ks_2samp interpretation
To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Your home for data science. Often in statistics we need to understand if a given sample comes from a specific distribution, most commonly the Normal (or Gaussian) distribution. As it happens with ROC Curve and ROC AUC, we cannot calculate the KS for a multiclass problem without transforming that into a binary classification problem. Somewhat similar, but not exactly the same. The result of both tests are that the KS-statistic is $0.15$, and the P-value is $0.476635$. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Hi Charles, used to compute an approximate p-value. 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. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Two-sample Kolmogorov-Smirnov test with errors on data points, Interpreting scipy.stats: ks_2samp and mannwhitneyu give conflicting results, Wasserstein distance and Kolmogorov-Smirnov statistic as measures of effect size, Kolmogorov-Smirnov p-value and alpha value in python, Kolmogorov-Smirnov Test in Python weird result and interpretation. What do you recommend the best way to determine which distribution best describes the data? The p-value returned by the k-s test has the same interpretation as other p-values. 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). Do you have any ideas what is the problem? It looks like you have a reasonably large amount of data (assuming the y-axis are counts). Sorry for all the questions. The p value is evidence as pointed in the comments . scipy.stats.kstest. During assessment of the model, I generated the below KS-statistic. how to select best fit continuous distribution from two Goodness-to-fit tests? Since D-stat =.229032 > .224317 = D-crit, we conclude there is a significant difference between the distributions for the samples. If b = FALSE then it is assumed that n1 and n2 are sufficiently large so that the approximation described previously can be used. Perhaps this is an unavoidable shortcoming of the KS test. Is there a single-word adjective for "having exceptionally strong moral principles"? This is the same problem that you see with histograms. Is there a proper earth ground point in this switch box? Connect and share knowledge within a single location that is structured and easy to search. MathJax reference. I have 2 sample data set. Finally, the formulas =SUM(N4:N10) and =SUM(O4:O10) are inserted in cells N11 and O11. 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. 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. 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. 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. scipy.stats.ks_2samp(data1, data2, alternative='two-sided', mode='auto') [source] . THis means that there is a significant difference between the two distributions being tested. Thank you for your answer. It should be obvious these aren't very different. Do new devs get fired if they can't solve a certain bug? We can use the KS 1-sample test to do that. Cell G14 contains the formula =MAX(G4:G13) for the test statistic and cell G15 contains the formula =KSINV(G1,B14,C14) for the critical value. ks_2samp Notes There are three options for the null and corresponding alternative hypothesis that can be selected using the alternative parameter. Charles. Are there tables of wastage rates for different fruit and veg? I would not want to claim the Wilcoxon test Why are trials on "Law & Order" in the New York Supreme Court? However, the test statistic or p-values can still be interpreted as a distance measure. We generally follow Hodges treatment of Drion/Gnedenko/Korolyuk [1]. that is, the probability under the null hypothesis of obtaining a test What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? KS Test is also rather useful to evaluate classification models, and I will write a future article showing how can we do that. Is this correct? @meri: there's an example on the page I linked to. I then make a (normalized) histogram of these values, with a bin-width of 10. And how does data unbalance affect KS score? 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. If so, in the basics formula I should use the actual number of raw values, not the number of bins? In the latter case, there shouldn't be a difference at all, since the sum of two normally distributed random variables is again normally distributed. There is even an Excel implementation called KS2TEST. Why does using KS2TEST give me a different D-stat value than using =MAX(difference column) for the test statistic? thanks again for your help and explanations. https://en.wikipedia.org/wiki/Gamma_distribution, How Intuit democratizes AI development across teams through reusability. calculate a p-value with ks_2samp. Assuming that one uses the default assumption of identical variances, the second test seems to be testing for identical distribution as well. Strictly, speaking they are not sample values but they are probabilities of Poisson and Approximated Normal distribution for selected 6 x values. We can also use the following functions to carry out the analysis. errors may accumulate for large sample sizes. rev2023.3.3.43278. Theoretically Correct vs Practical Notation. were not drawn from the same distribution. A place where magic is studied and practiced? ks_2samp(df.loc[df.y==0,"p"], df.loc[df.y==1,"p"]) It returns KS score 0.6033 and p-value less than 0.01 which means we can reject the null hypothesis