{"id":725687,"date":"2022-11-20T11:00:22","date_gmt":"2022-11-20T19:00:22","guid":{"rendered":"https:\/\/www.questionpro.com\/blog\/?p=565005"},"modified":"2026-07-16T23:50:04","modified_gmt":"2026-07-17T06:50:04","slug":"chi-square-test","status":"publish","type":"post","link":"https:\/\/www.questionpro.com\/blog\/chi-square-test\/","title":{"rendered":"Chi-square test: What is it &#038; How to Calculate"},"content":{"rendered":"\n<p><span style=\"font-weight: 400;\">The chi-square test is often referred to as Fisher&#8217;s exact test. It is a statistical test used to examine categorical data. This article<\/span><span style=\"font-weight: 400;\">&nbsp;will explain the chi-square test and how to calculate it.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">What is the chi-square test?<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The chi-square test is a statistical way of determining differences between what was expected and what was seen in one or more categories.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Researchers utilize this nonparametric test to compare categorical variables within the same sample population. It also helps verify or provide background for frequency counts.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The basic idea behind the test is to examine the actual data values to determine what would be anticipated if the null hypothesis was correct.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">Types of chi-square test<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">There are different types of chi-square tests that are frequently used:<\/span><\/p>\n\n\n\n<ul>\n<li><b>Goodness of fit test:<\/b><span style=\"font-weight: 400;\"> It is a statistical test to detect if a variable comes from a particular distribution.<\/span><\/li>\n\n\n\n<li><b>Independence test:<\/b><span style=\"font-weight: 400;\"> It is an <a href=\"https:\/\/www.questionpro.com\/blog\/inferential-statistics\/\">inferential statistical<\/a> test that draws conclusions about a population from a sample.<\/span><\/li>\n\n\n\n<li><b>Homogeneity test: <\/b><span style=\"font-weight: 400;\">It&#8217;s structured and runs like the independence test.<\/span><\/li>\n<\/ul>\n\n\n\n<p><span style=\"font-weight: 400;\">The independence test searches for a link between two categorical variables within the same population, while the homogeneity test checks whether a variable&#8217;s distribution is the same across populations.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">Chi-square test in research<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The Chi-square test makes it simple to comprehend and analyze the relationship between two categorical variables. Let&#8217;s examine the usefulness of this test to the research.<\/span><\/p>\n\n\n\n<ul>\n<li><span style=\"font-weight: 400;\">The researcher can determine whether the observed cell counts are significantly different from the expected cell counts by statistically calculating Chi-Square and comparing it to a critical value of the Chi-Square distribution.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">It is sensitive to how cells are distributed. By consistently using categorical variables with a small number of categories, this problem can be solved.<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">Learn About: <a href=\"https:\/\/www.questionpro.com\/blog\/180-vs-360-feedback\/\">180 vs 360 Feedback<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">Chi-Square test Perform guidelines<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Now that you are more familiar with the Chi-Square test, let us show you how to perform it:<\/span><\/p>\n\n\n\n<ul>\n<li><span style=\"font-weight: 400;\">Before beginning the data-gathering process, specify your null and alternative hypotheses.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Set alpha. This includes assessing how risky an incorrect conclusion is. Assume alpha = 0.05 for independence testing. In this scenario, you&#8217;ve chosen a 5% risk of assuming that two variables are independent when they&#8217;re not.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Verify the data for mistakes.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Verify the test&#8217;s underlying assumptions.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Get your test results.<\/span><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">How to calculate chi-square: The formula<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The chi-squared test is used to determine whether the observed value and expected value differ in any way. The chi-square formula is represented by the following;<\/span><\/p>\n\n\n\n<p><b>X<\/b><b>2<\/b><b> = \u2211<\/b><b>(O &#8211; E)<\/b><b>2<\/b><b>\/E<\/b><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Here,<\/span><\/p>\n\n\n\n<ul>\n<li><span style=\"font-weight: 400;\">O is the observed value<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">E is the expected value<\/span><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">Chi-Square test example for categorical data<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Let&#8217;s look at a society with 2000 residents divided into the four neighborhoods of A, B, C, and D as an example of <a class=\"wpil_keyword_link\" href=\"https:\/\/www.questionpro.com\/blog\/categorical-data\/\" title=\"categorical data\" data-wpil-keyword-link=\"linked\" data-wpil-monitor-id=\"70\">categorical data<\/a>.