{"id":180793,"date":"2024-04-24T22:06:43","date_gmt":"2024-04-24T21:06:43","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=180793"},"modified":"2024-02-28T23:22:58","modified_gmt":"2024-02-28T22:22:58","slug":"kolmogorov-smirnov-test-understanding-this-statistical-method","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/kolmogorov-smirnov-test-understanding-this-statistical-method","title":{"rendered":"Kolmogorov-Smirnov Test: Understanding this Statistical Method"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"180793\" class=\"elementor elementor-180793\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cbf2f6a e-flex e-con-boxed e-con\" data-id=\"cbf2f6a\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a4067a3 elementor-widget elementor-widget-heading\" data-id=\"a4067a3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">The Kolmogorov-Smirnov test is a widely used method for comparing data. Discover the amazing story of its invention, and how it is used today in Data Science!<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6bec4fc e-flex e-con-boxed e-con\" data-id=\"6bec4fc\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-de8a1aa elementor-widget elementor-widget-text-editor\" data-id=\"de8a1aa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>In 1933, Andrei Kolmogorov published an article entitled &#8220;Sulla determinazione empirica di una legge di distribuzione&#8221; (On the empirical determination of a distribution law).<\/p><p>In it, the mathematician presented the notion of <strong>empirical cumulative distribution (ECD)<\/strong> and the corresponding test statistic.<\/p><p>He was interested in how data could be compared with a theoretical distribution without assuming a specific form for the distribution.<\/p><p>His method was based on the maximum difference between the <strong>DCE and the DCT (theoretical cumulative distribution)<\/strong>, and he proposed a test statistic to quantify this difference.<\/p><p>A few years later, in 1939, Nikolai Smirnov developed a similar approach completely by accident, in his article <strong>&#8220;Estimation of the difference between empirical distribution functions in two independent samples&#8221;.<\/strong><\/p><p>His aim was also to propose a non-parametric method for comparing two independent samples of data.<\/p><p>For his part, he proposed defining a test statistic based on the <a href=\"https:\/\/datascientest.com\/en\/data-quality-10-mistakes-not-to-make\">maximum difference between the two EDFs of the data samples.<\/a><\/p><p>It was only at a mathematics conference that Kolmogorov and Smirnov met by chance. As they began to discuss their respective research, they realised that they were working on similar problems independently.<\/p><p>As they exchanged ideas and results, they were astonished to realise that their methods and formulas were extremely similar.<\/p><p>Surprised by this coincidence, the two mathematicians decided to work together to develop a common approach. They combined their ideas and expertise to create the <strong>&#8220;Kolmogorov-Smirnov Test&#8221;.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e170399 e-flex e-con-boxed e-con\" data-id=\"e170399\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e4d915e elementor-widget elementor-widget-heading\" data-id=\"e4d915e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is the Kolmogorov-Smirnov test?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d796f17 elementor-widget elementor-widget-text-editor\" data-id=\"d796f17\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Used in many fields, the<em> Kolomogorov-Smirnov<\/em> test is a powerful statistical tool. It is used to assess the similarity between an empirical distribution and a theoretical distribution, or to compare two distributions.<\/p><p>It is based on two key concepts: the ECD and the CTD. The ECD is the empirical cumulative distribution. It is constructed from observed data, and represents the proportion of observations less than or equal to a given value.<\/p><p>The TCD, on the other hand, is the theoretical cumulative distribution. It is based on a theoretical distribution specified by the user.<\/p><p>The aim of the test is to measure the maximum distance (test statistic D) between the TCD and the TCD. D is calculated by taking the absolute value of the greatest difference between the two cumulative distributions.<\/p><p>The higher its value, the <strong>greater the difference between the empirical distribution and the theoretical distribution.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-66ef64a elementor-widget elementor-widget-image\" data-id=\"66ef64a\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/05\/Test-de-Kolmogorov-Smirnov-1.jpg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c0fe05 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"9c0fe05\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Learn how to use the Kolmogorov-Smirnov test<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5c8d89 elementor-widget elementor-widget-text-editor\" data-id=\"b5c8d89\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>To assess the <strong>significance of the test<\/strong>, a P value is calculated. It represents the probability of obtaining a value of D that is as extreme or more extreme than the one observed.<\/p><p>In addition, the null hypothesis states that the two distributions are identical and the alternative hypothesis suggests that there is a significant difference between the two.