{"id":67011,"date":"2026-10-13T11:35:14","date_gmt":"2026-10-13T08:35:14","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67011"},"modified":"2026-10-13T11:35:14","modified_gmt":"2026-10-13T08:35:14","slug":"levenes-test-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/statistics\/levenes-test-calculator\/","title":{"rendered":"Levene's Test Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Check Whether Independent Groups Have Equal Variances<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67011\" data-favorite-title=\"Levene&#039;s Test\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/statistics\/levenes-test-calculator\/\" data-favorite-excerpt=\"Test whether independent groups have equal variances. Enter observations for two or more groups, one per line, choose mean or median centering, and get the F statistic, degrees of freedom, and p-value.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-wpcalc-bell-curve\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/statistics\/levenes-test-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67011\" data-post=\"67011\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Group observations<\/label><textarea id=\"field-1\" name=\"group_observations\">8 9 10 11 12\n8 10 12 14 16\n9 10 11 12 13<\/textarea><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Center each group on its<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"center_each_group_on_its\"><option value=\"mean\">Mean (Levene&#039;s original test)<\/option><option value=\"median\" selected>Median (Brown\u2013Forsythe variant)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67011\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Levene&#039;s Test Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Test statistic (F)<\/span><span class=\"result-term\">F<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Numerator degrees of freedom<\/span><span class=\"result-term\">df\u2081<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Denominator degrees of freedom<\/span><span class=\"result-term\">df\u2082<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>P-value<\/span><span class=\"result-term\">p<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Interpretation<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"67011\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span 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class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Levene's Test Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\\[ W = \\frac{N - k}{k - 1} \\cdot \\frac{\\sum_{i=1}^{k} n_i \\left( \\bar{Z}_i - \\bar{Z} \\right)^2}{\\sum_{i=1}^{k} \\sum_{j=1}^{n_i} \\left( Z_{ij} - \\bar{Z}_i \\right)^2} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 number of groups<\/li>\n<li>\\(N\\) \u2014 total number of observations across all groups<\/li>\n<li>\\(n_i\\) \u2014 number of observations in group \\(i\\)\n<li>\\(Z_{ij} = |Y_{ij} - \\tilde{Y}_i|\\) \u2014 the absolute deviation of observation \\(j\\) in group \\(i\\) from its group center (mean for the original Levene test, median for the Brown\u2013Forsythe variant)<\/li>\n<li>\\(\\bar{Z}_i\\) \u2014 mean of the absolute deviations in group \\(i\\)<\/li>\n<li>\\(\\bar{Z}\\) \u2014 mean of all absolute deviations<\/li>\n<\/ul>\n<p>The statistic \\(W\\) follows an F-distribution with \\(k-1\\) and \\(N-k\\) degrees of freedom under the null hypothesis that all group variances are equal. It is essentially a one-way ANOVA performed on the absolute deviations from the group centers.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Levene's Test \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> three groups of five measurements each, tested with the default median-centered (Brown\u2013Forsythe) method.<\/p>\n<p>Group 1: 8, 9, 10, 11, 12 &nbsp; Group 2: 8, 10, 12, 14, 16 &nbsp; Group 3: 9, 10, 11, 12, 13<\/p>\n<p>Group medians: 10, 12, 11. Absolute deviations from the medians:<\/p>\n<p>\\[ Z_1 = 2, 1, 0, 1, 2 \\quad (\\bar{Z}_1 = 1.2) \\]<\/p>\n<p>\\[ Z_2 = 4, 2, 0, 2, 4 \\quad (\\bar{Z}_2 = 2.4), \\qquad Z_3 = 2, 1, 0, 1, 2 \\quad (\\bar{Z}_3 = 1.2) \\]<\/p>\n<p>Overall mean deviation: \\(\\bar{Z} = 24\/15 = 1.6\\).<\/p>\n<p>\\[ \\sum n_i (\\bar{Z}_i - \\bar{Z})^2 = 5(0.4)^2 + 5(0.8)^2 + 5(0.4)^2 = 4.8 \\]<\/p>\n<p>\\[ \\sum\\sum (Z_{ij} - \\bar{Z}_i)^2 = 2.8 + 11.2 + 2.8 = 16.8 \\]<\/p>\n<p>\\[ W = \\frac{15 - 3}{3 - 1} \\cdot \\frac{4.8}{16.8} = 6 \\cdot 0.2857 = 1.7143 \\]<\/p>\n<p>With \\(df_1 = 2\\) and \\(df_2 = 12\\), the p-value is \\(p \\approx 0.221\\).<\/p>\n<p><strong>Result:<\/strong> \\(F = 1.7143\\), \\(df_1 = 2\\), \\(df_2 = 12\\), \\(p \\approx 0.221\\). Since \\(p &gt; 0.05\\), there is no sufficient evidence against equal variances in these three groups.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Levene's Test Calculator<\/h2>\n<ol>\n<li>Type your data into the <strong>Group observations<\/strong> field, with each group's values on its own line. Separate values with spaces or semicolons; decimal commas are accepted. Each group needs at least two observations, and you can enter between 2 and 20 groups.