{"id":139,"date":"2018-03-12T12:13:00","date_gmt":"2018-03-12T11:13:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/12\/kolmogorov-smirnov-goodness-of-fit-test\/"},"modified":"2020-11-05T14:03:38","modified_gmt":"2020-11-05T13:03:38","slug":"kolmogorov-smirnov-goodness-of-fit-test","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/kolmogorov-smirnov-goodness-of-fit-test\/","title":{"rendered":"Kolmogorov-Smirnov Goodness of Fit Test"},"content":{"rendered":"<div style=\"color: #555555; font-size: 18px; line-height: 30px; text-align: justify;\">\n<div style=\"font-family: 'segoe ui';\">In this lesson, we are going to discuss the Kolmogorov-Smirnov Goodness of Fit test, how and when to perform it.<br \/>Remember that the Kolmogorov-Smirnov Goodness of Fit test is one of the <a href=\"https:\/\/kindsonthegenius.com\/blog\/what-are-non-parametric-tests\/\" target=\"_blank\" rel=\"noopener noreferrer\">non-parametric tests<\/a> discussed previously. See <a href=\"https:\/\/kindsonthegenius.com\/blog\/what-are-non-parametric-tests\/\" target=\"_blank\" rel=\"noopener noreferrer\">What are Non-Parametric Tests<\/a><\/p>\n<p><b>Content<\/b><br \/>Here we are going to cover<\/p>\n<ol>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t1\">What is Kolmogorov-Smrmov Test<\/a><\/li>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t2\">When to use the K-S Test<\/a> <\/li>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t3\">How to Perform the Kolmogorov-Smirmov Test<\/a><\/li>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t4\">Komogorove-Smirnov Test P-Value Table<\/a><\/li>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t5\">Pros and Cons of the Kolmogorov-Smirnov Test<\/a><\/li>\n<li><a href=\"http:\/\/kindsonthegenius.blogspot.com\/#t6\">Final Notes<\/a><\/li>\n<\/ol>\n<p><ins data-ad-client=\"ca-pub-7041870931346451\" data-ad-format=\"fluid\" data-ad-layout=\"in-article\" data-ad-slot=\"4209786523\" style=\"display: block; text-align: center;\"><\/ins><br \/>   <b><\/p>\n<h2>1. What is the Kolmogorov-Smirnov Test(K-S Test)?<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>The K-S Goodness of Fit Test is a non-parametric test that compares a given data with a known distribution and helps you determine if they have the same distribution.<br \/>The K-S test does not assume any particular distribution.<\/p>\n<p><b><\/p>\n<h2>2. When to Apply the K-S Test<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>The K-S test is applied to test the normality of your data to see if it comes from a normally-distributed population.<br \/>It is also used in <a href=\"https:\/\/kindsonthegenius.com\/blog\/how-to-perform-analysis-of-variance-anova-step-by-step-procedure\/\" target=\"_blank\" rel=\"noopener noreferrer\">Analyis of Variance(ANOVA)<\/a> to check the assumption of normality.<br \/>In summary, the K-S test can be used to answer the following questions:<\/p>\n<ul>\n<li>Is the data taken from a normal distribution?<\/li>\n<li>Is the data taken from a&nbsp; log-normal distribution?<\/li>\n<li>Is the data taken from an exponential distribution?<\/li>\n<li>Is the data taken from a logistic distribution?<\/li>\n<\/ul>\n<p><b><\/p>\n<h2>3. How to Perform the Kolmogorov-Smirnov Test<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>Follow the steps the peform the K-S Test<\/p>\n<p>Step 1: Set up the Null and alternate hypothesis<br \/>This could be of the form<br \/><b>H<sub>0<\/sub>:<\/b> The groups are independent<br \/><b>H<sub>a<\/sub><\/b>: The values are not dependent<\/p>\n<p>Step 2: Create the EDF for your data<br \/>EDF stands for Empirical Distribution Function<\/p>\n<p>Step 3: Specify a parent distribution<br \/>This is the distribution that you will like to compare your sample data to<\/p>\n<p>Step 4:Plot the two distributions togeter<\/p>\n<p>Step 5: Measure the greatest vertical distance between the two graphs<\/p>\n<p>Step 6: Calculate the Test Statistic<\/p>\n<p>Step 7: Find the Critical Value from the K-S table<\/p>\n<p>Step 8: Compare the Crital Value to the calculated value<\/p>\n<p>Step 9: State your conclution<\/p>\n<p><b><\/p>\n<h2>4. The K-S Test P-Value Table<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>This is a <a href=\"https:\/\/kindsonthegenius.com\/blog\/statistical-tables\/\" target=\"_blank\" rel=\"noopener noreferrer\">statistical table<\/a> just like other tables used to look up critical values of statistics.<br \/>To get the P-Value, you need:<\/p>\n<ul>\n<li>degrees of freedom<\/li>\n<li>level of significance<\/li>\n<\/ul>\n<p> <ins data-ad-client=\"ca-pub-7041870931346451\" data-ad-format=\"fluid\" data-ad-layout=\"in-article\" data-ad-slot=\"4209786523\" style=\"display: block; text-align: center;\"><\/ins><br \/><b><\/p>\n<h2>5. Pros and Cons of Kolmogorov-Smirnov Test<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>The Kolmogorov-Smirnov test has both advantages and disadvantages as highlighted below<\/p>\n<p><b>Benefits of the K-S Test<\/b><\/p>\n<ul>\n<li>It can be used as goodness of fit test following regression analysis<\/li>\n<li>There are no restrictions ion the sample size. This means that small samples could work as well<\/li>\n<li>K-S tables are easily available <\/li>\n<li>The Test&nbsp; is distribution-free<\/li>\n<\/ul>\n<p><b>Disadvantages of the K-S Test<\/b><br \/>It only applies to continuous distribution<br \/>It tends to be more sensitive near the middle of the distribution than at the tails<br \/>The distribution to be copared with must be fully&nbsp; specified<\/p>\n<p><b><\/p>\n<h2>6. Final Notes<\/h2>\n<p><\/b><\/p>\n<hr \/>\n<p>As you can see from the discussion, the K-S test has a number of benefits but also disadvantages. Additionally, it&#8217;s better to used applications like MS Excel, SPSS or other packages to easily carry out this test.  <\/p><\/div>\n<\/div>\n<p><ins data-ad-client=\"ca-pub-7041870931346451\" data-ad-format=\"fluid\" data-ad-layout=\"in-article\" data-ad-slot=\"4209786523\" style=\"display: block; text-align: center;\"><\/ins><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this lesson, we are going to discuss the Kolmogorov-Smirnov Goodness of Fit test, how and when to perform it.Remember that the Kolmogorov-Smirnov Goodness of &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[223],"tags":[],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/139"}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=139"}],"version-history":[{"count":4,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/139\/revisions"}],"predecessor-version":[{"id":1744,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/139\/revisions\/1744"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}