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:by John Bohannon, io9.com, 27 May 2015 | :by John Bohannon, io9.com, 27 May 2015 | ||
Publishing under the pseudonym Johannes Bohannon, at his own | Publishing under the pseudonym Johannes Bohannon, at his own respectably named [http://instituteofdiet.com Institute of Diet and Health], the Bohannon announced the results of a deliberately faulty study designed to show that eating chocolate promotes weight loss. | ||
==Some math doodles== | ==Some math doodles== |
Revision as of 21:18, 8 June 2015
Mean vs. median: The case of the ox
Paul Alper sent a link to the following:
- I fooled millions into thinking chocolate helps weight soss. Here's how.
- by John Bohannon, io9.com, 27 May 2015
Publishing under the pseudonym Johannes Bohannon, at his own respectably named Institute of Diet and Health, the Bohannon announced the results of a deliberately faulty study designed to show that eating chocolate promotes weight loss.
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>
Parenting time
Yes, your time as a parent does make a difference
by Justin Wolfers, "Upshot" blog, New York Times, 1 April 2015
Why a claim about the irrelevance of parenting time doesn’t add up
by Justin Wolfers, "Upshot" blog, New York Times, 2 April 2015
In this pair of articles, Wolfers seeks to debunk a study on parenting time that was widely reported in the media (he cites articles from The Washington Post, The Guardian, and NBC News, among others). The study in question failed to find a significant correlation between parental time spent with children and outcomes later in life, such as scores on standardized tests. The common theme of all the media reports was that "quality beats quantity" in parenting time.
Wolfers's first article pointed out that the study in question was based on a survey that asked parents about two specific days, one during the the week and one on the weekend. He compares this with trying to predict your income by looking a particular day: the result would vary wildly based on whether the day in question happened to be a payday. Similary he quotes developmental psychologists saying, “What you did yesterday should not be taken as representative of what you did last year.”
The second article provides responds to some readers's objections, and gives a particularly careful discussion of statistical issues related to "errors in variables." Wolfers acknowledges that randomness in the sample could reasonably be expected to guarantee that the average parenting time balances out correctly in the measure, in that some parents will respond about more time-intensive days, and others about lesser days. The real problem, he explains, comes in correlating this with another measure. To illustrate, he constructs a set of three scatterplots, the first showing a positive correlation between the time you spent with your children today and the time you typically spend, the second showing a positive correlation between test scores and the time you typically spend, but the third showing near-zero correlation between test scores and the time you spend with your children today.
Submitted by Bill Peterson
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.
![BrokenTile.jpg](/wiki/chance/images/thumb/5/5f/BrokenTile.jpg/400px-BrokenTile.jpg)
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% |
![Montante plot1.png](/wiki/chance/images/thumb/f/fe/Montante_plot1.png/500px-Montante_plot1.png)
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.”
![Montante plot2.png](/wiki/chance/images/thumb/b/b7/Montante_plot2.png/500px-Montante_plot2.png)
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