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">1300 members who work in government, private, and doctors are chosen randomly. According to the null hypothesis, a person&#8217;s professional division is unrelated to the neighborhood in which they reside. The information is divided into<\/span><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><span style=\"font-weight: 400;\">Categories<\/span><\/td><td><span style=\"font-weight: 400;\">A<\/span><\/td><td><span style=\"font-weight: 400;\">B<\/span><\/td><td><span style=\"font-weight: 400;\">C<\/span><\/td><td><span style=\"font-weight: 400;\">D<\/span><\/td><td><span style=\"font-weight: 400;\">Total<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">Government service<\/span><\/td><td><span style=\"font-weight: 400;\">180<\/span><\/td><td><span style=\"font-weight: 400;\">120<\/span><\/td><td><span style=\"font-weight: 400;\">208<\/span><\/td><td><span style=\"font-weight: 400;\">190<\/span><\/td><td><span style=\"font-weight: 400;\">698<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">Private Service<\/span><\/td><td><span style=\"font-weight: 400;\">60<\/span><\/td><td><span style=\"font-weight: 400;\">100<\/span><\/td><td><span style=\"font-weight: 400;\">102<\/span><\/td><td><span style=\"font-weight: 400;\">40<\/span><\/td><td><span style=\"font-weight: 400;\">302<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">Doctor<\/span><\/td><td><span style=\"font-weight: 400;\">60<\/span><\/td><td><span style=\"font-weight: 400;\">80<\/span><\/td><td><span style=\"font-weight: 400;\">90<\/span><\/td><td><span style=\"font-weight: 400;\">70<\/span><\/td><td><span style=\"font-weight: 400;\">300<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">Total<\/span><\/td><td><span style=\"font-weight: 400;\">300<\/span><\/td><td><span style=\"font-weight: 400;\">300<\/span><\/td><td><span style=\"font-weight: 400;\">400<\/span><\/td><td><span style=\"font-weight: 400;\">300<\/span><\/td><td><span style=\"font-weight: 400;\">1300<\/span><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">To determine what percentage of the 2,000 people reside in neighborhood A, assume that the sample population of 300 is in area A.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Similarly, we take 698\/1300 to determine what proportion of the 2,000 comprises government employees. According to the independence presumption in the hypothesis, we should &#8220;expect&#8221; the following number of government employees in neighborhood A: 300 x (698 \/ 1300) = 161.08<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Therefore, using the chi-square test formula for that specific table cell A, we obtain;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">(Observed value \u2013 Expected value)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \/ Expected value = (180 &#8211; 161.08)<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">\/ 161.08 = 2.22<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: 400;\">Conclusion<\/span><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">In this section, we looked at the chi-square test and how to perform and calculate it. Because it applies to categorical variables, the chi-square test is most commonly used by researchers studying survey response data. This research includes demographics, consumer and marketing research, political science, and economics.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The QuestionPro research suite is a set of tools that can be used to make the most of research and change experiences. At QuestionPro, we give all kinds of researchers tools for collecting data, like our <a href=\"https:\/\/www.questionpro.com\/survey-software\/\">survey software<\/a> and insight repositories for all sorts of long-term research.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Talk to the QuestionPro team of experts if you need help researching how to make data-based decisions. QuestionPro can help you get the most out of your data and guide you through the process. Create a free account, or let us know what you need!<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"https:\/\/www.questionpro.com\/research-edition-survey-software\/\" target=\"_blank\" rel=\"noopener\"><button>LEARN MORE<\/button><\/a>&nbsp; &nbsp; &nbsp; &nbsp;<a href=\"https:\/\/www.questionpro.com\/a\/showEntry.do?classID=1053&amp;sourceRef=blog\" target=\"_blank\" rel=\"noopener\"><button>FREE TRIAL<\/button><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The chi-square test is often referred to as Fisher&#8217;s exact test. It is a statistical test used to examine categorical [&hellip;]<\/p>\n","protected":false},"author":51,"featured_media":566734,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"chi-square test","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Chi-square test analyses the differences between categorical variables from a sample to assess if observed findings are well-fitting.","_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[174],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chi-square test: What is it &amp; How to Calculate | QuestionPro<\/title>\n<meta name=\"description\" content=\"Chi-square test analyses the differences between categorical variables from a sample to assess if observed findings are well-fitting.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.questionpro.com\/blog\/chi-square-test\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Chi-square test: What is it &amp; 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