and concluding distribution of events and non . If KS2TEST doesnt bin the data, how does it work ? Two arrays of sample observations assumed to be drawn from a continuous scipy.stats.ks_2samp. @CrossValidatedTrading Should there be a relationship between the p-values and the D-values from the 2-sided KS test? Interpretting the p-value when inverting the null hypothesis. Thank you for the nice article and good appropriate examples, especially that of frequency distribution. It does not assume that data are sampled from Gaussian distributions (or any other defined distributions). How to prove that the supernatural or paranormal doesn't exist? Is it suspicious or odd to stand by the gate of a GA airport watching the planes? Compute the Kolmogorov-Smirnov statistic on 2 samples. distribution functions of the samples. So with the p-value being so low, we can reject the null hypothesis that the distribution are the same right? 11 Jun 2022. 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. Jr., The Significance Probability of the Smirnov The values in columns B and C are the frequencies of the values in column A. not entirely appropriate. If that is the case, what are the differences between the two tests? About an argument in Famine, Affluence and Morality. Really appreciate if you could help, Hello Antnio, with n as the number of observations on Sample 1 and m as the number of observations in Sample 2. 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. Asking for help, clarification, or responding to other answers. To this histogram I make my two fits (and eventually plot them, but that would be too much code). What video game is Charlie playing in Poker Face S01E07. I trained a default Nave Bayes classifier for each dataset. As shown at https://www.real-statistics.com/binomial-and-related-distributions/poisson-distribution/ Z = (X -m)/m should give a good approximation to the Poisson distribution (for large enough samples). betanormal1000ks_2sampbetanorm p-value=4.7405805465370525e-1595%betanorm 3 APP "" 2 1.1W 9 12 In this case, the bin sizes wont be the same. Defines the null and alternative hypotheses. Notes This tests whether 2 samples are drawn from the same distribution. I am not familiar with the Python implementation and so I am unable to say why there is a difference. the median). The chi-squared test sets a lower goal and tends to refuse the null hypothesis less often. par | Juil 2, 2022 | mitchell wesley carlson charged | justin strauss net worth | Juil 2, 2022 | mitchell wesley carlson charged | justin strauss net worth 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). rev2023.3.3.43278. I got why theyre slightly different. 90% critical value (alpha = 0.10) for the K-S two sample test statistic. Both ROC and KS are robust to data unbalance. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? 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). if the p-value is less than 95 (for a level of significance of 5%), this means that you cannot reject the Null-Hypothese that the two sample distributions are identical.". The region and polygon don't match. So let's look at largish datasets [2] Scipy Api Reference. {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 (. What exactly does scipy.stats.ttest_ind test? identical, F(x)=G(x) for all x; the alternative is that they are not Kolmogorov-Smirnov (KS) Statistics is one of the most important metrics used for validating predictive models. The only problem is my results don't make any sense? Time arrow with "current position" evolving with overlay number. from the same distribution. So, heres my follow-up question. This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. K-S tests aren't exactly Making statements based on opinion; back them up with references or personal experience. scipy.stats. Use the KS test (again!) 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. 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. To learn more, see our tips on writing great answers. How about the first statistic in the kstest output? Hodges, J.L. Call Us: (818) 994-8526 (Mon - Fri). The Kolmogorov-Smirnov statistic D is given by. Why is there a voltage on my HDMI and coaxial cables? D-stat) for samples of size n1 and n2. 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. Charles. If the the assumptions are true, the t-test is good at picking up a difference in the population means. 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. Are the two samples drawn from the same distribution ? Kolmogorov-Smirnov scipy_stats.ks_2samp Distribution Comparison, We've added a "Necessary cookies only" option to the cookie consent popup. How do I make function decorators and chain them together? The classifier could not separate the bad example (right), though. scipy.stats.ks_2samp. from scipy.stats import ks_2samp s1 = np.random.normal(loc = loc1, scale = 1.0, size = size) s2 = np.random.normal(loc = loc2, scale = 1.0, size = size) (ks_stat, p_value) = ks_2samp(data1 = s1, data2 = s2) . 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. [4] Scipy Api Reference. Now you have a new tool to compare distributions. 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. ks_2samp (data1, data2) [source] Computes the Kolmogorov-Smirnov statistic on 2 samples. 