{"id":67262,"date":"2019-02-04T21:38:22","date_gmt":"2019-02-05T05:38:22","guid":{"rendered":"https:\/\/www.questionpro.com\/blog\/?p=67262"},"modified":"2024-10-09T15:38:25","modified_gmt":"2024-10-09T22:38:25","slug":"spearmans-rank-coefficient-of-correlation","status":"publish","type":"post","link":"https:\/\/www.questionpro.com\/blog\/spearmans-rank-coefficient-of-correlation\/","title":{"rendered":"Spearman correlation coefficient: Formula + Calculation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Spearman correlation coefficient: Definition<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The Spearman\u2019s rank coefficient of correlation or Spearman correlation coefficient is a nonparametric measure of rank correlation (statistical dependence of ranking between two variables). <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Named after Charles Spearman, it is often denoted by the Greek letter <strong>&#8216;\u03c1&#8217; <\/strong>(rho) and is primarily used for <a href=\"https:\/\/www.questionpro.com\/blog\/data-analysis-simple-and-complex-a-primer\/\">data analysis<\/a>. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">It measures the strength and direction of the association between two ranked variables. But before we talk about the Spearman correlation coefficient, it is important to understand Pearson\u2019s correlation first. A Pearson correlation is a statistical measure of the strength of a linear relationship between paired data. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">For the calculation and significance testing of the ranking variable, it requires the following data assumption to hold true: <\/span><\/p>\n\n\n\n<ul>\n<li><span style=\"font-weight: 400;\"><a href=\"https:\/\/www.questionpro.com\/blog\/interval-scale\/\">Interval<\/a> or <a href=\"https:\/\/www.questionpro.com\/blog\/ratio-scale\/\">ratio<\/a> level<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Linearly related <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Bivariant distributed <\/span><\/li>\n<\/ul>\n\n\n\n<p><span style=\"font-weight: 400;\">If your data doesn\u2019t meet the above assumptions, then you would need Spearman\u2019s Coefficient. It is necessary to know what monotonic function is to understand Spearman correlation coefficient. A monotonic function is one that either never decreases or never increases as it is an independent variable increase. A monotonic function can be explained using the image below:<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/1-2.jpg\" alt=\"Spearman's Ran coefficient of Correlation\" class=\"wp-image-67390\"\/><\/figure><\/div>\n\n\n<p><span style=\"font-weight: 400;\">The image explains three concepts in monotonic function:<\/span><\/p>\n\n\n\n<ol>\n<li><span style=\"font-weight: 400;\">Monotonically increasing: When the &#8216;x&#8217; variable increases and the &#8216;y&#8217; variable never decreases. <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Monotonically decreasing: When the &#8216;x&#8217; variable increases but the &#8216;y&#8217; variable never increases<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Not monotonic: When the &#8216;x&#8217; variable increases and the &#8216;y&#8217; variable sometimes increases and sometimes decreases. <\/span><\/li>\n<\/ol>\n\n\n\n<p><span style=\"font-weight: 400;\">Monotonic relation is less restrictive when compared to a linear relationship that is used in Pearson\u2019s coefficient. Although monotonicity is not the ultimate requirement for Spearman correlation coefficient, it will not be meaningful to pursue Spearman\u2019s correlation without actually determining the strength and direction of a monotonic relationship if it was already known that the relationship between the variable is non-monotonic.<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">Learn more: <a href=\"https:\/\/www.questionpro.com\/blog\/correlational-research\/\">Correlational Research<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Spearman correlation coefficient: Formula and Calculation with Example<\/strong><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/2019-02-01_1548-1.png\" alt=\"Spearman's Rank Coefficient of Correlation\" class=\"wp-image-67263\"\/><\/figure><\/div>\n\n\n<p>Here,<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><em>n<\/em>= number of data points of the two variables <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><em>di<\/em>= difference in ranks of the \u201cith\u201d element<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The Spearman Coefficient,\u2374, can take a value between +1 to -1 where, <\/span><\/p>\n\n\n\n<ul>\n<li><span style=\"font-weight: 400;\">A \u2374 value of +1 means a perfect association of rank <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">A \u2374 value of 0 means no association of ranks <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">A \u2374 value of -1 means a perfect negative association between ranks. <\/span><\/li>\n<\/ul>\n\n\n\n<p><span style=\"font-weight: 400;\">Closer the \u2374 value to 0, weaker is the association between the two ranks. