ks_2samp interpretation ks_2samp interpretation

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. Further, it is not heavily impacted by moderate differences in variance. Learn more about Stack Overflow the company, and our products. I was not aware of the W-M-W test. statistic value as extreme as the value computed from the data. On the image above the blue line represents the CDF for Sample 1 (F1(x)), and the green line is the CDF for Sample 2 (F2(x)). Are you trying to show that the samples come from the same distribution? 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). Also, why are you using the two-sample KS test? What exactly does scipy.stats.ttest_ind test? Why do small African island nations perform better than African continental nations, considering democracy and human development? Why do small African island nations perform better than African continental nations, considering democracy and human development? If I make it one-tailed, would that make it so the larger the value the more likely they are from the same distribution? Are your distributions fixed, or do you estimate their parameters from the sample data? I know the tested list are not the same, as you can clearly see they are not the same in the lower frames. Making statements based on opinion; back them up with references or personal experience. What sort of strategies would a medieval military use against a fantasy giant? Check out the Wikipedia page for the k-s test. Using K-S test statistic, D max can I test the comparability of the above two sets of probabilities? 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. x1 tend to be less than those in x2. The Kolmogorov-Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. Interpreting ROC Curve and ROC AUC for Classification Evaluation. {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 (. Both ROC and KS are robust to data unbalance. Parameters: a, b : sequence of 1-D ndarrays. So i've got two question: Why is the P-value and KS-statistic the same? null hypothesis in favor of the default two-sided alternative: the data Interpretting the p-value when inverting the null hypothesis. By my reading of Hodges, the 5.3 "interpolation formula" follows from 4.10, which is an "asymptotic expression" developed from the same "reflectional method" used to produce the closed expressions 2.3 and 2.4. I am currently working on a binary classification problem with random forests, neural networks etc. While the algorithm itself is exact, numerical If so, in the basics formula I should use the actual number of raw values, not the number of bins? Value from data1 or data2 corresponding with the KS statistic; scipy.stats.kstwo. So I conclude they are different but they clearly aren't? ks_2samp (data1, data2) [source] Computes the Kolmogorov-Smirnov statistic on 2 samples. We choose a confidence level of 95%; that is, we will reject the null Hello Oleg, What's the difference between a power rail and a signal line? 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) from the same distribution. Histogram overlap? 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. Asking for help, clarification, or responding to other answers. I think I know what to do from here now. Is this correct? Compute the Kolmogorov-Smirnov statistic on 2 samples. It looks like you have a reasonably large amount of data (assuming the y-axis are counts). If R2 is omitted (the default) then R1 is treated as a frequency table (e.g. There is even an Excel implementation called KS2TEST. Finally, the formulas =SUM(N4:N10) and =SUM(O4:O10) are inserted in cells N11 and O11. For example, perhaps you only care about whether the median outcome for the two groups are different. Is it suspicious or odd to stand by the gate of a GA airport watching the planes? E.g. 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. 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 . The pvalue=4.976350050850248e-102 is written in Scientific notation where e-102 means 10^(-102). 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. Example 1: One Sample Kolmogorov-Smirnov Test Suppose we have the following sample data: If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? were not drawn from the same distribution. 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. does elena end up with damon; mental health association west orange, nj. A Medium publication sharing concepts, ideas and codes. What video game is Charlie playing in Poker Face S01E07. I'm trying to evaluate/test how well my data fits a particular 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. farmers' almanac ontario summer 2021. Find centralized, trusted content and collaborate around the technologies you use most. Any suggestions as to what tool we could do this with? Is there a proper earth ground point in this switch box? It is important to standardize the samples before the test, or else a normal distribution with a different mean and/or variation (such as norm_c) will fail the test. For Example 1, the formula =KS2TEST(B4:C13,,TRUE) inserted in range F21:G25 generates the output shown in Figure 2. 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) . Now you have a new tool to compare distributions. sample sizes are less than 10000; otherwise, the asymptotic method is used. Since D-stat =.229032 > .224317 = D-crit, we conclude there is a significant difference between the distributions for the samples. If interp = TRUE (default) then harmonic interpolation is used; otherwise linear interpolation is used. Most of the entries in the NAME column of the output from lsof +D /tmp do not begin with /tmp. To do that, I have two functions, one being a gaussian, and one the sum of two gaussians. The chi-squared test sets a lower goal and tends to refuse the null hypothesis less often. This is explained on this webpage. Where does this (supposedly) Gibson quote come from? OP, what do you mean your two distributions? hypothesis in favor of the alternative. 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. its population shown for reference. empirical distribution functions of the samples. CASE 1: statistic=0.06956521739130435, pvalue=0.9451291140844246; CASE 2: statistic=0.07692307692307693, pvalue=0.9999007347628557; CASE 3: statistic=0.060240963855421686, pvalue=0.9984401671284038. The medium classifier has a greater gap between the class CDFs, so the KS statistic is also greater. 