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. The distribution naturally only has values >= 0. the cumulative density function (CDF) of the underlying distribution tends It seems straightforward, give it: (A) the data; (2) the distribution; and (3) the fit parameters. Are there tables of wastage rates for different fruit and veg? We cannot consider that the distributions of all the other pairs are equal. underlying distributions, not the observed values of the data. 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. Hello Ramnath, There are several questions about it and I was told to use either the scipy.stats.kstest or scipy.stats.ks_2samp. For business teams, it is not intuitive to understand that 0.5 is a bad score for ROC AUC, while 0.75 is only a medium one. Is it correct to use "the" before "materials used in making buildings are"? Newbie Kolmogorov-Smirnov question. How do I determine sample size for a test? If p<0.05 we reject the null hypothesis and assume that the sample does not come from a normal distribution, as it happens with f_a. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. I have detailed the KS test for didatic purposes, but both tests can easily be performed by using the scipy module on python. Sure, table for converting D stat to p-value: @CrossValidatedTrading: Your link to the D-stat-to-p-value table is now 404. I wouldn't call that truncated at all. And how to interpret these values? Follow Up: struct sockaddr storage initialization by network format-string. How to handle a hobby that makes income in US. 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. +1 if the empirical distribution function of data1 exceeds Parameters: a, b : sequence of 1-D ndarrays. which is contributed to testing of normality and usefulness of test as they lose power as the sample size increase. sample sizes are less than 10000; otherwise, the asymptotic method is used. Is there a proper earth ground point in this switch box? 1. Here, you simply fit a gamma distribution on some data, so of course, it's no surprise the test yielded a high p-value (i.e. Time arrow with "current position" evolving with overlay number. How can I make a dictionary (dict) from separate lists of keys and values? As an example, we can build three datasets with different levels of separation between classes (see the code to understand how they were built). Default is two-sided. The a and b parameters are my sequence of data or I should calculate the CDFs to use ks_2samp? The Kolmogorov-Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. To learn more, see our tips on writing great answers. The two-sample KS test allows us to compare any two given samples and check whether they came from the same distribution. 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. You mean your two sets of samples (from two distributions)? Topological invariance of rational Pontrjagin classes for non-compact spaces. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's testing whether the samples come from the same distribution (Be careful it doesn't have to be normal distribution). The medium classifier has a greater gap between the class CDFs, so the KS statistic is also greater. It seems straightforward, give it: (A) the data; (2) the distribution; and (3) the fit parameters. If method='auto', an exact p-value computation is attempted if both Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics Can I still use K-S or not? Further, just because two quantities are "statistically" different, it does not mean that they are "meaningfully" different. 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. measured at this observation. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. ks_2samp(X_train.loc[:,feature_name],X_test.loc[:,feature_name]).statistic # 0.11972417623102555. When txt = TRUE, then the output takes the form < .01, < .005, > .2 or > .1. It is widely used in BFSI domain. The two-sided exact computation computes the complementary probability Also, why are you using the two-sample KS test? Let me re frame my problem. Two-sample Kolmogorov-Smirnov Test in Python Scipy, scipy kstest not consistent over different ranges. We can now perform the KS test for normality in them: We compare the p-value with the significance. 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. For Example 1, the formula =KS2TEST(B4:C13,,TRUE) inserted in range F21:G25 generates the output shown in Figure 2. What Is the Difference Between 'Man' And 'Son of Man' in Num 23:19? In any case, if an exact p-value calculation is attempted and fails, a You can find the code snippets for this on my GitHub repository for this article, but you can also use my article on Multiclass ROC Curve and ROC AUC as a reference: The KS and the ROC AUC techniques will evaluate the same metric but in different manners. to be less than the CDF underlying the second sample. Check it out! scipy.stats.kstwo. Note that the alternative hypotheses describe the CDFs of the hypothesis in favor of the alternative. Example 1: Determine whether the two samples on the left side of Figure 1 come from the same distribution. Hello Ramnath, Does a barbarian benefit from the fast movement ability while wearing medium armor? warning will be emitted, and the asymptotic p-value will be returned. Mail us for help: info@monterrosatax.com 14541 Sylvan St, Van nuys CA 91411 So i've got two question: Why is the P-value and KS-statistic the same? dosage acide sulfurique + soude; ptition assemble nationale edf 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. Dear Charles, KDE overlaps? I think I know what to do from here now.