{"id":250540,"date":"2024-07-18T07:27:46","date_gmt":"2024-07-18T07:27:46","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=250540"},"modified":"2024-07-18T07:27:46","modified_gmt":"2024-07-18T07:27:46","slug":"how-does-fdr-p-value-adjustment-work-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/","title":{"rendered":"How does FDR p-value adjustment work?"},"content":{"rendered":"<p>In the world of statistics, p-values play a crucial role in determining the significance of results. However, when conducting multiple hypothesis tests simultaneously, the chance of obtaining false positives increases. To tackle this problem, statisticians have developed various techniques for adjusting p-values. One such method is the False Discovery Rate (FDR) p-value adjustment. So, how does FDR p-value adjustment work and why is it important? Let&#8217;s explore this topic in detail.<\/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\/how-does-fdr-p-value-adjustment-work-2\/#Understanding_the_problem\" title=\"Understanding the problem:\">Understanding the problem:<\/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\/how-does-fdr-p-value-adjustment-work-2\/#The_intuition_behind_FDR_adjustment\" title=\"The intuition behind FDR adjustment:\">The intuition behind FDR adjustment:<\/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\/how-does-fdr-p-value-adjustment-work-2\/#How_does_FDR_p-value_adjustment_work\" title=\"How does FDR p-value adjustment work?\">How does FDR p-value adjustment work?<\/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\/how-does-fdr-p-value-adjustment-work-2\/#Why_is_FDR_p-value_adjustment_important\" title=\"Why is FDR p-value adjustment important?\">Why is FDR p-value adjustment important?<\/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\/how-does-fdr-p-value-adjustment-work-2\/#Frequently_Asked_Questions\" title=\"Frequently Asked Questions:\">Frequently Asked Questions:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#1_What_is_a_p-value\" title=\"1. What is a p-value?\">1. What is a p-value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#2_Why_do_we_need_p-value_adjustment\" title=\"2. Why do we need p-value adjustment?\">2. Why do we need p-value adjustment?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#3_What_is_the_Bonferroni_correction\" title=\"3. What is the Bonferroni correction?\">3. What is the Bonferroni correction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#4_How_does_FDR_adjustment_differ_from_the_Bonferroni_correction\" title=\"4. How does FDR adjustment differ from the Bonferroni correction?\">4. How does FDR adjustment differ from the Bonferroni correction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#5_When_is_FDR_adjustment_suitable\" title=\"5. When is FDR adjustment suitable?\">5. When is FDR adjustment suitable?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#6_Can_FDR_adjustment_be_too_liberal\" title=\"6. Can FDR adjustment be too liberal?\">6. Can FDR adjustment be too liberal?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#7_Is_FDR_p-value_adjustment_widely_used_in_research\" title=\"7. Is FDR p-value adjustment widely used in research?\">7. Is FDR p-value adjustment widely used in research?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#8_Does_FDR_adjustment_guarantee_valid_results\" title=\"8. Does FDR adjustment guarantee valid results?\">8. Does FDR adjustment guarantee valid results?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#9_Can_FDR_adjustment_be_applied_to_any_significance_level\" title=\"9. Can FDR adjustment be applied to any significance level?\">9. Can FDR adjustment be applied to any significance level?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#10_Are_there_other_p-value_adjustment_methods\" title=\"10. Are there other p-value adjustment methods?\">10. Are there other p-value adjustment methods?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#11_Can_FDR_adjustment_be_used_for_independent_tests_only\" title=\"11. Can FDR adjustment be used for independent tests only?\">11. Can FDR adjustment be used for independent tests only?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#12_Is_FDR_adjustment_only_applicable_to_hypothesis_testing\" title=\"12. Is FDR adjustment only applicable to hypothesis testing?\">12. Is FDR adjustment only applicable to hypothesis testing?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Understanding_the_problem\"><\/span>Understanding the problem:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\nWhen conducting multiple tests simultaneously, the likelihood of at least one test yielding a significant result purely due to chance increases. For example, if we perform 100 tests with a significance level of 0.05, we would expect five false positives on average. The significance level is the p-value threshold below which we consider a result statistically significant. To address this issue, we need a correction method that ensures a controlled rate of false discoveries.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_intuition_behind_FDR_adjustment\"><\/span>The intuition behind FDR adjustment:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\nUnlike other correction techniques like the Bonferroni correction, FDR adjustment focuses on controlling the proportion of false discoveries relative to all rejected hypotheses. The approach acknowledges that not all rejected hypotheses have the same importance. Some false discoveries are tolerable as long as the overall false discovery rate remains within an acceptable range.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_does_FDR_p-value_adjustment_work\"><\/span>How does FDR p-value adjustment work?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\nThe FDR adjustment methodology involves ordering the p-values from smallest to largest and comparing them to a series of thresholds. The critical aspect is to identify the largest threshold where all p-values below the threshold are declared significant, while controlling the overall proportion of false discoveries. This threshold is often denoted as the q-value.<\/p>\n<p>**To determine the q-value, FDR adjustment employs the following steps:**<\/p>\n<p>1. Order the p-values from smallest to largest.<br \/>\n2. Calculate the critical value based on the desired FDR control level (e.g., 0.05 or 0.10).<br \/>\n3. Starting from the smallest p-value, compare each p-value to its corresponding threshold.<br \/>\n4. The largest p-value that is smaller than or equal to its threshold is declared significant.<br \/>\n5. All p-values smaller than or equal to the identified threshold are marked as significant, and the corresponding q-values are calculated.