Applications — Starting on Correlation

In our Applications course, we develop some basic statistical reasoning.  I always start key topics (like what is statistics … what is correlation) by having students work in groups on discussion questions.  I recently changed the ‘correlation’ activity, and thought other people might be interested in seeing it.

My goal with statistics in this course is to develop statistical thinking (and caution!), in ways similar to the standards in GAISE (see http://www.amstat.org/education/gaise/GaiseCollege_Full.pdf)   We use real data whenever possible, and focus on reasoning first … computation later.

In the case of correlation, I originally used a variation of the “Cereal Plots” activity like that used in Statway™.  In the cereal plots, students are presented with various nutrition values plotted against the ranking of cereals by Consumer Reports.  Conceptually, this is really nice.  However, in practice, students have too much overhead — they don’t know about rankings in general, and certainly not cereal rankings by Consumer Reports.  We ended up spending about half of the class discussion time on secondary issues.

This semester, I created my own sample of graphs.  These scatterplots deal with contexts familiar to almost all students, such as cars (price, mileage, etc).  Here is my activity for this semester

So, this was the initial part of class yesterday.  Students were in groups of 3 to 5, and answered the 10 questions on the sheet.  The context for these graphs was much better — somebody in every group knew enough about cars to provide some additional wisdom, and everybody knew enough about cars to get started.  [The last graph, on grip strength versus arm strength, is accessible to all students.]

Overall, this new activity works much better.  All of the discussion was about the graphs and statistics.

This does not mean that students magically understood what correlation is … or how to judge it from a scatter plot.  We are still working on unlearning ideas about cause & effect.  However, we did make progress on judging a linear pattern in these graphs; when I say “negative correlation”, most students can connect this to a pattern like we visualize from the phrase.

In case you are curious, the application course is pretty limited in the statistical topics included.  We include some reasoning topics (samples, population, bias, correlation, and describing distributions); we also include some displays (frequency tables, bar graphs, etc) and a few calculations (mean – median – mode, standard deviation, rule of thumb for margin of error).  We do not calculate correlation coefficients, nor do we do regressions; we do not calculate actual margin of errors, though we do calculate 95% confidence intervals (using the 1/sqrt(n) rule of thumb).  Out of 16 weeks, we spend 3 weeks on statistics; 2 weeks are spent on basic probability.

By the way, all of the graphs on the correlation activity were taken from online searches.  I was honest with the class — we do not know how valid any of them are, though I believe that they are valid.

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