{"id":533,"date":"2016-06-24T23:30:09","date_gmt":"2016-06-25T03:30:09","guid":{"rendered":"http:\/\/aristotle2digital.blogwyrm.com\/?p=533"},"modified":"2016-06-24T10:48:57","modified_gmt":"2016-06-24T14:48:57","slug":"milling-about","status":"publish","type":"post","link":"https:\/\/aristotle2digital.blogwyrm.com\/?p=533","title":{"rendered":"Milling About"},"content":{"rendered":"<p>Arguing about cause and effect is a difficult enterprise even in the best of circumstances.\u00a0 Rarely is it as clean, or as boring, as introductory texts on logic make it out to be.\u00a0 Examples of simple cause and effect \u2013 it is raining and therefore the ground is getting wet \u2013 are neither controversial nor are they fun.\u00a0 Most everyone agrees on the matter and that\u2019s that.\u00a0 But arguments over new things undiscovered or unseen are one of the best things going.\u00a0 Who isn\u2019t thrilled by the prospect of figuring something out that none else have done?<\/p>\n<p>Interestingly enough, almost all of us use standard methods for arguing from effect to cause.\u00a0 Most likely, we\u2019ve all learned these methods by first watching others apply them and then by next jumping into the game and trying out the methods ourselves.\u00a0 As will be discussed in more detail below, these methods worm themselves into almost every aspect of life; often without our notice.\u00a0 They form the backbone of most editorials, advertisements, and dinner-table arguments.\u00a0 And despite their anonymity, they do have a name:\u00a0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mill%27s_Methods\">Mill\u2019s Methods<\/a>.<\/p>\n<p>First codified by John Stuart Mill in his book <em>A System of Logic<\/em> (1843), these methods, which no doubt date back to antiquity, go by the obscure names of:<\/p>\n<ul>\n<li>Method of Agreement<\/li>\n<li>Method of Difference<\/li>\n<li>Joint Method<\/li>\n<li>Method of Concomitant Variation<\/li>\n<li>Method of Residues<\/li>\n<\/ul>\n<p>As unfamiliar as these terms may be to the ear, their use and application is familiar to the thinking of anyone who has ever tried to figure out what food at dinner last night didn\u2019t agree with them or some similar scenario.\u00a0 Indeed, many of the examples presented in the community deal with food and indigestion.\u00a0 (In fact, application of Mill\u2019s Methods to epidemiology is the core component of the TV show <em>House<\/em>).<\/p>\n<p>Not wanting to dwell on food related illness (since it is done to death in the literature), I propose illustrating the methods using a more interesting question faced by parents and teachers across the country:\u00a0 what factors contribute to good grades.<\/p>\n<p>Consider a group of 10 students from a local school.\u00a0 After circulating a questionnaire, their teacher compiles a table listing various activities they pursued and the study method they used (written homework or online quizzes).\u00a0 The teacher wants to see what caused half the students to pass where the other half failed and so he looks for a factor that is both necessary and sufficient to explain why the first group passed. \u00a0He suspects that those students who play video games have been poisoned and that students who avoid this digital scourge are the ones that pass.\u00a0 But being a man of integrity he decides to pursue the answer with an open mind.\u00a0 To do this he employs Mill\u2019s Methods in succession.<\/p>\n<p>To apply the <strong><em>Method of Agreement<\/em><\/strong>, he looks to see what features all the passing students have in common.\u00a0 He starts by looking at a subset group composed of Amy, Carl and Walter.<\/p>\n<table>\n<tbody>\n<tr>\n<th width=\"72\"><strong>Student<\/strong><\/th>\n<th width=\"88\"><strong>Recreation<\/strong><\/th>\n<th width=\"81\"><strong>Musical Instrument<\/strong><\/th>\n<th width=\"82\"><strong>Teaching Technique<\/strong><\/th>\n<th width=\"78\"><strong>Exercise<\/strong><\/th>\n<th width=\"76\"><strong>(Pass\/Fail)<\/strong><\/th>\n<\/tr>\n<tr>\n<td width=\"72\">Amy<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">None<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">None<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Carl<\/td>\n<td width=\"88\">Drawing<\/td>\n<td width=\"81\">Piano<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Swimming<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Walter<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Clarinet<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>He notices that these 3 students have nothing in common in terms of their recreational pursuits, they don\u2019t play the same musical instrument (in fact Amy doesn\u2019t play any), that that they don\u2019t all engage in the same exercise.\u00a0 But all three of them were taught using the same technique of written homework.