% of the original examples (250), A dataset where the positive class has only 10% of the original examples (50). So let's look at largish datasets We cannot consider that the distributions of all the other pairs are equal. https://en.m.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test, soest.hawaii.edu/wessel/courses/gg313/Critical_KS.pdf, We've added a "Necessary cookies only" option to the cookie consent popup, Kolmogorov-Smirnov test statistic interpretation with large samples. There is even an Excel implementation called KS2TEST. Often in statistics we need to understand if a given sample comes from a specific distribution, most commonly the Normal (or Gaussian) distribution. Two arrays of sample observations assumed to be drawn from a continuous If KS2TEST doesnt bin the data, how does it work ? I calculate radial velocities from a model of N-bodies, and should be normally distributed. 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. Connect and share knowledge within a single location that is structured and easy to search. For instance it looks like the orange distribution has more observations between 0.3 and 0.4 than the green distribution. Low p-values can help you weed out certain models, but the test-statistic is simply the max error. The 2 sample KolmogorovSmirnov test of distribution for two different samples. The values in columns B and C are the frequencies of the values in column A. That seems like it would be the opposite: that two curves with a greater difference (larger D-statistic), would be more significantly different (low p-value) What if my KS test statistic is very small or close to 0 but p value is also very close to zero? Is there a proper earth ground point in this switch box? If so, it seems that if h(x) = f(x) g(x), then you are trying to test that h(x) is the zero function. The closer this number is to 0 the more likely it is that the two samples were drawn from the same distribution. How do you compare those distributions? {two-sided, less, greater}, optional, {auto, exact, asymp}, optional, KstestResult(statistic=0.5454545454545454, pvalue=7.37417839555191e-15), KstestResult(statistic=0.10927318295739348, pvalue=0.5438289009927495), KstestResult(statistic=0.4055137844611529, pvalue=3.5474563068855554e-08), K-means clustering and vector quantization (, Statistical functions for masked arrays (. The R {stats} package implements the test and $p$ -value computation in ks.test. Your samples are quite large, easily enough to tell the two distributions are not identical, in spite of them looking quite similar. That can only be judged based upon the context of your problem e.g., a difference of a penny doesn't matter when working with billions of dollars. I have Two samples that I want to test (using python) if they are drawn from the same distribution. I wouldn't call that truncated at all. There is clearly visible that the fit with two gaussians is better (as it should be), but this doesn't reflect in the KS-test. The classifier could not separate the bad example (right), though. To build the ks_norm(sample)function that evaluates the KS 1-sample test for normality, we first need to calculate the KS statistic comparing the CDF of the sample with the CDF of the normal distribution (with mean = 0 and variance = 1). measured at this observation. When to use which test, We've added a "Necessary cookies only" option to the cookie consent popup, Statistical Tests That Incorporate Measurement Uncertainty. To learn more, see our tips on writing great answers. On the scipy docs If the KS statistic is small or the p-value is high, then we cannot reject the hypothesis that the distributions of the two samples are the same. Its the same deal as when you look at p-values foe the tests that you do know, such as the t-test. Strictly, speaking they are not sample values but they are probabilities of Poisson and Approximated Normal distribution for selected 6 x values. Movie with vikings/warriors fighting an alien that looks like a wolf with tentacles. ks_2samp(X_train.loc[:,feature_name],X_test.loc[:,feature_name]).statistic # 0.11972417623102555. Is it a bug? And if I change commas on semicolons, then it also doesnt show anything (just an error). i.e., the distance between the empirical distribution functions is It provides a good explanation: https://en.m.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test. For each galaxy cluster, I have a photometric catalogue. Use the KS test (again!) Are there tables of wastage rates for different fruit and veg? If interp = TRUE (default) then harmonic interpolation is used; otherwise linear interpolation is used. to be rejected. The chi-squared test sets a lower goal and tends to refuse the null hypothesis less often. Since the choice of bins is arbitrary, how does the KS2TEST function know how to bin the data ? We see from Figure 4(or from p-value > .05), that the null hypothesis is not rejected, showing that there is no significant difference between the distribution for the two samples. It's testing whether the samples come from the same distribution (Be careful it doesn't have to be normal distribution). vegan) just to try it, does this inconvenience the caterers and staff? Charles. Even in this case, you wont necessarily get the same KS test results since the start of the first bin will also be relevant. Hello Oleg, Go to https://real-statistics.com/free-download/ To learn more, see our tips on writing great answers. Max, Is it correct to use "the" before "materials used in making buildings are"? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Making statements based on opinion; back them up with references or personal experience. alternative. As expected, the p-value of 0.54 is not below our threshold of 0.05, so Thanks for contributing an answer to Cross Validated! This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. When txt = FALSE (default), if the p-value is less than .01 (tails = 2) or .005 (tails = 1) then the p-value is given as 0 and if the p-value is greater than .2 (tails = 2) or .1 (tails = 1) then the p-value is given as 1. Indeed, the p-value is lower than our threshold of 0.05, so we reject the It only takes a minute to sign up. If lab = TRUE then an extra column of labels is included in the output; thus the output is a 5 2 range instead of a 1 5 range if lab = FALSE (default). How do I read CSV data into a record array in NumPy? My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? If method='exact', ks_2samp attempts to compute an exact p-value, that is, the probability under the null hypothesis of obtaining a test statistic value as extreme as the value computed from the data. Is there a reason for that? Charles. We can now perform the KS test for normality in them: We compare the p-value with the significance. The p-values are wrong if the parameters are estimated. Use MathJax to format equations. Example 1: One Sample Kolmogorov-Smirnov Test. The KS statistic for two samples is simply the highest distance between their two CDFs, so if we measure the distance between the positive and negative class distributions, we can have another metric to evaluate classifiers. On the good dataset, the classes dont overlap, and they have a good noticeable gap between them. If I have only probability distributions for two samples (not sample values) like Why does using KS2TEST give me a different D-stat value than using =MAX(difference column) for the test statistic? ks_2samp interpretation. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Find centralized, trusted content and collaborate around the technologies you use most. The result of both tests are that the KS-statistic is $0.15$, and the P-value is $0.476635$. Share Cite Follow answered Mar 12, 2020 at 19:34 Eric Towers 65.5k 3 48 115 Example 1: One Sample Kolmogorov-Smirnov Test Suppose we have the following sample data: If the first sample were drawn from a uniform distribution and the second [2] Scipy Api Reference. Somewhat similar, but not exactly the same. Lastly, the perfect classifier has no overlap on their CDFs, so the distance is maximum and KS = 1. rev2023.3.3.43278. We can do that by using the OvO and the OvR strategies. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? One such test which is popularly used is the Kolmogorov Smirnov Two Sample Test (herein also referred to as "KS-2"). The best answers are voted up and rise to the top, Not the answer you're looking for? KolmogorovSmirnov test: p-value and ks-test statistic decrease as sample size increases, Finding the difference between a normally distributed random number and randn with an offset using Kolmogorov-Smirnov test and Chi-square test, Kolmogorov-Smirnov test returning a p-value of 1, Kolmogorov-Smirnov p-value and alpha value in python, Kolmogorov-Smirnov Test in Python weird result and interpretation. All right, the test is a lot similar to other statistic tests. If R2 is omitted (the default) then R1 is treated as a frequency table (e.g. As seen in the ECDF plots, x2 (brown) stochastically dominates Making statements based on opinion; back them up with references or personal experience. It seems to assume that the bins will be equally spaced. null and alternative hypotheses. The procedure is very similar to the, The approach is to create a frequency table (range M3:O11 of Figure 4) similar to that found in range A3:C14 of Figure 1, and then use the same approach as was used in Example 1. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? When I compare their histograms, they look like they are coming from the same distribution. can I use K-S test here? 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: I am currently working on a binary classification problem with random forests, neural networks etc. 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. While I understand that KS-statistic indicates the seperation power between . the test was able to reject with P-value very near $0.$. Dear Charles, To subscribe to this RSS feed, copy and paste this URL into your RSS reader. https://en.wikipedia.org/wiki/Gamma_distribution, How Intuit democratizes AI development across teams through reusability. For example, $\mu_1 = 11/20 = 5.5$ and $\mu_2 = 12/20 = 6.0.$ Furthermore, the K-S test rejects the null hypothesis I figured out answer to my previous query from the comments. [1] Adeodato, P. J. L., Melo, S. M. On the equivalence between Kolmogorov-Smirnov and ROC curve metrics for binary classification. Copyright 2008-2023, The SciPy community. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. What is the right interpretation if they have very different results? It is most suited to The statistic Parameters: a, b : sequence of 1-D ndarrays. not entirely appropriate. Is there a single-word adjective for "having exceptionally strong moral principles"? identical. The distribution naturally only has values >= 0. Learn more about Stack Overflow the company, and our products. Finite abelian groups with fewer automorphisms than a subgroup. The overlap is so intense on the bad dataset that the classes are almost inseparable. What exactly does scipy.stats.ttest_ind test? If I understand correctly, for raw data where all the values are unique, KS2TEST creates a frequency table where there are 0 or 1 entries in each bin. rev2023.3.3.43278. Is a collection of years plural or singular? The two-sided exact computation computes the complementary probability that is, the probability under the null hypothesis of obtaining a test Under the null hypothesis the two distributions are identical, G (x)=F (x). La prueba de Kolmogorov-Smirnov, conocida como prueba KS, es una prueba de hiptesis no paramtrica en estadstica, que se utiliza para detectar si una sola muestra obedece a una determinada distribucin o si dos muestras obedecen a la misma distribucin. 