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==Mean vs. median: The case of the ox==
==A fake study on chocolate==
Mike Olinick sent a link to the following:
Paul Alper sent a link to the following:


:[http://www.nytimes.com/2015/05/12/upshot/more-consensus-on-coffees-benefits-than-you-might-think.html?abt=0002&abg=1 Voting on the ox]<br>
:[http://io9.com/i-fooled-millions-into-thinking-chocolate-helps-weight-1707251800 I fooled millions into thinking chocolate helps weight loss. Here's how.]<br>
:by Michel Balinski, ''The New York Review of Books'', 7 May 2015
:by John Bohannon, io9.com, 27 May 2015


This is a letter in response to an earlier article, [http://www.nybooks.com/articles/archives/2015/mar/05/cass-sunstein-right-choice-good-bargain/ Is the right choice a good bargain?] (5 March 2015), which argued that “statistical groups do especially well in answering factual questions. That article cited a 1907 publication by none other than Francis Galton, and gave the following quotation "The ox weighed 1,198 pounds; the average estimate…was 1,197 pounds, more accurate than any individual’s guess.
Publishing under the pseudonym Johannes Bohannon, at his own respectably named website, the Institute of Diet and Health], Bohannon [http://instituteofdiet.com/2015/03/29/international-press-release-slim-by-chocolate/ announced the results] of a deliberately faulty study designed to show that eating chocolate promotes weight lossThese 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.


Balinski notes that the alleged quotation does not appear in Galton's writing! In fact, he produces an earlier article by Galton, which includes the following:
The whole story is worth reading for details of how the hoax was conceived and conducted.  You can also listen to [http://www.npr.org/sections/thesalt/2015/05/29/410609184/trickster-journalist-explains-why-he-duped-the-media-on-chocolate-study 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 had 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."


<blockquote>How can the right conclusion be reached…? That conclusion is clearly not the average of all the estimates, which would give a voting power to “cranks” in proportion to their crankiness…. I wish to point out that the estimate to which least objection can be raised is the middlemost estimate, the number of votes that it is too high being exactly balanced by the number of votes that it is too low.</blockquote>
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.


In other words, the median is resistant to outliers!
For additional perspective on all of this, see [http://www.npr.org/sections/13.7/2015/06/08/412825282/what-junk-food-can-teach-us-about-junk-science What junk food can teach us about junk science] (NPR, 8 June 2015).


==Some math doodles==
==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>
<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==
[http://www.nytimes.com/2015/04/02/upshot/yes-your-time-as-a-parent-does-make-a-difference.html?abt=0002&abg=1 Yes, your time as a parent does make a difference]<br>
by Justin Wolfers, "Upshot" blog, ''New York Times'', 1 April 2015
[http://www.nytimes.com/2015/04/03/upshot/why-a-claim-about-the-irrelevance-of-parenting-time-doesnt-add-up.html?rref=upshot&module=Ribbon&version=context&region=Header&action=click&contentCollection=The%20Upshot&pgtype=article&abt=0002&abg=1 Why a claim about the irrelevance of parenting time doesn’t add up]<br>
by Justin Wolfers, "Upshot" blog, ''New York Times'', 2 April 2015
In this pair of articles, Wolfers seeks to debunk a story on parenting time that was widely reported in the media (he cites articles from [http://www.washingtonpost.com/local/making-time-for-kids-study-says-quality-trumps-quantity/2015/03/28/10813192-d378-11e4-8fce-3941fc548f1c_story.html The Washington Post], [http://www.theguardian.com/commentisfree/2015/apr/01/dont-stress-out-our-kids-are-just-fine-when-their-mothers-work-late The Guardian], and [http://www.today.com/parents/quality-over-quantity-new-study-brings-time-squeezed-parents-relief-t11746 NBC News], among others).  The central theme of all these reports is that "quality beats quantity" when it comes to time that parents spend with their children.
Submitted by Bill Peterson


==Accidental insights==
==Accidental insights==

Revision as of 14:34, 9 June 2015

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 had 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.

For additional perspective on all of this, see What junk food can teach us about junk science (NPR, 8 June 2015).

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.

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

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

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


The p-value ban

http://www.statslife.org.uk/opinion/2114-journal-s-ban-on-null-hypothesis-significance-testing-reactions-from-the-statistical-arena