\u00a0 He concludes that there is very likely possibility that written homework is the cause of their success in the class.<\/p>\n<p>To apply the <strong><em>Method of Difference<\/em><\/strong>, he then looks for a pair of students, one who has passed and one who has failed, that have almost everything in common.\u00a0 Any difference between them being a strong indication that it is the cause of success\/failure.\u00a0 He finds such a pair in Ben and Stacey.<\/p>\n<table>\n<tbody>\n<tr>\n<th width=\"72\"><strong>Student<\/strong><\/th>\n<th width=\"88\"><strong>Recreation<\/strong><\/th>\n<th width=\"81\"><strong>Musical Instrument<\/strong><\/th>\n<th width=\"82\"><strong>Teaching Technique<\/strong><\/th>\n<th width=\"78\"><strong>Exercise<\/strong><\/th>\n<th width=\"76\"><strong>(Pass\/Fail)<\/strong><\/th>\n<\/tr>\n<tr>\n<td width=\"72\">Ben<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">Running<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Stacey<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Running<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Both of them enjoy blogging, play guitar, and exercise by running.\u00a0 The difference between them seems to be that Stacey was required to do written homework while Ben was required to do online quizzes.\u00a0 He concludes that there is a very strong possibility that written homework leads to good grades.<\/p>\n<p>The <strong><em>Joint Method<\/em><\/strong> marries the two approaches together looking for support that this one factor, the teaching technique, is the primary cause of classroom success.\u00a0 To this end, our teacher combines all the students into the following table<\/p>\n<table>\n<tbody>\n<tr>\n<th width=\"72\"><strong>Student<\/strong><\/th>\n<th width=\"88\"><strong>Recreation<\/strong><\/th>\n<th width=\"81\"><strong>Musical Instrument<\/strong><\/th>\n<th width=\"82\"><strong>Teaching Technique<\/strong><\/th>\n<th width=\"78\"><strong>Exercise<\/strong><\/th>\n<th width=\"76\"><strong>(Pass\/Fail)<\/strong><\/th>\n<\/tr>\n<tr>\n<td width=\"72\">Amy<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">None<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">None<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Ben<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">Running<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Carl<\/td>\n<td width=\"88\">Drawing<\/td>\n<td width=\"81\">Piano<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Swimming<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Diane<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">None<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Ethan<\/td>\n<td width=\"88\">Drawing<\/td>\n<td width=\"81\">Piano<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">None<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Vanda<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Walter<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Clarinet<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Thomas<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">Clarinet<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">None<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Ursula<\/td>\n<td width=\"88\">Drawing<\/td>\n<td width=\"81\">None<\/td>\n<td width=\"82\">Online Quizzes<\/td>\n<td width=\"78\">Swimming<\/td>\n<td width=\"76\">Fail<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Stacey<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">Written Homework<\/td>\n<td width=\"78\">Running<\/td>\n<td width=\"76\">Pass<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>and he notices that in each case, the only factor that correlates with passing or failing, is written homework or online quizzes, respectively.\u00a0 Despite his preconception that video games were dangerous he finds that two of the three students (Amy and Vanda) who play actually passed the course.<\/p>\n<p>The final two of Mill\u2019s Methods deal with matters of degree.\u00a0 They help to answer how much written homework really helps and if there is another factor that might contribute to success.\u00a0 To this end the teacher modifies the table to list the hours each student spends completing their written homework and their GPA.