{"id":3748,"date":"2013-09-06T22:05:00","date_gmt":"2013-09-06T22:05:00","guid":{"rendered":""},"modified":"2019-08-29T16:59:11","modified_gmt":"2019-08-29T16:59:11","slug":"statistics","status":"publish","type":"post","link":"https:\/\/jessicaeblack.org\/everythingelse\/2013\/09\/06\/statistics\/","title":{"rendered":"Probability and breast cancer"},"content":{"rendered":"<p>From my stats homework:<\/p>\n<div><\/div>\n<ul>\n<li>Approximately 1% of women aged 40-50 have breast cancer. A woman with breast cancer has a 90% chance of a positive test from a mammogram, while a woman without has a 10% chance of a false positive result. What is the probability a woman has breast cancer given that she just had a positive test?<\/li>\n<\/ul>\n<p><o:p><\/o:p><\/p>\n<div>So.. you are 45 and receive a &#8220;positive&#8221; mammogram. &nbsp;Not sure what that means, but maybe it means they&#8217;ve detected a dark patch, a lump you cannot feel. &nbsp;In real life they don&#8217;t tell you that you have cancer. &nbsp;They most likely schedule a repeat mammogram, and then maybe a biopsy. &nbsp;But anyway, given that &#8220;positive&#8221; mammogram, make a stab at how likely it is that you have breast cancer.<\/div>\n<div><\/div>\n<div>My professor (whom I really like, even though he can give the most amazingly obtuse examples) had rushed through a sample problem of the same sort:<\/div>\n<div><\/div>\n<ul>\n<li>The incidence of schizophrenia in adults is about 2%. A proposed screening test is estimated to have at least 95% accuracy in making the positive diagnosis (sensitivity) and about 97% accuracy in declaring normality (specificity). Formally stated, P(normal | Ho) = .97, P(schizophrenia|Hi) &gt; .95. So, let<\/li>\n<ul>\n<ul>\n<li>Ho = The case is normal<\/li>\n<li>Hi = The case is schizophrenic<\/li>\n<li>D = The test result (the data) is positive for schizophrenia<\/li>\n<\/ul>\n<\/ul>\n<li>What is the probability of the case being normal (ie the patient <b>not<\/b>&nbsp;having schizophrenia) if s\/he tests positive? &nbsp;ie was is p(Ho|D)?<\/li>\n<\/ul>\n<p><\/p>\n<div>He did not give credit where credit was due; the example is from a famous (to statisticians) piece by Cohen (1994) called <a href=\"http:\/\/www.ics.uci.edu\/~sternh\/courses\/210\/cohen94_pval.pdf\">&#8220;The earth is round, <i>p<\/i>&nbsp;&lt; .05.&#8221;<\/a>&nbsp; That evening I sent him an email saying I had found the article and liked it&#8230; Two minutes later he emailed the entire class, saying that he had got the example from the piece, and asking us to read it \ud83d\ude09 &nbsp;He also thanked me in class for bringing it to his attention that he had not already assigned it. &nbsp;I may have to dig out my bullet proof vest.<\/div>\n<div><\/div>\n<div>The probability of someone who tests positive for schizophrenia being, in fact, normal, is .607. &nbsp;60.7% of people testing positive for schizophrenia are not schizophrenic.<\/div>\n<div><\/div>\n<div>The probability of me finding a parking space on campus lots that allow anyone with a permit to park (and are closer to the psych department than parking in the street would be), and during <i>normal<\/i>&nbsp;hours (that is, between 9:00 and 16:00, with a brief window of more availability around noon)&nbsp;is much smaller. &nbsp;I don&#8217;t have formal data here, but I&#8217;d place it at about .10; 10% of the time I will find a parking space if I arrive after nine. &nbsp;And if I do find one, it will be at the TOP of the parking garage, which means a long slow line to get out of the lot when I leave, so I might as well park by the duck pond (~0.75 miles from Dale Hall). &nbsp;Before I spent $195 on a parking permit I was consistently parking 0.5-0.6 miles from Dale Hall (psych dept), on the street. &nbsp; What a waste of money. &nbsp;As soon as it gets cooler, I&#8217;m riding my bike.<\/div>\n<div><\/div>\n<div>The probability of having breast cancer, given a positive mammogram is .0833; only about eight out of 100 women who have a positive mammogram actually have cancer.<\/div>\n<div><\/div>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>From my stats homework: Approximately 1% of women aged 40-50 have breast cancer. A woman with breast cancer has a 90% chance of a positive test from a mammogram, while a woman without has a 10% chance of a false positive result. What is the probability a woman has breast cancer given that she just&hellip;&nbsp;<a href=\"https:\/\/jessicaeblack.org\/everythingelse\/2013\/09\/06\/statistics\/\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Probability and breast cancer<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","jetpack_post_was_ever_published":false,"_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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[3,4],"tags":[61],"class_list":["post-3748","post","type-post","status-publish","format-standard","hentry","category-backgound","category-statistics","tag-statistics-probability-breast-cancer-parking-spot"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Probability and breast cancer : Wild Woman&#039;s World<\/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:\/\/jessicaeblack.org\/everythingelse\/2013\/09\/06\/statistics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability and breast cancer : Wild Woman&#039;s World\" \/>\n<meta property=\"og:description\" content=\"From my stats homework: Approximately 1% of women aged 40-50 have breast cancer. 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