11 Jun 2022. The KOLMOGOROV-SMIRNOV TWO SAMPLE TEST command automatically saves the following parameters. More precisly said 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. I want to know when sample sizes are not equal (in case of the country) then which formulae i can use manually to find out D statistic / Critical value. Is it possible to create a concave light? As stated on this webpage, the critical values are c()*SQRT((m+n)/(m*n)) In order to quantify the difference between the two distributions with a single number, we can use Kolmogorov-Smirnov distance. The two-sample Kolmogorov-Smirnov test attempts to identify any differences in distribution of the populations the samples were drawn from. To learn more, see our tips on writing great answers. Context: I performed this test on three different galaxy clusters. The same result can be achieved using the array formula. There are several questions about it and I was told to use either the scipy.stats.kstest or scipy.stats.ks_2samp. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? Now heres the catch: we can also use the KS-2samp test to do that! the empirical distribution function of data2 at Are there tables of wastage rates for different fruit and veg? hypothesis that can be selected using the alternative parameter. 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. We can use the same function to calculate the KS and ROC AUC scores: Even though in the worst case the positive class had 90% fewer examples, the KS score, in this case, was only 7.37% lesser than on the original one. The only problem is my results don't make any sense? It only takes a minute to sign up. In the first part of this post, we will discuss the idea behind KS-2 test and subsequently we will see the code for implementing the same in Python. To test the goodness of these fits, I test the with scipy's ks-2samp test. How can I proceed. Recovering from a blunder I made while emailing a professor. Posted by June 11, 2022 cabarrus county sheriff arrests on ks_2samp interpretation June 11, 2022 cabarrus county sheriff arrests on ks_2samp interpretation There are three options for the null and corresponding alternative Can I tell police to wait and call a lawyer when served with a search warrant? It is distribution-free. After training the classifiers we can see their histograms, as before: The negative class is basically the same, while the positive one only changes in scale. 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. MathJax reference. Fitting distributions, goodness of fit, p-value. range B4:C13 in Figure 1). desktop goose android. When doing a Google search for ks_2samp, the first hit is this website. 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). were drawn from the standard normal, we would expect the null hypothesis A p_value of pvalue=0.55408436218441004 is saying that the normal and gamma sampling are from the same distirbutions? empirical distribution functions of the samples. We can also check the CDFs for each case: As expected, the bad classifier has a narrow distance between the CDFs for classes 0 and 1, since they are almost identical. Check out the Wikipedia page for the k-s test. How to follow the signal when reading the schematic? Finally, the bad classifier got an AUC Score of 0.57, which is bad (for us data lovers that know 0.5 = worst case) but doesnt sound as bad as the KS score of 0.126. How can I define the significance level? were not drawn from the same distribution. On it, you can see the function specification: To subscribe to this RSS feed, copy and paste this URL into your RSS reader. I only understood why I needed to use KS when I started working in a place that used it. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Interpreting ROC Curve and ROC AUC for Classification Evaluation. So with the p-value being so low, we can reject the null hypothesis that the distribution are the same right? You should get the same values for the KS test when (a) your bins are the raw data or (b) your bins are aggregates of the raw data where each bin contains exactly the same values. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? To this histogram I make my two fits (and eventually plot them, but that would be too much code). null hypothesis in favor of the default two-sided alternative: the data Now you have a new tool to compare distributions. Can you show the data sets for which you got dissimilar results? two-sided: The null hypothesis is that the two distributions are against the null hypothesis. What is the correct way to screw wall and ceiling drywalls? Python's SciPy implements these calculations as scipy.stats.ks_2samp (). Follow Up: struct sockaddr storage initialization by network format-string. We carry out the analysis on the right side of Figure 1. When I apply the ks_2samp from scipy to calculate the p-value, its really small = Ks_2sampResult(statistic=0.226, pvalue=8.66144540069212e-23). scipy.stats.ks_1samp. errors may accumulate for large sample sizes. Say in example 1 the age bins were in increments of 3 years, instead of 2 years. The test is nonparametric. GitHub Closed on Jul 29, 2016 whbdupree on Jul 29, 2016 use case is not covered original statistic is more intuitive new statistic is ad hoc, but might (needs Monte Carlo check) be more accurate with only a few ties The distribution that describes the data "best", is the one with the smallest distance to the ECDF. For instance, I read the following example: "For an identical distribution, we cannot reject the null hypothesis since the p-value is high, 41%: (0.41)". It should be obvious these aren't very different. Do you think this is the best way? I then make a (normalized) histogram of these values, with a bin-width of 10.