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This is the last post in the series of articles on real-life facts you need to know for GMAT Critical Reasoning.<\/p>\nThis is the last post in the series of articles on real-life facts you need to know for GMAT Critical Reasoning.<\/p>\n
Here's the full list:<\/p>\n
Most research in the natural and social sciences involves statistics.\u00a0 Researchers are looking at a large number of cases, and determining patterns of association.\u00a0 The question often arises: is a particular pattern the result of chance, or does it result from a meaningful connection to the reputed cause?<\/p>\n
Let's think about a concrete hypothetical example.\u00a0 Suppose there's some horrible disease: Mongolian Bagpipe Fever (MBF).\u00a0 For simplicity, suppose there are just two extreme outcomes: either people die of this disease, or they recover completely.\u00a0 Suppose I have a new medicine that I think will help people with MBF, and we test it against a\u00a0placebo<\/a>\u00a0(a standard design in medical tests.)\u00a0 Now, consider the following results.<\/p>\n Example #1 is an entirely unrealistic scenario --- a case of completely unambiguous certainty: everyone who gets the medicine survives, and everyone who doesn't get the medicine dies.\u00a0 In real research, nothing is ever this unambiguously clear: that's why this is unrealistic.<\/p>\n Example #2 is also unambiguously clear: folks survive the disease equally well, regardless of whether they are getting the medicine or the placebo.\u00a0 This clearly suggests: the medicine is no better than a sugar pill --- in other words, the new medicine has, in fact, no medicinal value.\u00a0 Again, real data is never this crystal clear, so this is also unrealistic.<\/p>\n Real cases, cases involving real data, are always somewhere between those two scenarios.\u00a0 Consider these two:<\/p>\n These are more representative of real data, insofar as there's ambiguity and uncertainty.\u00a0 In each case, the survival rate for folks not getting the medicine is 50%.\u00a0 In each case, the survival rate of folks receiving the medicine is at least somewhat higher the 50%.\u00a0 The question is: is this slightly high rate actually due to the efficacy of the medicine, or is it just a chance fluctuation in the data?<\/p>\n Statisticians evaluate these questions by calculating probabilities: how likely each scenario is to arise from chance fluctuations?\u00a0 For the GMAT, you do\u00a0not<\/em><\/strong>\u00a0need to know anything about the details of that probability calculation.\u00a0 As it happens, in the example #3 chart, results this pronounced or more would result about 39% of the time by chance --- they are relatively likely to occur by chance.\u00a0 By contrast, in the example #4 chart, results this pronounced or more would result about 1.6% of the time by chance --- they are comparatively unlikely to occur by chance.\u00a0 Another way to say this is: the results in example #4 are\u00a0statistically significant<\/strong>.<\/p>\n In the case of example #3, the explanation that the results arose by chance is quite cogent: since those results are likely to arise by chance, it's not surprising that in a chance scenario they would arise.\u00a0 In the case of example #4, the explanation that the results arose by chance is not particularly persuasive.\u00a0 Saying that these results are statistically significant means they are not likely to result from chance, which implies that their explanation as a product of chance is not compelling, which in turn requires us to look elsewhere, for something other than chance, to explain the difference.\u00a0 In this example #4, the fact that the results are not adequately explained by chance means that the only plausible explanation for these results is that medicine actually worked.\u00a0 The results in #4 constitute evidence that the medicine worked, whereas the results in #3 do not.\u00a0 In scientifically designed studies, to say results are statistically significant implies that we have found persuasive evidence for factor we were testing.<\/p>\n All scientific studies involving a large pool of data will involve chance fluctuations.\u00a0 Whenever you are trying to test or measure a certain effect, the first explanation you always have to rule out is that of chance itself --- that the results are no more than the product of chance.\u00a0 To say the results are statistically significant is to say (a) results are not likely to arise by chance; (b) therefore, explaining the results as a product of chance fluctuations is untenable; (c) therefore, we have compelling evidence for whatever factor we were testing.\u00a0 Any time the word \"significant\" or \"significantly\" is used in the context of a research study (\"significantly increased\", \"significantly reduced\", etc.), it directly implies this entire nexus of ideas.\u00a0 In fact, this set of logical relationships underlies the vast majority of studies in the natural and social sciences.<\/p>\n <\/p>\n Here's a practice question to try this out:\u00a0\u00a0https:\/\/gmat.magoosh.com\/ This post was written by Mike McGarry, GMAT expert at Magoosh<\/a>, and originally posted here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":" This is the last post in the series of articles on real-life facts you need to know for GMAT Critical Reasoning. Here’s the full list: Economics: Supply and Demand Economics:…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,721,735],"tags":[],"class_list":["post-15211","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-critical-reasoning-gmat","category-verbal-gmat-blog","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15211","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=15211"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15211\/revisions"}],"predecessor-version":[{"id":15214,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15211\/revisions\/15214"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=15211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=15211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=15211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/magoosh.com\/gmat\/files\/2012\/10\/frlftkfgcr_img1.png\" "\\"frlftkfgcr_img1\\"")
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