Iowa Caucus Statistics in Albuquerque Journal

I am always looking for good examples of statistics or geometry to use in class with an eye for misrepresentations of the math that might lead people to make incorrect assumptions. Tuesday's paper (Feb. 2, 2016) offered coverage of the results of the Iowa caucus and also provided an excellent opportunity for us to explore how the results were displayed to the readers of the Journal. Indeed, election year media coverage seems to always provide good material for me to use in class.

This is not meant to be a partisan blog; both sides of the aisle are guilty of misrepresenting the truth.  News media, however, does tend to be particularly biased in their reporting.  HOWEVER, if the readership is savvy and informed, the presentation of "facts" backfires. People tend to get irritated when they think they are not being told the truth.

So the above image appeared on the Front Page (FRONT page, mind you) of our own Albuquerque Journal. Based on the image, you'd think that Rafael "Ted" Cruz had won the primary in Iowa by a landslide -- after all, look at the size of his circle compared to those of  DonaldTrump and Marco Rubio.  I'm glad they printed the percentage of votes right there so I don't have to look them up.  Let's do some math.

I pulled the image into Geometer's Sketchpad and measured the radii of the three circles representing the votes for each of these three republican candidates.

We can then find the approximate areas of the three circles.  Cruz: 87.9 square cm; Trump: 17.5 square cm; Rubio: 16.6 square cm.  Senator Cruz appears to be cruising, with his image covering an area just over 5 times that of Trump's image and nearly 5 and 1/3 times that of Rubio's image.

But reality?   Look at the percentages of the votes received.

First of all, notice that 28%, 24% and 23% do not add up to 100%.  We are missing 25%.  How did that 25% vote (likely for other candidates)?  We don't know from this front page image. Also notice that 28%, 24% and 23% are not that far apart. Furthermore, Cruz did not win a simple majority (that is, more than 50% of the vote.) Numerically, this does not particularly look like a landslide.

Of the 75% of the votes represented by these three circles, Cruz earned 37% of those votes.  Trump and Rubio earned 32% and 31%, respectively (notice my 37, 32, and 31 sum to 100% of the 75 percentage points). Cruz earned nowhere near 5 times the votes of Trump.   No landslide here, either.

So the newspaper was interested in having people believe, on some level (perhaps even unconsciously), that Cruz won by a wide margin.  Might that bias affect what the readers think or or what they might perceive their peers in Iowa think?  We can debate that until the cows come home.  But this visual image seems to misrepresent the success of Cruz: it was actually a pretty close election.

Your blog can take one of several routes.

1. Find something else that's mathematically misrepresented in the media.  Anything.  And explain why the data is misrepresented.  You'll need to show an image and complete an interpretation of what's incorrect and perhaps how the information should have been represented.

2.  Explain my geometry.  How did I construct the exact center of each circle?  (I did NOT just guess!)  Then how did I find the area of the circles?  Why did I use ratios of area and not ratios of radii?  How might the numbers have turned out it I had compared radii? Find those values and interpret.   Is the ratio of the radii the same as the ratio of the areas?