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">We must be able to rank the data before proceeding with the Spearman\u2019s Rank Coefficient of Correlation. It is important to observe if increasing one variable, the other variable follows a monotonic relation. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">At every level, you will need to compare the values of the two variables. Here is how the calculations work: <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The scores of 9 students in History and Geography are mentioned in the table below.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 1-<\/strong> Create a table of the data obtained. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 2-<\/strong> Start by ranking the two data sets. Data ranking can be achieved by assigning the ranking \u201c1\u201d &nbsp;to the biggest number in the column, \u201c2\u201d to the second biggest number and so forth. The smallest value will usually get the lowest ranking. This should be done for both sets of measurements. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 3-<\/strong> Add a third column d to your data set, d here denotes the difference between ranks. For example, if the first student\u2019s physics rank is 3 and the math rank is 5 then the difference in the rank is 3. In the fourth column, square your <em>d<\/em> values. <\/span><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><span style=\"font-weight: 400;\">History <\/span><\/td><td><span style=\"font-weight: 400;\">Rank<\/span><\/td><td><span style=\"font-weight: 400;\">Geography<\/span><\/td><td><span style=\"font-weight: 400;\">Rank<\/span><\/td><td><span style=\"font-weight: 400;\">d<\/span><\/td><td><span style=\"font-weight: 400;\">d square <\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">35<\/span><\/td><td><span style=\"font-weight: 400;\">3<\/span><\/td><td><span style=\"font-weight: 400;\">30<\/span><\/td><td><span style=\"font-weight: 400;\">5<\/span><\/td><td><span style=\"font-weight: 400;\">2<\/span><\/td><td><span style=\"font-weight: 400;\">4<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">23<\/span><\/td><td><span style=\"font-weight: 400;\">5<\/span><\/td><td><span style=\"font-weight: 400;\">33<\/span><\/td><td><span style=\"font-weight: 400;\">3<\/span><\/td><td><span style=\"font-weight: 400;\">2<\/span><\/td><td><span style=\"font-weight: 400;\">4<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">47<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">45<\/span><\/td><td><span style=\"font-weight: 400;\">2<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">17<\/span><\/td><td><span style=\"font-weight: 400;\">6<\/span><\/td><td><span style=\"font-weight: 400;\">23<\/span><\/td><td><span style=\"font-weight: 400;\">6<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">10<\/span><\/td><td><span style=\"font-weight: 400;\">7<\/span><\/td><td><span style=\"font-weight: 400;\">8<\/span><\/td><td><span style=\"font-weight: 400;\">8<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">43<\/span><\/td><td><span style=\"font-weight: 400;\">2<\/span><\/td><td><span style=\"font-weight: 400;\">49<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">9<\/span><\/td><td><span style=\"font-weight: 400;\">8<\/span><\/td><td><span style=\"font-weight: 400;\">12<\/span><\/td><td><span style=\"font-weight: 400;\">7<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><td><span style=\"font-weight: 400;\">1<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">6<\/span><\/td><td><span style=\"font-weight: 400;\">9<\/span><\/td><td><span style=\"font-weight: 400;\">4<\/span><\/td><td><span style=\"font-weight: 400;\">9<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><\/tr><tr><td><span style=\"font-weight: 400;\">28<\/span><\/td><td><span style=\"font-weight: 400;\">4<\/span><\/td><td><span style=\"font-weight: 400;\">31<\/span><\/td><td><span style=\"font-weight: 400;\">4<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><td><span style=\"font-weight: 400;\">0<\/span><\/td><\/tr><tr><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td><strong>12<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 4-<\/strong> Add up all your <em>d<\/em> square values, which is <strong>12<\/strong> (\u2211d square)<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 5-<\/strong> Insert these values in the formula <\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/2019-02-01_1548-1.png\" alt=\"Spearman's Rank Coefficient of Correlation\" class=\"wp-image-67263\"\/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">=1-(6*12)\/<\/span><span style=\"font-weight: 400;\">(9(81-1))<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">=1-72\/720<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">=1-01<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">=0.9<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The Spearman\u2019s Rank Correlation for this data is 0.9 and as mentioned above if the <strong>\u2374<\/strong> value is nearing +1 then they have a perfect association of rank.