{"id":802,"date":"2024-04-12T10:30:51","date_gmt":"2024-04-12T08:30:51","guid":{"rendered":"https:\/\/guillaume-guerard.com\/?page_id=802"},"modified":"2024-04-12T10:52:41","modified_gmt":"2024-04-12T08:52:41","slug":"erreur-du-taux-de-base","status":"publish","type":"page","link":"https:\/\/guillaume-guerard.com\/en\/cours-de-methodologie\/erreur-du-taux-de-base\/","title":{"rendered":"Base Rate Error or Forgotten Base Frequency"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"802\" class=\"elementor elementor-802\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a0db98f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a0db98f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column 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elementor-top-column elementor-element elementor-element-6e0934d\" data-id=\"6e0934d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7778d45 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7778d45\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Data Science<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-673e8b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"673e8b4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d925d37\" data-id=\"d925d37\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ba6b2ae elementor-widget elementor-widget-heading\" data-id=\"ba6b2ae\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 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\" style=\"cursor:inherit\">Page 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 Contents\"><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:\/\/guillaume-guerard.com\/en\/cours-de-methodologie\/erreur-du-taux-de-base\/#Erreur_du_taux_de_base\" >Base rate error<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/guillaume-guerard.com\/en\/cours-de-methodologie\/erreur-du-taux-de-base\/#Exemples\" >Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/guillaume-guerard.com\/en\/cours-de-methodologie\/erreur-du-taux-de-base\/#Comment_eviter_les_erreurs_du_taux_de_base\" >How to Avoid Base Rate Mistakes<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Erreur_du_taux_de_base\"><\/span>Base rate error<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0b1d6ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0b1d6ce\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0b80fc1\" data-id=\"0b80fc1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f23815c elementor-widget elementor-widget-text-editor\" data-id=\"f23815c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Base rate error refers to the tendency to ignore relevant statistical information in favor of case-specific information. Instead of taking into account the base rate or prior probability of an event. For this reason, people often make inaccurate probability judgments in decision-making contexts. Base rate error is also called base rate neglect or base rate bias or base frequency forgetting.<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-49 size-thumbnail\" src=\"http:\/\/guillaume-guerard.com\/wp-content\/uploads\/2023\/07\/logo_sc-150x150.png\" alt=\"Erreur du taux de base\" width=\"150\" height=\"150\" srcset=\"https:\/\/guillaume-guerard.com\/wp-content\/uploads\/2023\/07\/logo_sc-150x150.png 150w, https:\/\/guillaume-guerard.com\/wp-content\/uploads\/2023\/07\/logo_sc-70x70.png 70w, https:\/\/guillaume-guerard.com\/wp-content\/uploads\/2023\/07\/logo_sc-125x125.png 125w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b5e5c42 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b5e5c42\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a4a55ac\" data-id=\"a4a55ac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cf874f5 elementor-widget elementor-widget-heading\" data-id=\"cf874f5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exemples\"><\/span>Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-85416df elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"85416df\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e68eee8\" data-id=\"e68eee8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-484db5c elementor-widget elementor-widget-text-editor\" data-id=\"484db5c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Or a city of one million individuals present on its territory. Of this million (1,000,000) individuals, 100 are presumed delinquents and listed as such on a list, the other 999,900 being presumed non-delinquents. In order to detect the presence of an offender on its territory, the city installs video surveillance cameras with an automatic facial recognition device: this must trigger an alert when the face filmed is that of one of the 100 offenders in the list. Unfortunately, the facial recognition device is not perfect. Suppose it has an &quot;error rate of 1 %&quot;, or, more precisely, that:<\/p><p>its sensitivity is 99 %, or a rate of 1 % of false negatives among real offenders;<br \/>its specificity is 99 %, or a false positive rate of 1 % among non-offenders.<br \/>When an alert is triggered, what is the probability that we are in the presence of an offender listed on the list?<\/p><p>If we reason with &quot;forgetting the base frequency&quot;, that is to say by only retaining the &quot;error rate is 1 %&quot;, we answer a little quickly that there are 99 % probability that the individual is actually an offender when an alert is triggered. Which is wrong. Indeed, when counting all the alerts, two situations must be taken into account simultaneously:<\/p><p>99 % of offenders trigger the alert, i.e. 99 offenders out of the 100 on the list (according to the definition of sensitivity);<br \/>1 % of non-offenders trigger the alert, i.e. 9,999 non-offenders out of 999,900 (according to the definition of specificity).<\/p><p>That&#039;s a total of 99 + 9999 = 10,098 alerts. When an alert is triggered, the probability that the individual is actually an offender is therefore 99 out of 10,098, or 0.98 % and not 99 %. This probability can be found by Bayes&#039; theorem.<\/p><p>Here&#039;s another example.<\/p><p>During the pandemic, we have often heard or read statistics in the news, such as \u201c70 % of hospitalized Covid patients have been vaccinated\u201d or \u201c7 in 10 hospitalized Covid patients are vaccinated\u201d. At the time, many wondered what this implied about the vaccine&#039;s effectiveness.<\/p><p>The key to correctly interpreting this information is the baseline vaccination rate (i.e. the percentage of the population vaccinated). If a large proportion of the population is vaccinated and only a small fraction is unvaccinated, we can expect a higher ratio of vaccinated to unvaccinated individuals in the hospital.<\/p><p>For example, suppose that a population is vaccinated at 99 % and that 51 % of the infected individuals have been vaccinated. The base rate error would lead most people to believe that the vaccine has no preventive effect. However, if the vaccine was ineffective, we would expect that approximately 99 % of infected people would have been vaccinated.<\/p><p>The base rate fallacy has created the misconception that vaccines are ineffective because, in highly vaccinated populations, the majority of COVID-19 cases occur among vaccinated people.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de6f13d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de6f13d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ab66652\" data-id=\"ab66652\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d35452 elementor-widget elementor-widget-heading\" data-id=\"7d35452\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Comment_eviter_les_erreurs_du_taux_de_base\"><\/span>How to Avoid Base Rate Mistakes<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-73699dc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"73699dc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9cc3760\" data-id=\"9cc3760\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2052221 elementor-widget elementor-widget-text-editor\" data-id=\"2052221\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This is very simple, in addition to statistics, you must know the number of individuals in each population tested. The simplest way to avoid a base rate error is to rely on a confusion matrix.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Home Data Science Base Rate Error A base rate error refers to the tendency\u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":47,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-802","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/pages\/802","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/comments?post=802"}],"version-history":[{"count":7,"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/pages\/802\/revisions"}],"predecessor-version":[{"id":812,"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/pages\/802\/revisions\/812"}],"up":[{"embeddable":true,"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/pages\/47"}],"wp:attachment":[{"href":"https:\/\/guillaume-guerard.com\/en\/wp-json\/wp\/v2\/media?parent=802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}