{"id":227878,"date":"2024-04-04T15:23:35","date_gmt":"2024-04-04T15:23:35","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=227878"},"modified":"2024-04-04T15:23:35","modified_gmt":"2024-04-04T15:23:35","slug":"what-is-test-statistic-and-critical-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/","title":{"rendered":"What is test statistic and critical value?"},"content":{"rendered":"<p><\/p>\n<p>A test statistic is a value calculated from sample data used to make inferences about a population parameter. It is an essential component in hypothesis testing, a statistical method used to determine whether an assumption about a population is supported by the sample data. On the other hand, a critical value is a threshold or cut-off point that determines when to reject or fail to reject the null hypothesis based on the test statistic.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#What_is_a_Test_Statistic\" title=\"What is a Test Statistic?\">What is a Test Statistic?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#What_is_a_Critical_Value\" title=\"What is a Critical Value?\">What is a Critical Value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#How_are_Test_Statistic_and_Critical_Value_Related\" title=\"How are Test Statistic and Critical Value Related?\">How are Test Statistic and Critical Value Related?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#How_is_the_Test_Statistic_Calculated\" title=\"How is the Test Statistic Calculated?\">How is the Test Statistic Calculated?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#How_is_the_Critical_Value_Determined\" title=\"How is the Critical Value Determined?\">How is the Critical Value Determined?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#What_is_the_Significance_Level_in_Relation_to_Critical_Value\" title=\"What is the Significance Level in Relation to Critical Value?\">What is the Significance Level in Relation to Critical Value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#What_Happens_if_the_Test_Statistic_is_Greater_than_the_Critical_Value\" title=\"What Happens if the Test Statistic is Greater than the Critical Value?\">What Happens if the Test Statistic is Greater than the Critical Value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#What_Happens_if_the_Test_Statistic_is_Less_than_the_Critical_Value\" title=\"What Happens if the Test Statistic is Less than the Critical Value?\">What Happens if the Test Statistic is Less than the Critical Value?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Test_Statistic\"><\/span><b>What is a Test Statistic?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>A test statistic is a numerical value calculated from sample data that measures the strength of evidence against the null hypothesis. It helps in determining if the observed results are significantly different from what is expected under the null hypothesis. The test statistic is used to make decisions regarding hypothesis testing, such as accepting or rejecting the null hypothesis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Critical_Value\"><\/span><b>What is a Critical Value?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>A critical value is a point on the test distribution that separates the rejection region from the non-rejection region. It is compared to the test statistic to determine whether the null hypothesis should be rejected or not. If the test statistic exceeds the critical value, it provides evidence against the null hypothesis, leading to its rejection.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_are_Test_Statistic_and_Critical_Value_Related\"><\/span><b>How are Test Statistic and Critical Value Related?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>The test statistic and critical value are closely connected in hypothesis testing. The test statistic is compared to the critical value to determine the level of significance at which the null hypothesis can be rejected. If the test statistic exceeds the critical value, it falls in the rejection region, indicating that there is sufficient evidence to reject the null hypothesis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_is_the_Test_Statistic_Calculated\"><\/span><b>How is the Test Statistic Calculated?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>The calculation of the test statistic depends on the specific statistical test being used. It involves comparing the observed data to what is expected under the null hypothesis. Common test statistics include t-scores and z-scores, which measure how many standard deviations the observed data deviates from the expected results.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_is_the_Critical_Value_Determined\"><\/span><b>How is the Critical Value Determined?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>The critical value is determined based on the desired level of significance (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The critical value corresponds to a certain level of alpha and is found using statistical tables or software. Higher values of alpha result in lower critical values, making it easier to reject the null hypothesis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Significance_Level_in_Relation_to_Critical_Value\"><\/span><b>What is the Significance Level in Relation to Critical Value?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>The significance level, also known as alpha, is the predetermined threshold at which the null hypothesis is rejected. It is directly related to the critical value, as the critical value is determined based on the chosen significance level. Commonly used significance levels are 0.05 and 0.01, corresponding to critical values of 1.96 and 2.58, respectively, for a two-tailed z-test.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_Happens_if_the_Test_Statistic_is_Greater_than_the_Critical_Value\"><\/span><b>What Happens if the Test Statistic is Greater than the Critical Value?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>If the test statistic exceeds the critical value, it means that the observed data is unlikely to have occurred if the null hypothesis were true. This provides evidence to reject the null hypothesis in favor of the alternative hypothesis. The larger the difference between the test statistic and critical value, the stronger the evidence against the null hypothesis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_Happens_if_the_Test_Statistic_is_Less_than_the_Critical_Value\"><\/span><b>What Happens if the Test Statistic is Less than the Critical Value?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>If the test statistic is smaller than the critical value, it falls within the non-rejection region, indicating that there is insufficient evidence to reject the null hypothesis. In this case, the null hypothesis is retained as a plausible explanation for the observed data.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A test statistic is a value calculated from sample data used to make inferences about a population parameter. It is an essential component in hypothesis testing, a statistical method used to determine whether an assumption about a population is supported by the sample data. On the other hand, a critical value is a threshold or &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What is test statistic and critical value?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-is-test-statistic-and-critical-value\/#more-227878\">Read more<span class=\"screen-reader-text\">What is test statistic and critical value?<\/span><\/a><\/p>\n","protected":false},"author":57,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-227878","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is test statistic and critical value?<\/title>\n<meta name=\"description\" content=\"A test statistic is a value calculated from sample data used to make inferences about a population parameter. 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