<br \/>\n6. The q-value represents the minimum FDR at which a given result is called significant.<\/p>\n<p>This sequential method allows researchers to identify significant results while also maintaining control over the rate of false discoveries.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Why_is_FDR_p-value_adjustment_important\"><\/span>Why is FDR p-value adjustment important?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\nFDR p-value adjustment is a valuable statistical tool for several reasons:<\/p>\n<p>1. **Controlling the rate of false discoveries**: By adjusting p-values using FDR, researchers can mitigate the risk of falsely accepting hypotheses in multiple testing scenarios.<br \/>\n2. **Focus on relevant discoveries**: FDR acknowledges that not all discoveries carry equal importance, allowing researchers to identify the most relevant findings without an overly conservative correction.<br \/>\n3. **Increased statistical power**: FDR adjustment enhances statistical power by reducing the number of incorrectly rejected hypotheses, leading to more accurate and meaningful results in multiple testing situations.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span>Frequently Asked Questions:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_a_p-value\"><\/span>1. What is a p-value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nA p-value represents the probability of obtaining observed results, or more extreme results, if the null hypothesis is true.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Why_do_we_need_p-value_adjustment\"><\/span>2. Why do we need p-value adjustment?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nP-value adjustment is necessary to account for the increased risk of false positives when conducting multiple hypothesis tests simultaneously.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_What_is_the_Bonferroni_correction\"><\/span>3. What is the Bonferroni correction?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe Bonferroni correction is a conservative method for adjusting p-values that controls the family-wise error rate (FWER) by dividing the significance threshold by the number of tests.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_How_does_FDR_adjustment_differ_from_the_Bonferroni_correction\"><\/span>4. How does FDR adjustment differ from the Bonferroni correction?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nFDR adjustment controls the false discovery rate, allowing for a controlled proportion of false positives, while the Bonferroni correction controls the family-wise error rate more strictly.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_When_is_FDR_adjustment_suitable\"><\/span>5. When is FDR adjustment suitable?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nFDR adjustment is particularly useful in exploratory studies, where multiple tests are conducted simultaneously to identify potential relationships or associations.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_Can_FDR_adjustment_be_too_liberal\"><\/span>6. Can FDR adjustment be too liberal?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, FDR adjustment can lead to some false positives as it allows for a controlled proportion of them. It strikes a balance between avoiding excessive false positives and maintaining statistical power.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_Is_FDR_p-value_adjustment_widely_used_in_research\"><\/span>7. Is FDR p-value adjustment widely used in research?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, the FDR adjustment method is commonly used in various fields, including genomics, neuroscience, and economics, to analyze high-dimensional datasets.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_Does_FDR_adjustment_guarantee_valid_results\"><\/span>8. Does FDR adjustment guarantee valid results?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nWhile FDR adjustment is a powerful tool, it does not guarantee valid results. It is important to apply it appropriately and interpret the findings within the context of the study.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_Can_FDR_adjustment_be_applied_to_any_significance_level\"><\/span>9. Can FDR adjustment be applied to any significance level?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, FDR adjustment can be applied to any significance level, depending on the desired level of control over the false discovery rate.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_Are_there_other_p-value_adjustment_methods\"><\/span>10. Are there other p-value adjustment methods?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, apart from FDR and Bonferroni corrections, other methods such as the Holm-Bonferroni method, the Benjamini-Hochberg method, and Storey&#8217;s q-value method are also frequently used for p-value adjustment.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Can_FDR_adjustment_be_used_for_independent_tests_only\"><\/span>11. Can FDR adjustment be used for independent tests only?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, FDR adjustment is suitable for both independent and dependent tests, although it assumes positive dependence among the tests.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Is_FDR_adjustment_only_applicable_to_hypothesis_testing\"><\/span>12. Is FDR adjustment only applicable to hypothesis testing?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nFDR adjustment is primarily used in hypothesis testing scenarios to control the rate of false discoveries, but it can also be applied to control the proportion of false positive findings in other statistical analyses.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the world of statistics, p-values play a crucial role in determining the significance of results. However, when conducting multiple hypothesis tests simultaneously, the chance of obtaining false positives increases. To tackle this problem, statisticians have developed various techniques for adjusting p-values. One such method is the False Discovery Rate (FDR) p-value adjustment. So, how &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How does FDR p-value adjustment work?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-does-fdr-p-value-adjustment-work-2\/#more-250540\">Read more<span class=\"screen-reader-text\">How does FDR p-value adjustment work?<\/span><\/a><\/p>\n","protected":false},"author":63,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-250540","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>How does FDR p-value adjustment work?<\/title>\n<meta name=\"description\" content=\"In the world of statistics, p-values play a crucial role in determining the significance of results. 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