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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 can find tables online for the conversion of the D statistic into a p-value if you are interested in the procedure. . Example 1: Determine whether the two samples on the left side of Figure 1 come from the same distribution. The result of both tests are that the KS-statistic is $0.15$, and the P-value is $0.476635$. scipy.stats.ks_2samp SciPy v0.15.1 Reference Guide 99% critical value (alpha = 0.01) for the K-S two sample test statistic. Connect and share knowledge within a single location that is structured and easy to search. Hello Ramnath, The null hypothesis is H0: both samples come from a population with the same distribution. Comparing sample distributions with the Kolmogorov-Smirnov (KS) test How to react to a students panic attack in an oral exam? Excel does not allow me to write like you showed: =KSINV(A1, B1, C1). There are three options for the null and corresponding alternative To do that, I have two functions, one being a gaussian, and one the sum of two gaussians. We've added a "Necessary cookies only" option to the cookie consent popup. Asking for help, clarification, or responding to other answers. The values of c()are also the numerators of the last entries in the Kolmogorov-Smirnov Table. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. I can't retrieve your data from your histograms. 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. I dont understand the rest of your comment. ks_2samp interpretation. Why is this the case? Copyright 2008-2023, The SciPy community. The only problem is my results don't make any sense? 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. two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different. 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. Statistics for applications thanks again for your help and explanations. How to interpret `scipy.stats.kstest` and `ks_2samp` to evaluate `fit` of data to a distribution? We first show how to perform the KS test manually and then we will use the KS2TEST function. Further, it is not heavily impacted by moderate differences in variance. How do I make function decorators and chain them together? . I have detailed the KS test for didatic purposes, but both tests can easily be performed by using the scipy module on python. 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 to handle a hobby that makes income in US, Minimising the environmental effects of my dyson brain. Ah. vegan) just to try it, does this inconvenience the caterers and staff? 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.