<\/span><\/p>\n\n\n\n\t<div class=\"banner-section wf-section\" lang=\"\" >\n\t\t<div class=\"right-column-container\">\n\t\t\t<div class=\"bannerbg white\">\n\t\t\t\t<span class=\"h1-2\">Create memorable experiences based on real-time data, insights and advanced analysis.<\/span>\n\t\t\t\t<a href=\"#userliteForm\" data-toggle=\"modal\" class=\"button w-button\">Request Demo<\/a>\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/div>\n\t<div class=\"userlite-modal modal fade\" id=\"userliteForm\" tabindex=\"-1\" role=\"dialog\" style=\"display: none;\">\n\t\t<div class=\"modal-dialog\" role=\"document\">\n\t\t\t<div class=\"modal-content\" role=\"document\">\n\t\t\t\t<div class=\"modal-body\">\n\t\t\t\t\t<div class=\"modal-header\">\n\t\t\t\t\t\t<button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\">\n\t\t\t\t\t\t\t<i class=\"material-icons\">close<\/i>\n\t\t\t\t\t\t<\/button>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"contact-us-form-wrapper contact-box\">\n\t\t\t\t\t\t<div class=\"userlite-form-wrapper\">\n\t\t\t\t\t\t\t<iframe src=\"https:\/\/www.questionpro.com\/userlite-form-blog-en.html?product=Workforce&amp;referralurl=https:\/\/www.questionpro.com\/blog\/wp-json\/wp\/v2\/posts\/67262&amp;lang=en&amp;cat=workforce-2\" style=\"display: block;\" ><\/iframe>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"demo-form-wrapper success-message-div\" style=\"display:none\">\n\t\t\t\t\t\t\t<p class=\"success-message-para\"><\/p>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>How to Conduct a correlation coefficient with QuestionPro<\/strong><\/h3>\n\n\n\n<p><span style=\"font-weight: 400;\">In this section, you will learn how you can run Spearman&#8217;s Rank Coefficient of Correlation for your survey. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 1:<\/strong> Go to My Surveys \u2192Select Survey\u2192Analytics <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Step 2:<\/strong> Click on Correlational Analysis under Analysis <\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/SCOC1-1-1.png\" alt=\"Spearman's Rank Coefficient of Correlation\" class=\"wp-image-67264\"\/><\/figure><\/div>\n\n\n<p><br><span style=\"font-weight: 400;\"><strong>Step 3:<\/strong> Click on Generate Spearman Coefficient button to get a detailed report<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/SCOC2-1-1.png\" alt=\"Spearman's Rank Coefficient of Correlation\" class=\"wp-image-67265\"\/><\/figure><\/div>\n\n\n<p><br><span style=\"font-weight: 400;\">In the above example, the Spearman coefficient of correlation is used to find out the relationship between the two variables, Work experience and Monthly income. A general notion is<\/span> monthly income should increase with <span style=\"font-weight: 400;\">work experience, which means there should be a positive association between the two variables which is proved by the rs value which is 0.97<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">Learn more: <a href=\"https:\/\/www.questionpro.com\/blog\/gap-analysis\/\">GAP Analysis- Definition, Method and Template with Example&nbsp;&nbsp;<\/a><\/p>\n\n\n\n<p class=\"has-text-align-center\"><a class=\"square-cta secondary-lined-cta\" href=\"https:\/\/www.questionpro.com\/a\/showEntry.do?mode=workforce&amp;classID=1024&amp;sourceRef=blog-workforce\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Create a free account<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Spearman correlation coefficient: Definition The Spearman\u2019s rank coefficient of correlation or Spearman correlation coefficient is a nonparametric measure of rank [&hellip;]<\/p>\n","protected":false},"author":86,"featured_media":67392,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Spearman Correlation Coefficient","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"The Spearman correlation coefficient is for ranking correlation between two ranked variables or a ranked variable and a measurement variable.","_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":[179],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Spearman correlation coefficient: Formula + Calculation<\/title>\n<meta name=\"description\" content=\"The Spearman correlation coefficient is for 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