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by Justin Wolfers, "Upshot" blog, ''New York Times'', 2 April 2015
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 [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.
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 [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 study in question failed to find a significant correlation between parental time spent with children and outcomes later in life.  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.”  
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 some detailed responses to reader's objections, and gives a careful discussion of statistical issues.  In particular, 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 comes in correlating this with another measure.





Revision as of 14:49, 8 June 2015

Mean vs. median: The case of the ox

Mike Olinick sent a link to the following:

Voting on the ox
by Michel Balinski, The New York Review of Books, 7 May 2015

This is a letter in response to an earlier article, 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.”

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:

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.

In other words, the median is resistant to outliers!

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. 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 some detailed responses to reader's objections, and gives a careful discussion of statistical issues. In particular, 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 comes in correlating this with another measure.


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

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