By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Ahh I just saw it was a mistake in my calculation, thanks! Perhaps this is an unavoidable shortcoming of the KS test. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? 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. Hello Ramnath, The p-values are wrong if the parameters are estimated. What is a word for the arcane equivalent of a monastery? The alternative hypothesis can be either 'two-sided' (default), 'less' or . Assuming that one uses the default assumption of identical variances, the second test seems to be testing for identical distribution as well. Is there a proper earth ground point in this switch box? So, CASE 1 refers to the first galaxy cluster, let's say, etc. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It seems straightforward, give it: (A) the data; (2) the distribution; and (3) the fit parameters. hypothesis in favor of the alternative. 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. If that is the case, what are the differences between the two tests? Interpreting ROC Curve and ROC AUC for Classification Evaluation. MathJax reference. If the first sample were drawn from a uniform distribution and the second Is it possible to create a concave light? What is the point of Thrower's Bandolier? hypothesis in favor of the alternative if the p-value is less than 0.05. The pvalue=4.976350050850248e-102 is written in Scientific notation where e-102 means 10^(-102). 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. I can't retrieve your data from your histograms. were not drawn from the same 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. 90% critical value (alpha = 0.10) for the K-S two sample test statistic. You can find tables online for the conversion of the D statistic into a p-value if you are interested in the procedure. Thanks for contributing an answer to Cross Validated! It seems to assume that the bins will be equally spaced. Is it correct to use "the" before "materials used in making buildings are"? And also this post Is normality testing 'essentially useless'? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. It is a very efficient way to determine if two samples are significantly different from each other. The two-sample Kolmogorov-Smirnov test attempts to identify any differences in distribution of the populations the samples were drawn from. Example 2: Determine whether the samples for Italy and France in Figure 3come from the same distribution. 99% critical value (alpha = 0.01) for the K-S two sample test statistic. Here are histograms of the two sample, each with the density function of However, the test statistic or p-values can still be interpreted as a distance measure. Does Counterspell prevent from any further spells being cast on a given turn? warning will be emitted, and the asymptotic p-value will be returned. 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). If you assume that the probabilities that you calculated are samples, then you can use the KS2 test. The a and b parameters are my sequence of data or I should calculate the CDFs to use ks_2samp? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Share Cite Follow answered Mar 12, 2020 at 19:34 Eric Towers 65.5k 3 48 115 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. 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 . Connect and share knowledge within a single location that is structured and easy to search. Histogram overlap? Now, for the same set of x, I calculate the probabilities using the Z formula that is Z = (x-m)/(m^0.5). 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. 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 this case, probably a paired t-test is appropriate, or if the normality assumption is not met, the Wilcoxon signed-ranks test could be used. It only takes a minute to sign up. 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. If method='asymp', the asymptotic Kolmogorov-Smirnov distribution is 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. How about the first statistic in the kstest output? empirical distribution functions of the samples. A place where magic is studied and practiced? Is this the most general expression of the KS test ? 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. For this intent we have the so-called normality tests, such as Shapiro-Wilk, Anderson-Darling or the Kolmogorov-Smirnov test. We can evaluate the CDF of any sample for a given value x with a simple algorithm: As I said before, the KS test is largely used for checking whether a sample is normally distributed. [3] Scipy Api Reference. When txt = TRUE, then the output takes the form < .01, < .005, > .2 or > .1. Therefore, we would KSINV(p, n1, n2, b, iter0, iter) = the critical value for significance level p of the two-sample Kolmogorov-Smirnov test for samples of size n1 and n2. scipy.stats.ks_2samp(data1, data2) [source] Computes the Kolmogorov-Smirnov statistic on 2 samples. How can I test that both the distributions are comparable. It's testing whether the samples come from the same distribution (Be careful it doesn't have to be normal distribution). Can you please clarify the following: in KS two sample example on Figure 1, Dcrit in G15 cell uses B/C14 cells, which are not n1/n2 (they are both = 10) but total numbers of men/women used in the data (80 and 62). the cumulative density function (CDF) of the underlying distribution tends 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. {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 (. Taking m =2, I calculated the Poisson probabilities for x= 0, 1,2,3,4, and 5. [2] Scipy Api Reference. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 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. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. It only takes a minute to sign up. draw two independent samples s1 and s2 of length 1000 each, from the same continuous distribution. Learn more about Stack Overflow the company, and our products. I then make a (normalized) histogram of these values, with a bin-width of 10. The null hypothesis is H0: both samples come from a population with the same distribution. Why do many companies reject expired SSL certificates as bugs in bug bounties? How to follow the signal when reading the schematic? How to interpret KS statistic and p-value form scipy.ks_2samp? Business interpretation: in the project A, all three user groups behave the same way. Your samples are quite large, easily enough to tell the two distributions are not identical, in spite of them looking quite similar. I would not want to claim the Wilcoxon test Find centralized, trusted content and collaborate around the technologies you use most. I have some data which I want to analyze by fitting a function to it. In the figure I showed I've got 1043 entries, roughly between $-300$ and $300$. makes way more sense now. "We, who've been connected by blood to Prussia's throne and people since Dppel". What hypothesis are you trying to test? 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)). 31 Mays 2022 in paradise hills what happened to amarna Yorum yaplmam 0 . 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. 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. 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 learn more, see our tips on writing great answers. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 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. The f_a sample comes from a F distribution. You can download the add-in free of charge. Learn more about Stack Overflow the company, and our products. The overlap is so intense on the bad dataset that the classes are almost inseparable. Follow Up: struct sockaddr storage initialization by network format-string. 95% critical value (alpha = 0.05) for the K-S two sample test statistic. I am sure I dont output the same value twice, as the included code outputs the following: (hist_cm is the cumulative list of the histogram points, plotted in the upper frames). When doing a Google search for ks_2samp, the first hit is this website. a normal distribution shifted toward greater values. Finally, we can use the following array function to perform the test. 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. 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. 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 trained a default Nave Bayes classifier for each dataset. As an example, we can build three datasets with different levels of separation between classes (see the code to understand how they were built). Please see explanations in the Notes below. scipy.stats. The statistic 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). MIT (2006) Kolmogorov-Smirnov test. What exactly does scipy.stats.ttest_ind test? Is there a proper earth ground point in this switch box? [1] Scipy Api Reference. Interpretting the p-value when inverting the null hypothesis. 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. There cannot be commas, excel just doesnt run this command. Why do small African island nations perform better than African continental nations, considering democracy and human development? For example I have two data sets for which the p values are 0.95 and 0.04 for the ttest(tt_equal_var=True) and the ks test, respectively. P(X=0), P(X=1)P(X=2),P(X=3),P(X=4),P(X >=5) shown as the Ist sample values (actually they are not). we cannot reject the null hypothesis. how to select best fit continuous distribution from two Goodness-to-fit tests? I wouldn't call that truncated at all. Hi Charles, The test statistic $D$ of the K-S test is the maximum vertical distance between the As stated on this webpage, the critical values are c()*SQRT((m+n)/(m*n)) Is normality testing 'essentially useless'? If method='auto', an exact p-value computation is attempted if both Scipy ttest_ind versus ks_2samp. So let's look at largish datasets And if I change commas on semicolons, then it also doesnt show anything (just an error). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 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. 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. Finite abelian groups with fewer automorphisms than a subgroup. When you say that you have distributions for the two samples, do you mean, for example, that for x = 1, f(x) = .135 for sample 1 and g(x) = .106 for sample 2? If KS2TEST doesnt bin the data, how does it work ? [4] Scipy Api Reference. The only problem is my results don't make any sense? ks_2samp interpretation. It is most suited to Could you please help with a problem. scipy.stats.ks_2samp(data1, data2, alternative='two-sided', mode='auto') [source] . 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. 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. Example 1: One Sample Kolmogorov-Smirnov Test. used to compute an approximate p-value. edit: If you wish to understand better how the KS test works, check out my article about this subject: All the code is available on my github, so Ill only go through the most important parts. 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). 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. For example, perhaps you only care about whether the median outcome for the two groups are different. Can you please clarify? The p value is evidence as pointed in the comments . empirical CDFs (ECDFs) of the samples. Do you think this is the best way? Do you have some references? For example, x1 (blue) because the former plot lies consistently to the right 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. From the docs scipy.stats.ks_2samp This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution scipy.stats.ttest_ind This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. Figure 1 Two-sample Kolmogorov-Smirnov test. Does Counterspell prevent from any further spells being cast on a given turn? MathJax reference. To learn more, see our tips on writing great answers. On it, you can see the function specification: To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It is widely used in BFSI domain. The p-value returned by the k-s test has the same interpretation as other p-values. Charles. 