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 only takes a minute to sign up. And how does data unbalance affect KS score? Already have an account? distribution functions of the samples. If the sample sizes are very nearly equal it's pretty robust to even quite unequal variances. [I'm using R.]. Are there tables of wastage rates for different fruit and veg? Max, Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Do I need a thermal expansion tank if I already have a pressure tank? 1 st sample : 0.135 0.271 0.271 0.18 0.09 0.053 Example 1: Determine whether the two samples on the left side of Figure 1 come from the same distribution. Thanks for contributing an answer to Cross Validated! is about 1e-16. Is there a single-word adjective for "having exceptionally strong moral principles"? Even if ROC AUC is the most widespread metric for class separation, it is always useful to know both. the median). Define. to be rejected. Is it correct to use "the" before "materials used in making buildings are"? About an argument in Famine, Affluence and Morality. How to interpret p-value of Kolmogorov-Smirnov test (python)? If you assume that the probabilities that you calculated are samples, then you can use the KS2 test. I can't retrieve your data from your histograms. There are three options for the null and corresponding alternative empirical CDFs (ECDFs) of the samples. How to follow the signal when reading the schematic? Therefore, for each galaxy cluster, I have two distributions that I want to compare. Is a PhD visitor considered as a visiting scholar? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. with n as the number of observations on Sample 1 and m as the number of observations in Sample 2. This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. distribution, sample sizes can be different. i.e., the distance between the empirical distribution functions is Hello Ramnath, The statistic Posted by June 11, 2022 cabarrus county sheriff arrests on ks_2samp interpretation June 11, 2022 cabarrus county sheriff arrests on ks_2samp interpretation Can I still use K-S or not? Uncategorized . My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? All other three samples are considered normal, as expected. 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). Use MathJax to format equations. 2. [4] Scipy Api Reference. The two-sample Kolmogorov-Smirnov test is used to test whether two samples come from the same distribution. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. You could have a low max-error but have a high overall average error. Using Scipy's stats.kstest module for goodness-of-fit testing. As stated on this webpage, the critical values are c()*SQRT((m+n)/(m*n)) Fitting distributions, goodness of fit, p-value. If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? Under the null hypothesis the two distributions are identical, G (x)=F (x). Charles. Follow Up: struct sockaddr storage initialization by network format-string. Suppose we wish to test the null hypothesis that two samples were drawn I have some data which I want to analyze by fitting a function to it. Am I interpreting this incorrectly? Use MathJax to format equations. calculate a p-value with ks_2samp. Charles. Here are histograms of the two sample, each with the density function of 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. Is it correct to use "the" before "materials used in making buildings are"? So, CASE 1 refers to the first galaxy cluster, let's say, etc. Perform a descriptive statistical analysis and interpret your results. cell E4 contains the formula =B4/B14, cell E5 contains the formula =B5/B14+E4 and cell G4 contains the formula =ABS(E4-F4). To do that I use the statistical function ks_2samp from scipy.stats. ks_2samp (data1, data2) Computes the Kolmogorov-Smirnof statistic on 2 samples. 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. The ks calculated by ks_calc_2samp is because of the searchsorted () function (students who are interested can simulate the data to see this function by themselves), the Nan value will be sorted to the maximum by default, thus changing the original cumulative distribution probability of the data, resulting in the calculated ks There is an error Somewhat similar, but not exactly the same. Even in this case, you wont necessarily get the same KS test results since the start of the first bin will also be relevant. If the first sample were drawn from a uniform distribution and the second Notes This tests whether 2 samples are drawn from the same distribution. There cannot be commas, excel just doesnt run this command. 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. In this case, 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. 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)". How can I make a dictionary (dict) from separate lists of keys and values? Excel does not allow me to write like you showed: =KSINV(A1, B1, C1). Minimising the environmental effects of my dyson brain, Styling contours by colour and by line thickness in QGIS. Why is this the case? rev2023.3.3.43278. The null hypothesis is H0: both samples come from a population with the same distribution. 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. The best answers are voted up and rise to the top, 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. and then subtracts from 1. You need to have the Real Statistics add-in to Excel installed to use the KSINV function. This performs a test of the distribution G (x) of an observed random variable against a given distribution F (x). So, heres my follow-up question. Suppose, however, that the first sample were drawn from Charles. The p value is evidence as pointed in the comments . rev2023.3.3.43278. 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: The distribution naturally only has values >= 0. Hodges, J.L. One such test which is popularly used is the Kolmogorov Smirnov Two Sample Test (herein also referred to as "KS-2"). The p-value returned by the k-s test has the same interpretation as other p-values. Accordingly, I got the following 2 sets of probabilities: Poisson approach : 0.135 0.271 0.271 0.18 0.09 0.053 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 . It seems straightforward, give it: (A) the data; (2) the distribution; and (3) the fit parameters. 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.". 