Sandbox
A fake study on chocolate
Paul Alper sent a link to the following:
- I fooled millions into thinking chocolate helps weight loss. Here's how.
- by John Bohannon, io9.com, 27 May 2015
Publishing under the pseudonym Johannes Bohannon, at his own respectably named website, the Institute of Diet and Health], Bohannon announced the results of a deliberately faulty study designed to show that eating chocolate promotes weight loss. These findings should have sounded too good to be true, but that didn't stop the news and social media outlets from uncritically reporting the findings. The i09.com story linked above includes screen captures from a number of these reports.
The whole story is worth reading for details of how the hoax was conceived and conducted. You can also listen to an NPR interview ("All Things Considered," 29 May 2015). The study used Facebook to recruit a mere 15 volunteers, and randomly assigned them to one of three groups: low carb diet, low carb diet plus a daily chocolate bar, and a control group. Subjects weighed themselves daily, reported on sleep quality and other measures, and a variety of measures taken from blood work, for a total of 18 variables. As Bohannon explains, as long as you don't specify up front what you are looking for, a study with so few subjects and so many variables is bound to turn up a statistically significant result. On ion.com, he calls the design "a recipe for false positives."
Of course, such results will not be reproducible, but the story went viral before anyone asked hard questions. NRP host Robert Siegel wondered if we can take some solace in the fact that reputable sources like the Associated Press or the New York Times did not pick up the story. Bohannon responds that the tabloid press, with its much larger readership, had already done the damage.
Some math doodles
<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>
Accidental insights
My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.
While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.
As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.
Piece | Sq. Inches | % of Total |
---|---|---|
1 | 43.25 | 31.9% |
2 | 35.25 | 26.0% |
3 | 23.25 | 17.2% |
4 | 14.10 | 10.4% |
5 | 7.10 | 5.2% |
6 | 4.70 | 3.5% |
7 | 3.60 | 2.7% |
8 | 3.03 | 2.2% |
9 | 0.66 | 0.5% |
10 | 0.61 | 0.5% |
The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”
My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Shattered eggs reveal secrets of explosions. As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.
Submitted by William Montante