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. 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. 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 (data1, data2) Computes the Kolmogorov-Smirnof statistic on 2 samples. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 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. (this might be a programming question). The medium classifier has a greater gap between the class CDFs, so the KS statistic is also greater. KS2TEST gives me a higher d-stat value than any of the differences between cum% A and cum%B, The max difference is 0.117 Can you give me a link for the conversion of the D statistic into a p-value? 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. @O.rka But, if you want my opinion, using this approach isn't entirely unreasonable. https://en.wikipedia.org/wiki/Gamma_distribution, How Intuit democratizes AI development across teams through reusability. Is it suspicious or odd to stand by the gate of a GA airport watching the planes? How do I align things in the following tabular environment? Asking for help, clarification, or responding to other answers. What is a word for the arcane equivalent of a monastery? We can also use the following functions to carry out the analysis. * specifically for its level to be correct, you need this assumption when the null hypothesis is true. This test compares the underlying continuous distributions F(x) and G(x) 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 Kolmogorov-Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. So i've got two question: Why is the P-value and KS-statistic the same? Max, There are several questions about it and I was told to use either the scipy.stats.kstest or scipy.stats.ks_2samp. I know the tested list are not the same, as you can clearly see they are not the same in the lower frames. Can airtags be tracked from an iMac desktop, with no iPhone? How to fit a lognormal distribution in Python? The only problem is my results don't make any sense? This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Notes This tests whether 2 samples are drawn from the same distribution. There is even an Excel implementation called KS2TEST. Making statements based on opinion; back them up with references or personal experience. Scipy2KS scipy kstest from scipy.stats import kstest import numpy as np x = np.random.normal ( 0, 1, 1000 ) test_stat = kstest (x, 'norm' ) #>>> test_stat # (0.021080234718821145, 0.76584491300591395) p0.762 Hodges, J.L. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. It is weaker than the t-test at picking up a difference in the mean but it can pick up other kinds of difference that the t-test is blind to. [5] Trevisan, V. Interpreting ROC Curve and ROC AUC for Classification Evaluation. Also, I'm pretty sure the KT test is only valid if you have a fully specified distribution in mind beforehand. 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? Use MathJax to format equations. The only difference then appears to be that the first test assumes continuous distributions. 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. 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. Can I tell police to wait and call a lawyer when served with a search warrant? Thanks for contributing an answer to Cross Validated! Hello Oleg, Confidence intervals would also assume it under the alternative. which is contributed to testing of normality and usefulness of test as they lose power as the sample size increase. [1] Adeodato, P. J. L., Melo, S. M. On the equivalence between Kolmogorov-Smirnov and ROC curve metrics for binary classification. Most of the entries in the NAME column of the output from lsof +D /tmp do not begin with /tmp. About an argument in Famine, Affluence and Morality. 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? I have detailed the KS test for didatic purposes, but both tests can easily be performed by using the scipy module on python. 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. 1. to be less than the CDF underlying the second sample. Check out the Wikipedia page for the k-s test. I dont understand the rest of your comment. Let me re frame my problem. Main Menu. suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in The chi-squared test sets a lower goal and tends to refuse the null hypothesis less often. Is it possible to do this with Scipy (Python)? Is there a reason for that? 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. 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. A Medium publication sharing concepts, ideas and codes. where KINV is defined in Kolmogorov Distribution. Connect and share knowledge within a single location that is structured and easy to search. 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). Help please! Charles. Indeed, the p-value is lower than our threshold of 0.05, so we reject the Is it possible to rotate a window 90 degrees if it has the same length and width? x1 tend to be less than those in x2. 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. is the magnitude of the minimum (most negative) difference between the So I conclude they are different but they clearly aren't? The calculations dont assume that m and n are equal. Is a collection of years plural or singular? ks_2samp Notes There are three options for the null and corresponding alternative hypothesis that can be selected using the alternative parameter. Further, just because two quantities are "statistically" different, it does not mean that they are "meaningfully" different. And how to interpret these values? does elena end up with damon; mental health association west orange, nj.
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