{"id":262693,"date":"2024-04-19T01:14:08","date_gmt":"2024-04-19T01:14:08","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=262693"},"modified":"2024-04-19T01:14:08","modified_gmt":"2024-04-19T01:14:08","slug":"how-to-calculate-bonferroni-adjusted-p-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-calculate-bonferroni-adjusted-p-value\/","title":{"rendered":"How to calculate Bonferroni adjusted p value?"},"content":{"rendered":"<p>The Bonferroni adjustment is a method used to control the family-wise error rate (FWER) when performing multiple statistical tests simultaneously. It adjusts the p-values to minimize the risk of obtaining false positives. This article will explain how to calculate the Bonferroni adjusted p value step-by-step.<\/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-to-calculate-bonferroni-adjusted-p-value\/#Step_1_Determine_the_significance_level\" title=\"Step 1: Determine the significance level\">Step 1: Determine the significance level<\/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-to-calculate-bonferroni-adjusted-p-value\/#Step_2_Collect_the_p-values\" title=\"Step 2: Collect the p-values\">Step 2: Collect the p-values<\/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-to-calculate-bonferroni-adjusted-p-value\/#Step_3_Divide_the_significance_level\" title=\"Step 3: Divide the significance level\">Step 3: Divide the significance level<\/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-to-calculate-bonferroni-adjusted-p-value\/#Step_4_Compare_the_p-values\" title=\"Step 4: Compare the p-values\">Step 4: Compare the p-values<\/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-to-calculate-bonferroni-adjusted-p-value\/#Step_5_Interpret_the_results\" title=\"Step 5: Interpret the results\">Step 5: Interpret the results<\/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\/how-to-calculate-bonferroni-adjusted-p-value\/#Example\" title=\"Example:\">Example:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/how-to-calculate-bonferroni-adjusted-p-value\/#Question_1_What_is_the_significance_level_for_each_test_after_Bonferroni_adjustment\" title=\"Question 1: What is the significance level for each test after Bonferroni adjustment?\">Question 1: What is the significance level for each test after Bonferroni 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-to-calculate-bonferroni-adjusted-p-value\/#Question_2_If_a_p-value_is_0012_is_it_statistically_significant_after_Bonferroni_adjustment\" title=\"Question 2: If a p-value is 0.012, is it statistically significant after Bonferroni adjustment?\">Question 2: If a p-value is 0.012, is it statistically significant after Bonferroni adjustment?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_3_Can_the_Bonferroni_adjustment_make_a_non-significant_p-value_significant\" title=\"Question 3: Can the Bonferroni adjustment make a non-significant p-value significant?\">Question 3: Can the Bonferroni adjustment make a non-significant p-value significant?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_4_Is_the_Bonferroni_adjustment_suitable_for_all_types_of_tests\" title=\"Question 4: Is the Bonferroni adjustment suitable for all types of tests?\">Question 4: Is the Bonferroni adjustment suitable for all types of tests?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_5_What_are_the_limitations_of_the_Bonferroni_adjustment\" title=\"Question 5: What are the limitations of the Bonferroni adjustment?\">Question 5: What are the limitations of the Bonferroni adjustment?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_6_Are_there_alternative_methods_to_the_Bonferroni_adjustment\" title=\"Question 6: Are there alternative methods to the Bonferroni adjustment?\">Question 6: Are there alternative methods to the Bonferroni adjustment?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_7_Does_the_Bonferroni_adjustment_account_for_the_sample_size\" title=\"Question 7: Does the Bonferroni adjustment account for the sample size?\">Question 7: Does the Bonferroni adjustment account for the sample size?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_8_Can_the_Bonferroni_adjustment_be_retrospectively_applied_to_published_results\" title=\"Question 8: Can the Bonferroni adjustment be retrospectively applied to published results?\">Question 8: Can the Bonferroni adjustment be retrospectively applied to published results?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_9_How_do_I_compute_the_adjusted_p_value_using_statistical_software\" title=\"Question 9: How do I compute the adjusted p value using statistical software?\">Question 9: How do I compute the adjusted p value using statistical software?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_10_Can_you_have_an_adjusted_p_value_greater_than_1\" title=\"Question 10: Can you have an adjusted p value greater than 1?\">Question 10: Can you have an adjusted p value greater than 1?<\/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-to-calculate-bonferroni-adjusted-p-value\/#Question_11_Can_the_Bonferroni_adjustment_be_used_in_exploratory_data_analysis\" title=\"Question 11: Can the Bonferroni adjustment be used in exploratory data analysis?\">Question 11: Can the Bonferroni adjustment be used in exploratory data analysis?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/namso-gen.co\/blog\/how-to-calculate-bonferroni-adjusted-p-value\/#Question_12_Does_the_Bonferroni_adjustment_guarantee_the_absence_of_false_positives\" title=\"Question 12: Does the Bonferroni adjustment guarantee the absence of false positives?\">Question 12: Does the Bonferroni adjustment guarantee the absence of false positives?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Step_1_Determine_the_significance_level\"><\/span>Step 1: Determine the significance level<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Before calculating the Bonferroni adjusted p value, you need to determine the desired significance level for your analysis. The significance level usually ranges from 0.01 to 0.05, depending on the stringency required for the study.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Step_2_Collect_the_p-values\"><\/span>Step 2: Collect the p-values<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Collect a set of p-values obtained from multiple tests or comparisons. These p-values represent the statistical significance of each test individually. Ensure that the p-values collected are all from tests that are independent of each other. <\/p>\n<h2><span class=\"ez-toc-section\" id=\"Step_3_Divide_the_significance_level\"><\/span>Step 3: Divide the significance level<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Divide the determined significance level (from Step 1) by the number of tests being performed. This step allows us to adjust the significance level for each individual test, thus controlling the overall false positive rate.<\/p>\n<p class=\"highlight\">How to calculate Bonferroni adjusted p value?<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Step_4_Compare_the_p-values\"><\/span>Step 4: Compare the p-values<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For each individual p-value, compare it to the Bonferroni-adjusted significance level obtained in Step 3. If the p-value is smaller than or equal to the adjusted significance level, it is considered statistically significant.