Truly a Best Fit?

By Stephan Bisaha

Emma Pierson’s recent article on FiveThirtyEight.com calls into question the narrative that only college students abuse Adderall.

One way she did this was by challenging a 2006-2007 government report that suggested that college students were twice as likely to use Adderall as their peers who did not attend college.  The data she used was based on a random sample of 55,000 Americans in the National Survey on Drug Use and Health.  The issue with the random sample however, is that certain groups are unlikely to have an equal response rate.  To compensate for this, Pierson weighed the responses.  While weighing responses is not a panacea, as it is difficult to know exactly how to distribute the weights, it does help with the problems of not having a completely random sample.

Pierson also charted a survey conducted by niche.com asking students how popular “study drugs” are on campus against the 75th percentile ACT scores for incoming students of those schools.  After plotting the chart, Pierson imposed a linear “best fit” line and said that the positive correlation was “statistically significant.”  It is hard to say what exactly she means by this (she put some data on Github, but the niche.com data is confidential).  An issue with the line, however, is that it seems to violate the “plot thickens” condition.  A large proportion of the schools that had a score of 34 for the 75th percentile of the ACT fell below the line and all 3 schools with a score of 35 were below the line.  This suggests a nonlinear shift in the trend that contradicts the best fit line.

Emma Pierson’s chart on FiveThirtyEight.com

Still, the rest of the graph suggests a linear model best fit line is appropriate, with no other trends in the residuals or random variance amongst the residuals.  While the best fit line may not fully live up to its name, it does illustrate a trend and makes the chart more approachable to the average reader while conveying important information they may struggle to grasp otherwise.

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