{"id":1684,"date":"2025-12-16T00:11:02","date_gmt":"2025-12-16T00:11:02","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1684"},"modified":"2025-12-16T00:11:04","modified_gmt":"2025-12-16T00:11:04","slug":"sat-math-scores-gender-difference-or-selection-bias","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2025\/12\/16\/sat-math-scores-gender-difference-or-selection-bias\/","title":{"rendered":"SAT math scores: gender difference or selection bias?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The video from my <a href=\"https:\/\/pydata.org\/boston2025\/schedule\">PyData Boston<\/a> talk is up now:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/6pwtbNVgyzg?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Resources<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <a href=\"https:\/\/docs.google.com\/presentation\/d\/e\/2PACX-1vQ64XmhBYSAfIKHgBIWz8Pbvbgdk-9FxUUMpAGVqouR3eAVqR6hJytfl3-ffZ1qXTNMnNuQiCHr7QWs\/pub\">slides are here<\/a><\/li>\n\n\n\n<li>Run the <a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/ThinkBayes2\/blob\/master\/examples\/bread.ipynb\">first notebook (Poincar\u00e9 problem) on Colab<\/a><\/li>\n\n\n\n<li>Run the <a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/SelectionSAT\/blob\/main\/selection_bias3.ipynb\">second notebook (analysis of SAT data) on Colab<\/a><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If you want to learn to do this kind of analysis, you can sign up for the <a href=\"https:\/\/www.pymc-labs.com\/workshops\/applied-bayesian-modeling\">January 2026 offering of the Applied Bayesian Modeling Workshop<\/a>, which I teach along with my colleagues at PyMC Labs.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And as always, you can read <em><a href=\"https:\/\/allendowney.github.io\/ThinkBayes2\/\">Think Bayes<\/a><\/em> in hard copy or free online.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Abstract<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Why do male test takers consistently score about 30 points higher than female test takers on the mathematics section of the SAT? Does this reflect an actual difference in math ability, or is it an artifact of selection bias\u2014if young men with low math ability are less likely to take the test than young women with the same ability?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This talk presents a Bayesian model that estimates how much of the observed difference can be explained by selection effects. We\u2019ll walk through a complete Bayesian workflow, including prior elicitation with PreliZ, model building in PyMC, and validation with ArviZ, showing how Bayesian methods disentangle latent traits from observed outcomes and separate the signal from the noise.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The video from my PyData Boston talk is up now: Resources If you want to learn to do this kind of analysis, you can sign up for the January 2026 offering of the Applied Bayesian Modeling Workshop, which I teach along with my colleagues at PyMC Labs. And as always, you can read Think Bayes in hard copy or free online. Abstract Why do male test takers consistently score about 30 points higher than female test takers on the mathematics&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2025\/12\/16\/sat-math-scores-gender-difference-or-selection-bias\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[71,108,109],"class_list":["post-1684","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bayesian-statistics","tag-pymc","tag-standardized-testing"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>SAT math scores: gender difference or selection bias? - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2025\/12\/16\/sat-math-scores-gender-difference-or-selection-bias\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SAT math scores: gender difference or selection bias? - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"The video from my PyData Boston talk is up now: Resources If you want to learn to do this kind of analysis, you can sign up for the January 2026 offering of the Applied Bayesian Modeling Workshop, which I teach along with my colleagues at PyMC Labs. And as always, you can read Think Bayes in hard copy or free online. Abstract Why do male test takers consistently score about 30 points higher than female test takers on the mathematics... Read More Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.allendowney.com\/blog\/2025\/12\/16\/sat-math-scores-gender-difference-or-selection-bias\/\" \/>\n<meta property=\"og:site_name\" content=\"Probably Overthinking It\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-16T00:11:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-16T00:11:04+00:00\" \/>\n<meta name=\"author\" content=\"AllenDowney\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:site\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"AllenDowney\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2025\\\/12\\\/16\\\/sat-math-scores-gender-difference-or-selection-bias\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2025\\\/12\\\/16\\\/sat-math-scores-gender-difference-or-selection-bias\\\/\"},\"author\":{\"name\":\"AllenDowney\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#\\\/schema\\\/person\\\/4e5bfb2e9af6c3446cb0031a7bf83207\"},\"headline\":\"SAT math scores: gender difference or selection bias?\",\"datePublished\":\"2025-12-16T00:11:02+00:00\",\"dateModified\":\"2025-12-16T00:11:04+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2025\\\/12\\\/16\\\/sat-math-scores-gender-difference-or-selection-bias\\\/\"},\"wordCount\":215,\"publisher\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#organization\"},\"keywords\":[\"bayesian statistics\",\"PyMC\",\"standardized testing\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2025\\\/12\\\/16\\\/sat-math-scores-gender-difference-or-selection-bias\\\/\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2025\\\/12\\\/16\\\/sat-math-scores-gender-difference-or-selection-bias\\\/\",\"name\":\"SAT math scores: gender difference or selection bias? 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