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Step_5_Interpret_the_results\"><\/span>Step 5: Interpret the results<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Once you have calculated the Bonferroni adjusted p value for each individual test, interpret the results accordingly. The adjusted p value determines the new, stricter significance threshold that must be met for statistical significance. If a p-value is below this threshold, it indicates a significant finding.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Example\"><\/span>Example:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Suppose you have conducted five independent statistical tests with an initial significance level of 0.05.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_1_What_is_the_significance_level_for_each_test_after_Bonferroni_adjustment\"><\/span>Question 1: What is the significance level for each test after Bonferroni adjustment?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>After dividing the significance level (0.05) by the number of tests (5), the adjusted significance level for each test is 0.05\/5 = 0.01.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_2_If_a_p-value_is_0012_is_it_statistically_significant_after_Bonferroni_adjustment\"><\/span>Question 2: If a p-value is 0.012, is it statistically significant after Bonferroni adjustment?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>Yes, the p-value of 0.012 is smaller than the adjusted significance level (0.01), indicating statistical significance.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_3_Can_the_Bonferroni_adjustment_make_a_non-significant_p-value_significant\"><\/span>Question 3: Can the Bonferroni adjustment make a non-significant p-value significant?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>No, the Bonferroni adjustment only controls the overall probability of Type I error, but it does not change the individual p-values. If a p-value is not statistically significant before adjustment, it will also remain non-significant after adjustment.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_4_Is_the_Bonferroni_adjustment_suitable_for_all_types_of_tests\"><\/span>Question 4: Is the Bonferroni adjustment suitable for all types of tests?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>Yes, the Bonferroni adjustment can be applied to any statistical test as long as the tests are independent of each other.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_5_What_are_the_limitations_of_the_Bonferroni_adjustment\"><\/span>Question 5: What are the limitations of the Bonferroni adjustment?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>The Bonferroni adjustment can be conservative, meaning that it may increase the risk of Type II errors (false negatives). It assumes independence between tests and is less optimal when correlations exist among the tests.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_6_Are_there_alternative_methods_to_the_Bonferroni_adjustment\"><\/span>Question 6: Are there alternative methods to the Bonferroni adjustment?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>Yes, other methods like the Benjamini-Hochberg procedure (False Discovery Rate control) and Tukey&#8217;s Honest Significant Difference (HSD) test also address the issue of multiple comparisons.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_7_Does_the_Bonferroni_adjustment_account_for_the_sample_size\"><\/span>Question 7: Does the Bonferroni adjustment account for the sample size?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>No, the Bonferroni adjustment does not account for sample size in its calculation. It focuses solely on the number of tests being performed.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_8_Can_the_Bonferroni_adjustment_be_retrospectively_applied_to_published_results\"><\/span>Question 8: Can the Bonferroni adjustment be retrospectively applied to published results?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>No, the Bonferroni adjustment should ideally be planned and applied prior to conducting the statistical tests. Applying it post hoc can be misleading.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_9_How_do_I_compute_the_adjusted_p_value_using_statistical_software\"><\/span>Question 9: How do I compute the adjusted p value using statistical software?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>Most statistical software packages have built-in functions for adjusting p-values, including the Bonferroni adjustment. Consult the software documentation or statistical textbooks for instructions specific to your chosen tool.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_10_Can_you_have_an_adjusted_p_value_greater_than_1\"><\/span>Question 10: Can you have an adjusted p value greater than 1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>No, the Bonferroni adjustment ensures that the adjusted p values remain limited to the range of 0 to 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_11_Can_the_Bonferroni_adjustment_be_used_in_exploratory_data_analysis\"><\/span>Question 11: Can the Bonferroni adjustment be used in exploratory data analysis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>Yes, the Bonferroni adjustment can be used in exploratory data analysis to control the overall type I error rate when testing multiple hypotheses.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Question_12_Does_the_Bonferroni_adjustment_guarantee_the_absence_of_false_positives\"><\/span>Question 12: Does the Bonferroni adjustment guarantee the absence of false positives?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><\/p>\n<p>No, although the Bonferroni adjustment reduces the risk of false positives, it cannot completely eliminate them. It remains crucial to interpret the results cautiously and consider context-specific factors.<\/p>\n<p>By following the steps outlined above, you can effectively calculate the Bonferroni adjusted p value for your statistical tests. Remember to apply this adjustment when conducting multiple tests to ensure the reliability and validity of your findings.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Bonferroni adjustment is a method used to control the family-wise error rate (FWER) when performing multiple statistical tests simultaneously. It adjusts the p-values to minimize the risk of obtaining false positives. This article will explain how to calculate the Bonferroni adjusted p value step-by-step. Step 1: Determine the significance level Before calculating the Bonferroni &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How to calculate Bonferroni adjusted p value?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-to-calculate-bonferroni-adjusted-p-value\/#more-262693\">Read more<span class=\"screen-reader-text\">How to calculate Bonferroni adjusted p value?<\/span><\/a><\/p>\n","protected":false},"author":66,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-262693","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 to calculate Bonferroni adjusted p value?<\/title>\n<meta name=\"description\" content=\"The Bonferroni adjustment is a method used to control the family-wise error rate (FWER) when performing multiple statistical tests simultaneously. 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