<\/li>\n<li>Choose the centering method in the <strong>Center each group on its<\/strong> dropdown: <em>Mean (Levene's original test)<\/em> or <em>Median (Brown\u2013Forsythe variant)<\/em>.<\/li>\n<li>Read the results: the test statistic <strong>F<\/strong>, the two degrees of freedom, the <strong>p-value<\/strong>, and a plain-language interpretation of whether the group variances can be assumed equal at the 0.05 level.<\/li>\n<\/ol>\n<h2>What Is Levene's Test and When Do You Need It?<\/h2>\n<p>Levene's test is a statistical procedure for checking the <strong>homogeneity of variance<\/strong> assumption \u2014 the idea that several independent groups share the same population variance. Many classical methods, including the two-sample t-test, one-way ANOVA, and repeated-measures designs, assume equal variances across groups. When that assumption fails, the nominal error rates of these tests can be distorted: you may declare a result \"significant\" more often than the stated 5%, or lose power.<\/p>\n<p>The test works by transforming the raw data. Each observation is replaced by its absolute distance from the group center, and a one-way ANOVA is run on those distances. If the groups truly have equal variances, the average absolute deviation will be similar across groups, and the resulting F statistic will be small. If one group is noticeably more spread out than the others, its deviations will be larger on average, inflating the statistic.<\/p>\n<p>Interpreting the output is straightforward: a small p-value (typically below 0.05) provides evidence that at least one group's variance differs, so you should either use a variance-stabilizing transformation (e.g., a log transform) or switch to a procedure that does not assume equal variances, such as Welch's ANOVA. A large p-value means the data are consistent with equal variances \u2014 but it does not prove the variances are exactly equal. The test simply finds no evidence against the assumption.<\/p>\n<p>Levene's test is usually preferred over older alternatives such as Bartlett's test because it is far less sensitive to non-normal data. It is a natural companion to parametric group comparisons; if you later move to nonparametric methods, the <a href=\"https:\/\/wpcalc.com\/en\/statistics\/kruskal-wallis-test-calculator\/\">Kruskal\u2013Wallis Test<\/a> or the <a href=\"https:\/\/wpcalc.com\/en\/statistics\/friedman-test-calculator\/\">Friedman Test<\/a> may be appropriate depending on your design.<\/p>\n<h2>Assumptions, Limitations, and Practical Tips<\/h2>\n<ul>\n<li><strong>Independence.<\/strong> Observations must be independent within and between groups. Levene's test is not appropriate for paired or repeated-measures data.<\/li>\n<li><strong>Two versions of the test.<\/strong> The original Levene test centers each group on its mean, which makes it sensitive to outliers and skewed distributions. The Brown\u2013Forsythe variant centers on the median and is more robust; it is the default in this calculator and in most statistical software.<\/li>\n<li><strong>Group size matters.<\/strong> With very small groups, the test has low power and may miss real differences in variance. With very large samples, it can flag trivially small differences as significant. Always consider the practical size of the variance difference, not just the p-value.<\/li>\n<li><strong>Equal variances is not the same as equal means.<\/strong> This test says nothing about whether group averages differ \u2014 it only examines spread. To compare means across groups, look instead at procedures such as the <a href=\"https:\/\/wpcalc.com\/en\/statistics\/z-test-for-a-mean-calculator\/\">Z-Test for a Mean<\/a>.<\/li>\n<li><strong>Don't forget the underlying test.<\/strong> A variance check is usually a preliminary step. If your design continues to further analysis, the <a href=\"https:\/\/wpcalc.com\/en\/statistics\/statistical-power-calculator\/\">Statistical Power Calculator<\/a> can help you assess whether your sample sizes are adequate for detecting the effects you care about.<\/li>\n<li><strong>Sensible data limits.<\/strong> The calculator accepts up to 20 groups and 1,000 observations in total, with values up to a trillion in absolute value \u2014 enough for typical classroom and research datasets.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Test whether independent groups have equal variances. Enter observations for two or more groups, one per line, choose mean or median centering, and get the F statistic, degrees of freedom, and p-value.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[79],"class_list":["post-67011","post","type-post","status-publish","format-standard","hentry","category-statistics","tag-hypothesis-testing"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67011","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=67011"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67011\/revisions"}],"predecessor-version":[{"id":67043,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67011\/revisions\/67043"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67011"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67011"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67011"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}