{"id":185807,"date":"2025-01-23T07:25:40","date_gmt":"2025-01-23T07:25:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185807"},"modified":"2025-01-23T07:25:44","modified_gmt":"2025-01-23T07:25:44","slug":"a-critical-values-of-the-pearson-correlation-coefficient-r-note","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/23\/a-critical-values-of-the-pearson-correlation-coefficient-r-note\/","title":{"rendered":"A Critical Values Of The Pearson Correlation Coefficient R NOTE"},"content":{"rendered":"\n<p>A Critical Values Of The Pearson Correlation Coefficient R NOTE: To Test Ho: P= 0 Jagainst Hi: P*0, Reject Ho If The Absolute Value Of Ris Greater Than The Critical Value In The Table. 0.602 Critical Values Of The Pearson Correlation Coefficient A = 0.05 A = 0.01 0.950 0.990 0.878 0.959 10.811 0.917 0.754 10.875 0.707 0.834 0.666 0.798 0.632 0.765 10.735<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The Pearson correlation coefficient (r) is a statistical measure used to evaluate the strength and direction of the linear relationship between two variables. The null hypothesis (H0) for a correlation test typically states that there is no relationship between the variables, i.e., \u03c1 = 0, where \u03c1 is the population correlation coefficient. The alternative hypothesis (Ha) asserts that \u03c1 \u2260 0, meaning there is some significant linear relationship.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Critical Values of the Pearson Correlation Coefficient:<\/h3>\n\n\n\n<p>The table you\u2019ve provided includes the critical values of Pearson&#8217;s correlation coefficient (r) at two significance levels (\u03b1 = 0.05 and \u03b1 = 0.01). These critical values are used to determine whether the observed correlation coefficient is significantly different from zero, which would indicate a significant linear relationship between the variables.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significance level \u03b1 = 0.05<\/strong>: This means there&#8217;s a 5% chance of rejecting the null hypothesis if it is true.<\/li>\n\n\n\n<li><strong>Significance level \u03b1 = 0.01<\/strong>: This is a more stringent threshold, meaning there\u2019s only a 1% chance of a Type I error.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to Use the Critical Values:<\/h3>\n\n\n\n<p>To test whether the observed correlation coefficient (r) is significant, you compare it to the critical values at the chosen significance level. The process is as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>State the hypotheses:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H0: \u03c1 = 0 (no linear relationship).<\/li>\n\n\n\n<li>Ha: \u03c1 \u2260 0 (there is a linear relationship).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compute the Pearson correlation coefficient (r)<\/strong> based on the sample data.<\/li>\n\n\n\n<li><strong>Find the appropriate critical value<\/strong> from the table corresponding to the sample size and the chosen significance level (\u03b1 = 0.05 or \u03b1 = 0.01).<\/li>\n\n\n\n<li><strong>Decision rule<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the absolute value of the computed r is greater than the critical value, reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha).<\/li>\n\n\n\n<li>If the absolute value of r is less than or equal to the critical value, fail to reject the null hypothesis.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Example:<\/h3>\n\n\n\n<p>If your computed r value is 0.85 with a sample size of 20 and you&#8217;re testing at \u03b1 = 0.05, you would compare it to the critical value of 0.602 (based on the table for n = 20). Since 0.85 &gt; 0.602, you would reject the null hypothesis and conclude that there is a significant linear relationship between the two variables.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The critical values of the Pearson correlation coefficient are essential tools for hypothesis testing, helping to assess whether a significant linear relationship exists between two variables. By comparing the observed r value with the critical values at different significance levels, researchers can make informed decisions about the relationship between variables in their data.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Critical Values Of The Pearson Correlation Coefficient R NOTE: To Test Ho: P= 0 Jagainst Hi: P*0, Reject Ho If The Absolute Value Of Ris Greater Than The Critical Value In The Table. 0.602 Critical Values Of The Pearson Correlation Coefficient A = 0.05 A = 0.01 0.950 0.990 0.878 0.959 10.811 0.917 0.754 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-185807","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185807","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=185807"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185807\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}