{"id":436,"date":"2019-03-11T19:39:43","date_gmt":"2019-03-11T19:39:43","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?p=436"},"modified":"2019-03-11T19:39:43","modified_gmt":"2019-03-11T19:39:43","slug":"doing-it-10","status":"publish","type":"post","link":"https:\/\/alandix.com\/statistics\/2019\/03\/11\/doing-it-10\/","title":{"rendered":"Doing it (making sense of statistics) &#8211; 10 &#8211; a quick experiment"},"content":{"rendered":"<p><a href=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide59.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-495 alignright\" src=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide59-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide59-300x225.jpg 300w, https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide59.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Now here is a small exercise to get a feeling for that p &lt; 5% figure \u2026 are your coins really fair?<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" title=\"Doing it! (making sense of statistics)  \u2013 a quick experiment\" width=\"584\" height=\"329\" src=\"https:\/\/www.youtube.com\/embed\/OSwxpYOY6v8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><a href=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide60.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-496\" src=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide60-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide60-300x225.jpg 300w, https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide60.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Choose a coin, any coin.<\/p>\n<p>If a coin is fair then the probability of six heads is 1\/64 as is the probability of six tails, and the probability of six of either is 2\/64, approximately 3%.<\/p>\n<p>So we can do an experiment.<\/p>\n<p style=\"padding-left: 30px;\">H<sub>0<\/sub> the null hypothesis is that the coin is fair.<\/p>\n<p style=\"padding-left: 30px;\">H<sub>1<\/sub> the alternative hypothesis is that the coin is not fair.<\/p>\n<p>The likelihood of HHHHHH or TTTTTT given H0 is less than 5%, so if you get six heads or six tails, you can reject the null hypothesis and conclude that the coin is not fair.<\/p>\n<p><a href=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide61.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-497\" src=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide61-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide61-300x225.jpg 300w, https:\/\/alandix.com\/statistics\/files\/2017\/12\/Slide61.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Try it, and if it doesn&#8217;t work try again. How long before you end up with a &#8216;statistically significant&#8217; test?<\/p>\n<p>Think back to the discussion of cherry picking and multiple tests \u2026<\/p>\n<p>This might seem a little artificial, but imagine rather than coin tossing it is six users preferences for software A or B.<\/p>\n<p>Having done this, how do you feel about whether 5% is a suitable level to regard as evidence?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Now here is a small exercise to get a feeling for that p &lt; 5% figure \u2026 are your coins really fair? &nbsp; &nbsp; &nbsp; &nbsp; Choose a coin, any coin. If a coin is fair then the probability of &hellip; <a href=\"https:\/\/alandix.com\/statistics\/2019\/03\/11\/doing-it-10\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[4],"tags":[3,9],"class_list":["post-436","post","type-post","status-publish","format-standard","hentry","category-chi-course-notes","tag-chi-2017","tag-doing-it"],"_links":{"self":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/comments?post=436"}],"version-history":[{"count":4,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/436\/revisions"}],"predecessor-version":[{"id":515,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/436\/revisions\/515"}],"wp:attachment":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/media?parent=436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/categories?post=436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/tags?post=436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}