{"id":104,"date":"2014-10-03T12:46:18","date_gmt":"2014-10-03T17:46:18","guid":{"rendered":"http:\/\/new.causeweb.org\/blog\/randomization\/?p=104"},"modified":"2015-02-21T10:46:33","modified_gmt":"2015-02-21T15:46:33","slug":"why-used-randomization-based-methods-for-inference","status":"publish","type":"post","link":"https:\/\/www.causeweb.org\/sbi\/?p=104","title":{"rendered":"Why I chose to teach with simulation-based methods"},"content":{"rendered":"

Josh Tabor, Canyon del Oro High School<\/strong><\/p>\n

\"Tabor\"<\/a><\/p>\n

Short answer<\/em>: I teach with simulation-based methods because I believe they make it easier for students to understand the logic of inference and see statistics as a complete investigative process from asking questions to drawing conclusions.<\/p>\n

[pullquote]<\/p>\n

I settled on two guiding principles that would inform the way I designed the course:<\/p>\n

    \n
  1. Emphasize that Statistics is an investigative process, not a set of isolated skills.<\/li>\n
  2. Stay focused on the logic of inference.<\/li>\n<\/ol>\n

    [\/pullquote]<\/p>\n

    <\/p>\n

    The long answer<\/em> begins in the spring of 2009, when our high school was looking to create new 4th<\/sup>-year math courses to satisfy revised graduation requirements in the state of Arizona.\u00a0 As a long-time teacher of AP Statistics, and an even longer-time fan of sports, I proposed a course called \u00a0“Statistical Reasoning in Sports.” \u00a0The course would be primarily about statistical reasoning, with the motivational hook of using sports contexts throughout.<\/p>\n

    Because there was no existing curriculum or standards that I needed to cover, I could teach the course in the best way I saw fit.\u00a0 I could use as much or as little technology as I wanted to.\u00a0 I could teach the course in the traditional order or mix it up.\u00a0 Having so many options is great\u2014but also a challenge.\u00a0 To know how to build the course, I had to identify the principles that I valued most.<\/p>\n

    I settled on two guiding principles that would inform the way I designed the course:<\/p>\n

      \n
    1. Emphasize that Statistics is an investigative process, not a set of isolated skills.<\/li>\n
    2. Stay focused on the logic of inference.<\/li>\n<\/ol>\n

      Using randomization-based methods allowed me to stay true to both of these guiding principles.<\/p>\n

      Historically in K-12 education, Statistics has been presented to students as an unconnected set of skills\u2014if Statistics has been taught at all.\u00a0 In one course, students might learn how to calculate means and medians.\u00a0 In another course, they might learn how to make a box-and-whisker plot and a stem-and-leaf plot.\u00a0 But these graphs are typically an end in themselves.\u00a0 Because they aren\u2019t used to help answer interesting statistical questions, students write them off as tedious and useless.<\/p>\n

      To counter this perception, every unit in my course starts with a question (e.g., Is there a home-field advantage in the NFL?) and we spend the rest of the chapter learning the skills necessary to answer this question.\u00a0 We learn how to collect the relevant data, how to analyze the data, and how to make inferential conclusions using the data.<\/p>\n

      Yes, we are making inferential conclusions starting in the first week of school!\u00a0 Randomization-based methods allow us to estimate p<\/em>-values and make inferential conclusions without having to know anything about Normal (or t<\/em>) distributions.\u00a0 Because the inferential piece fits so naturally as the last step in the statistical process, students never wonder \u201cwhy are we doing inference so early?\u201d\u00a0 In fact, they find it strange when I tell them that my AP students won\u2019t be learning about p<\/em>-values for five months!*<\/p>\n

      *Actually, I use randomization-based methods in my AP class as well, even though the AP curriculum is much more traditional; I have discussed my experiences with the simulation-based methods in AP Statistics classes here<\/a>. \u00a0During the first semester, we do several activities that conclude with what is essentially a randomization test.\u00a0 During the second semester, I try to introduce each major inference procedure (e.g., test for a difference in proportions, test for slope) with the equivalent randomization test.\u00a0 <\/em><\/p>\n

      The second guiding principle for my course was to stay focused on the logic of inference.\u00a0 I want students to leave knowing that all tests of significance are essentially the same: comparing the observed result with what might happen by chance alone.\u00a0 Using randomization tests helps students keep their eyes on the bigger picture by avoiding the specific technical details that accompany each of the different traditional tests.<\/p>\n

      This makes my course much more accessible to students\u2014once they learn how to do a test comparing two proportions, they can easily extend the same logic to a test comparing two means, or a test comparing two standard deviations.\u00a0 In a traditional course, these are three very different tests that use three different distributions.\u00a0 In a course that uses randomization-based methods, they are essentially the same test.<\/p>\n

      Randomization-based methods also make it easy to utilize hands-on activities that better facilitate student understanding.\u00a0 And the development of easy to use applets** makes it easy to automate the simulation process once students understand what is going on.<\/p>\n

      **Applets for the randomization tests we use in Statistical Reasoning in Sports can be found at <\/em>www.whfreeman.com\/SRIS<\/em><\/a>.\u00a0<\/em><\/p>\n

      The accessibility of randomization-based methods has made it much easier for me to expose a wide audience to the power of the statistical investigative process.<\/p>\n

      That\u2019s the long answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Josh Tabor, Canyon del Oro High School Short answer: I teach with simulation-based methods because I believe they make it easier for students to understand the logic of inference and see statistics as a complete investigative process from asking questions to drawing conclusions. [pullquote] I settled on two guiding principles that would inform the way […]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-104","post","type-post","status-publish","format-standard","hentry","category-why"],"_links":{"self":[{"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/posts\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=104"}],"version-history":[{"count":5,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/posts\/104\/revisions"}],"predecessor-version":[{"id":747,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=\/wp\/v2\/posts\/104\/revisions\/747"}],"wp:attachment":[{"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.causeweb.org\/sbi\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}