{"id":2688,"date":"2012-10-16T00:26:25","date_gmt":"2012-10-16T05:26:25","guid":{"rendered":"http:\/\/www.thejuliagroup.com\/blog\/?p=2688"},"modified":"2012-10-16T00:26:25","modified_gmt":"2012-10-16T05:26:25","slug":"how-to-solve-any-statistics-problem","status":"publish","type":"post","link":"https:\/\/www.thejuliagroup.com\/blog\/how-to-solve-any-statistics-problem\/","title":{"rendered":"How to solve any statistics problem"},"content":{"rendered":"<p>I was grading the quizzes from my Advanced Quantitative Data Analysis class. This is a class of really smart people in a doctoral program at a selective university. And yet, some of them still had problems with the quiz. Therefore, in however many parts I feel like doing, I am going to discuss how to solve any statistics problem.<\/p>\n<p><strong>#1 CHILL !<\/strong><\/p>\n<p><a href=\"http:\/\/www.thejuliagroup.com\/blog\/wp-content\/uploads\/2012\/10\/sunbathe.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-2689\" title=\"Sun bathing in Tunisia\" src=\"http:\/\/www.thejuliagroup.com\/blog\/wp-content\/uploads\/2012\/10\/sunbathe-300x124.jpg\" alt=\"Sun bathing in Tunisia\" width=\"300\" height=\"124\" srcset=\"https:\/\/www.thejuliagroup.com\/blog\/wp-content\/uploads\/2012\/10\/sunbathe-300x124.jpg 300w, https:\/\/www.thejuliagroup.com\/blog\/wp-content\/uploads\/2012\/10\/sunbathe.jpg 719w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>I mean this most seriously. Often, I see people make mistakes because they panic, think they can&#8217;t do it, underestimate themselves and think, &#8220;The problem cannot be that easy&#8221;.<\/p>\n<p>Here is an example:<\/p>\n<p>For 17 girls diagnosed with anorexia, weight change after family therapy was as follows:<\/p>\n<p>11,11, 6, 9, 14, -3, 0, 7, 22, -5 , -4, 13, 13, 9, 4 , 6, 11<\/p>\n<p>Partial results are shown below. Fill in the missing results:<\/p>\n<p>&nbsp;<\/p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>Lower C.L.<\/td>\n<td>Upper C.L.<\/td>\n<td>t-value<\/td>\n<td>df<\/td>\n<td>2-tail Sig<\/td>\n<\/tr>\n<tr>\n<td>3.60<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>.0007<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>#2 UNDERSTAND!<\/strong><\/p>\n<p>What is it you are asked to do in the problem? You need to find the upper confidence limit for the mean, the t-value and the degrees of freedom.<\/p>\n<p>What are the degrees of freedom for a t-test?<\/p>\n<p><a href=\"http:\/\/www.tufts.edu\/~gdallal\/dof.htm\">&#8220;<strong>A single sample:<\/strong> There are <em>n<\/em> observations. There&#8217;s one parameter (the mean) that needs to be estimated. That leaves <em>n-1<\/em> degrees of freedom for estimating variability. &#8220;<\/a><\/p>\n<p>The degrees of freedom when you are estimating the mean with one sample is N-1, or\u00a0 17-1, which is 16.<\/p>\n<p>To understand a problem, look at the numbers you DO have.<\/p>\n<ul>\n<li>You have the lower confidence limit.<\/li>\n<li>You have all of the individual scores<\/li>\n<li>You know the number of scores (17)<\/li>\n<\/ul>\n<p>Think about what you DO know (or can look up in a textbook)<\/p>\n<ul>\n<li>The mean is the sum of the scores divided by the number of scores<\/li>\n<li>The lower confidence limit is the obtained mean MINUS (t * standard error).<\/li>\n<li>The UPPER confidence limit is the obtained mean PLUS (t * standard error).<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>#3 SELECT A STRATEGY<\/strong><\/p>\n<p>There are a number of ways to find the upper confidence limit but all involve adding the value of (t*standard error)\u00a0 to the mean. With what you have from #2, I&#8217;d think the easiest strategy is<\/p>\n<ul>\n<li>Find what the mean is<\/li>\n<li>Find the difference between the lower confidence limit and the mean<\/li>\n<li>Add that number to the mean<\/li>\n<\/ul>\n<p>This is often the step where people have trouble. I think it comes from three missteps. One is that they are too stressed out. The second is they don&#8217;t relax a minute and think about what they DO know first. The third is that they don&#8217;t relax a minute and think about what is the right strategy. In short, I think most people (and I am as guilty of this as anyone) don&#8217;t spend enough time on the first three steps before jumping right to number four.<\/p>\n<p><strong>#4 DO IT<\/strong><\/p>\n<p>Carry out your strategy.<\/p>\n<ul>\n<li>The mean is 7.29<\/li>\n<li>7.29 -3.6 = 3.69<\/li>\n<li>Add 3.69 to 7.29\u00a0 to get 10.98<\/li>\n<\/ul>\n<p>That&#8217;s your answer.<\/p>\n<p><strong>#5 TEST IT<\/strong><\/p>\n<p>Do a reality check. The mean is 7.29 . If it doesn&#8217;t fall between your upper and lower confidence limits, you did something wrong.<\/p>\n<p>Check back tomorrow for further proof that these steps can be applied to any statistics problem (and any math problem &#8211; maybe any problem in life. )<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I was grading the quizzes from my Advanced Quantitative Data Analysis class. This is a class of really smart people in a doctoral program at a selective university. And yet, some of them still had problems with the quiz. Therefore, in however many parts I feel like doing, I am going to discuss how to&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2688","post","type-post","status-publish","format-standard","hentry","category-statistics"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/2688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/comments?post=2688"}],"version-history":[{"count":1,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/2688\/revisions"}],"predecessor-version":[{"id":2690,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/2688\/revisions\/2690"}],"wp:attachment":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/media?parent=2688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/categories?post=2688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/tags?post=2688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}