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). to be consistent with the null hypothesis most of the time. Ejemplo 1: Prueba de Kolmogorov-Smirnov de una muestra Defines the method used for calculating the p-value. Is it a bug? 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. The region and polygon don't match. KS uses a max or sup norm. of two independent samples. What Is the Difference Between 'Man' And 'Son of Man' in Num 23:19? Connect and share knowledge within a single location that is structured and easy to search. After some research, I am honestly a little confused about how to interpret the results. Time arrow with "current position" evolving with overlay number. 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. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? For each galaxy cluster, I have a photometric catalogue. In the same time, we observe with some surprise . Asking for help, clarification, or responding to other answers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 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. 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. I only understood why I needed to use KS when I started working in a place that used it. How to handle a hobby that makes income in US, Minimising the environmental effects of my dyson brain. Nevertheless, it can be a little hard on data some times. THis means that there is a significant difference between the two distributions being tested. x1 (blue) because the former plot lies consistently to the right edit: A p_value of pvalue=0.55408436218441004 is saying that the normal and gamma sampling are from the same distirbutions? expect the null hypothesis to be rejected with alternative='less': and indeed, with p-value smaller than our threshold, we reject the null My only concern is about CASE 1, where the p-value is 0.94, and I do not know if it is a problem or not. How do I align things in the following tabular environment? Your question is really about when to use the independent samples t-test and when to use the Kolmogorov-Smirnov two sample test; the fact of their implementation in scipy is entirely beside the point in relation to that issue (I'd remove that bit). Hello Sergey, The 2 sample KolmogorovSmirnov test of distribution for two different samples. where c() = the inverse of the Kolmogorov distribution at , which can be calculated in Excel as. Can you show the data sets for which you got dissimilar results? alternative is that F(x) > G(x) for at least one x. of the latter. Thank you for the nice article and good appropriate examples, especially that of frequency distribution. Master in Deep Learning for CV | Data Scientist @ Banco Santander | Generative AI Researcher | http://viniciustrevisan.com/, # Performs the KS normality test in the samples, norm_a: ks = 0.0252 (p-value = 9.003e-01, is normal = True), norm_a vs norm_b: ks = 0.0680 (p-value = 1.891e-01, are equal = True), Count how many observations within the sample are lesser or equal to, Divide by the total number of observations on the sample, We need to calculate the CDF for both distributions, We should not standardize the samples if we wish to know if their distributions are. 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. scipy.stats.ks_1samp. The KOLMOGOROV-SMIRNOV TWO SAMPLE TEST command automatically saves the following parameters. When you say it's truncated at 0, can you elaborate? Often in statistics we need to understand if a given sample comes from a specific distribution, most commonly the Normal (or Gaussian) distribution. How to prove that the supernatural or paranormal doesn't exist? This is a very small value, close to zero. Learn more about Stack Overflow the company, and our products. For example, $\mu_1 = 11/20 = 5.5$ and $\mu_2 = 12/20 = 6.0.$ Furthermore, the K-S test rejects the null hypothesis Is it possible to create a concave light? The codes for this are available on my github, so feel free to skip this part. ks_2samp interpretation. Ahh I just saw it was a mistake in my calculation, thanks! To subscribe to this RSS feed, copy and paste this URL into your RSS reader. I tried this out and got the same result (raw data vs freq table). Two arrays of sample observations assumed to be drawn from a continuous Why does using KS2TEST give me a different D-stat value than using =MAX(difference column) for the test statistic? rev2023.3.3.43278. epidata.it/PDF/H0_KS.pdf. Most of the entries in the NAME column of the output from lsof +D /tmp do not begin with /tmp. If your bins are derived from your raw data, and each bin has 0 or 1 members, this assumption will almost certainly be false. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The f_a sample comes from a F distribution. Really appreciate if you could help, Hello Antnio, All of them measure how likely a sample is to have come from a normal distribution, with a related p-value to support this measurement. I just performed a KS 2 sample test on my distributions, and I obtained the following results: How can I interpret these results? You can have two different distributions that are equal with respect to some measure of the distribution (e.g. Are <0 recorded as 0 (censored/Winsorized) or are there simply no values that would have been <0 at all -- they're not observed/not in the sample (distribution is actually truncated)? suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in Why is this the case? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. [3] Scipy Api Reference. The KS method is a very reliable test. situations in which one of the sample sizes is only a few thousand. All right, the test is a lot similar to other statistic tests. 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). This isdone by using the Real Statistics array formula =SortUnique(J4:K11) in range M4:M10 and then inserting the formula =COUNTIF(J$4:J$11,$M4) in cell N4 and highlighting the range N4:O10 followed by Ctrl-R and Ctrl-D. To test the goodness of these fits, I test the with scipy's ks-2samp test. Perhaps this is an unavoidable shortcoming of the KS test. On a side note, are there other measures of distribution that shows if they are similar? Is this the most general expression of the KS test ? To learn more, see our tips on writing great answers. What is a word for the arcane equivalent of a monastery? It returns 2 values and I find difficulties how to interpret them. I am not familiar with the Python implementation and so I am unable to say why there is a difference.