<\/p>\n<table>\n<tbody>\n<tr>\n<th width=\"72\"><strong>Student<\/strong><\/th>\n<th width=\"88\"><strong>Recreation<\/strong><\/th>\n<th width=\"81\"><strong>Musical Instrument<\/strong><\/th>\n<th width=\"82\"><strong>Homework Hours per Week<\/strong><\/th>\n<th width=\"78\"><strong>Exercise<\/strong><\/th>\n<th width=\"76\"><strong>GPA<\/strong><\/th>\n<\/tr>\n<tr>\n<td width=\"72\">Amy<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">None<\/td>\n<td width=\"82\">12<\/td>\n<td width=\"78\">None<\/td>\n<td width=\"76\">3.8<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Carl<\/td>\n<td width=\"88\">Drawing<\/td>\n<td width=\"81\">Piano<\/td>\n<td width=\"82\">7<\/td>\n<td width=\"78\">Swimming<\/td>\n<td width=\"76\">3.5<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Vanda<\/td>\n<td width=\"88\">Video games<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">5<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">3.2<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Walter<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Clarinet<\/td>\n<td width=\"82\">10<\/td>\n<td width=\"78\">Yoga<\/td>\n<td width=\"76\">4.0<\/td>\n<\/tr>\n<tr>\n<td width=\"72\">Stacey<\/td>\n<td width=\"88\">Blogging<\/td>\n<td width=\"81\">Guitar<\/td>\n<td width=\"82\">8<\/td>\n<td width=\"78\">Running<\/td>\n<td width=\"76\">3.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>In the case of the <strong><em>Method of Concomitant Variation<\/em><\/strong>, the teacher notices that in there is a strong correlation between the number of hours of homework each week and the student\u2019s GPA.\u00a0 Vanda does the least amount of homework each week and she has the lowest GPA.\u00a0 Carl and Stacey are in the middle in terms of time invested in homework and so is their GPA.\u00a0 And finally, Amy and Walter have the highest time spent on homework and the highest GPA.\u00a0 This behavior is a strong indication that requiring students to complete written homework causes students to have high GPAs.<\/p>\n<p>The <strong><em>Method of Residues<\/em><\/strong> helps to point towards additional factors that have not been considered but which contribute to the cause and effect relationship.\u00a0 In the case of the two top performing students, the teacher notices that although Amy spends the greatest amount of time on homework each week she doesn\u2019t have the highest GPA.\u00a0 Of course, this minor difference between her and Walter might be explained in many ways (e.g. her courses are harder).\u00a0 But let\u2019s suppose that the table exhaustively lists all the relevant attributes and that Walter and Amy are in the same class in elementary school so that they see all the same material and are assigned the same homework.\u00a0 Our teacher might be inclined to conclude that either playing a musical instrument or exercising might be the cause of the remaining difference.\u00a0 This method can also be applied to the situation were the differences are a matter of quality rather than quantity.<\/p>\n<p>One of the most famous examples of the application of the Method of Residues was to the motion of the planet Mercury.\u00a0 After all the known contributions of Mercury\u2019s orbit had been accounted by astronomers of the late 1800s there was still a remaining 53 arcseconds\/century of precession that could be ascribed to any particular cause.\u00a0 This difference, though small, helped to spur Einstein to create the theory of General Relativity.<\/p>\n<p>While the discussion above was both illustrating and interesting it is hardly the only nor primary application of Mill\u2019s Methods.\u00a0 As <a href=\"https:\/\/faculty.unlv.edu\/beisecker\/Courses\/Phi-102\/Mills_Methods.htm\">Prof. Dave Beisecker points out on his discussion<\/a>, Mill\u2019s Methods are used in all sorts of persuasive arguments about products, policies, and the like. \u00a0I would encourage the reader to visit his page as some of his examples are both educational and laugh-out-loud funny.\u00a0 Consider this gem used to illustrate how the Method of Difference is used in advertising<\/p>\n<div class = \"myQuoteDiv\">Jiffy Squid fries are the best, and you know what the secret is? While the recipe, the potatoes, and everything else is the same as at Burger Thing, the fries at Jiffy Squid are cooked in oil that has been through the crankcase of a &#8217;57 Desoto. The result &#8211; mmm-mmm fries! <\/p>\n<div class = \"myAttrib\">\u2013 Dave Beisecker<\/div>\n<\/div>\n<p>Of course real life is never so clear cut as the contrived examples seem to imply.\u00a0 But that\u2019s what makes it so fun.\u00a0 Putting one\u2019s skill to the test to find <i>what<\/i> causes <i>what<\/i> can lead to amazing discoveries and brings out the best in us.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Arguing about cause and effect is a difficult enterprise even in the best of circumstances.\u00a0 Rarely is it as clean, or as boring, as introductory texts on logic make it&#8230; <a class=\"read-more-button\" href=\"https:\/\/aristotle2digital.blogwyrm.com\/?p=533\">Read more &gt;<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-533","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=533"}],"version-history":[{"count":0,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/533\/revisions"}],"wp:attachment":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}