Visual Inference: Using Sesame Street Logic to Introduce Key Statistical Ideas

As outlined by Cobb (2007), most introductory statistics books teach classical hypothesis tests as

  1. formulating null and alternative hypotheses, 
  2. calculating a test statistic from the observed data, 
  3. comparing the test statistic to a reference (null) distribution, and 
  4. deriving a p-value on which a conclusion is based.

This is still true for the first course, even after the 2016 GAISE guidelines were adapted to include normal- and simulation-based methods. Further, most textbooks attempt to carefully talk through the logic of hypothesis testing, perhaps showing a static example of hypothetical samples that go into the reference distribution. Applets, such as StatKey and the Rossman Chance ISI applets, take this a step further, allowing students to gradually create these simulated reference distributions in an effort to build student intuition and understanding. While these are fantastic tools, I have found that many students still struggle to understand what the purpose of a reference distribution is and the overarching logic of testing. To remedy this, I have been using visual inference to introduce statistical testing, where “plots take on the role of test statistics, and human cognition the role of statistical tests” (Buja et al., 2009). In this process, I continually encourage students to apply Sesame Street logic: which one of these is not like the other? By using this alternative approach that focuses on visual displays over numerical summaries, I have been pleased with the improvement in student understanding, so I thought I would share the idea with the community.

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