<\/p><p>This test can be used with a single sample to check whether the distribution follows a specific distribution, or with two independent samples to compare two different distributions.<\/p><p>If the <strong>P value is above a predefined significance level,<\/strong> the null hypothesis is verified. If it is lower, this proves that there is a difference and that the two distributions are incompatible.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4da7d7b e-flex e-con-boxed e-con\" data-id=\"4da7d7b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1db2e82 elementor-widget elementor-widget-heading\" data-id=\"1db2e82\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is the purpose of the Kolmogorov-Smirnov test?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8dc3dd9 elementor-widget elementor-widget-text-editor\" data-id=\"8dc3dd9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The <strong>Kolmogorov-Smirnov<\/strong> test is used in many fields, including the social sciences, economics, biology, physics, engineering and many others.<\/p><p>One of the most common applications is to assess the normality of a distribution. An <strong>empirical distribution<\/strong> is compared with a theoretical normal distribution to check whether the data show any significant deviations.<\/p><p>This method can also be used to determine whether two independent samples come from the same population, or whether they differ significantly. This is very useful in comparative studies, controlled experiments or group analyses.<\/p><p>It is also used to check the adequacy of a statistical model. The aim is to check whether the model fitted to the data faithfully reproduces the distribution observed. If it does not, potential gaps or errors can be identified.<\/p><p>It is therefore a highly versatile tool for Data Science,<a href=\"https:\/\/datascientest.com\/en\/unraveling-machine-learning-vs-deep-learning-key-differences-explained\"> Machine Learning<\/a> and <a href=\"https:\/\/datascientest.com\/en\/artificial-intelligence-definition\">Artificial Intelligence<\/a>. It is used not only to compare model performance, but also for feature selection and anomaly detection.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-603b980 e-flex e-con-boxed e-con\" data-id=\"603b980\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3923fa8 elementor-widget elementor-widget-heading\" data-id=\"3923fa8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e7747b2 elementor-widget elementor-widget-text-editor\" data-id=\"e7747b2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>As well as highlighting the importance of encounters and chance in major scientific discoveries, this anecdote gave rise to a tool that is still widely used today to analyse data reliably.<\/p><p>To learn all the methods and tools of Data Science, DataScientest is the place to be. Our various training courses enable you to acquire all the skills needed to become a Data Analyst, Data Engineer, Data Scientist, Machine Learning Engineer or Data Product Manager.<\/p><p>In particular, you will learn about the Python language and its libraries, DataViz, Business Intelligence, data analysis and machine learning.<\/p><p>All our programmes can be completed entirely by distance learning, and our state-recognised organisation is eligible for funding options. Thanks to a partnership with <strong>MINES ParisTech,<\/strong> learners receive certification at the end of the course. Discover DataScientest!<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-96423c9 elementor-widget__width-initial elementor-widget elementor-widget-video\" data-id=\"96423c9\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/pVNzVvHV1No&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;right:0;bottom:0;left:0;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%;aspect-ratio:var(--video-aspect-ratio);-o-object-fit:cover;object-fit:cover;-o-object-position:center center;object-position:center center}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-custom-embed-image-overlay{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-custom-embed-image-overlay img{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-20fbb6a elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"20fbb6a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Find out more about our training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-022fecb e-flex e-con-boxed e-con\" data-id=\"022fecb\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1fb4fa4 elementor-widget elementor-widget-html\" data-id=\"1fb4fa4\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"What is the Kolmogorov-Smirnov test?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Used in many fields, the Kolomogorov-Smirnov test is a powerful statistical tool. 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Discover the amazing story of its invention, and how it is used today in Data Science! In 1933, Andrei Kolmogorov published an article entitled &#8220;Sulla determinazione empirica di una legge di distribuzione&#8221; (On the empirical determination of a distribution law). In it, the mathematician [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":180805,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Kolmogorov-Smirnov Test: Understanding this Statistical Method<\/title>\n<meta name=\"description\" content=\"Explore the Kolmogorov-Smirnov test, a powerful statistical method used to compare two probability distributions. 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