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==Lotto mania==
==A stopping problem==
[http://www.counterpunch.org/2015/02/12/lottomania-mega-millions-madness/ Lottomania: Mega Millions madness]<br>
[http://wordplay.blogs.nytimes.com/2015/02/09/tijms/?_r=0 Henk Tijms: Dropping balls Into bins]<br>
by John White, ''Counterpunch'', 12 February 2015.
By Gary Antonick, "Numberplay" blog, ''New York Times'', 9 February 2015


John is a longtime Chance News reader who references here a past correspondence with with Laurie Snell regarding lottery odds.
Here is the puzzle, as posed by Prof Tijms:
<blockquote>
A game machine is used to drop balls into four bins. The balls are dropped one at a time and any ball will land at random into one of the bins. You can turn off the machine whenever you wish. At the end of the game you win a dollar for every bin containing exactly one ball and you lose half a dollar for every bin containing two or more balls. What stopping rule will maximize your expected gain? In other words, when should you turn off the machine?
</blockquote>
He notes that B=4 bins is the first case that gets very complicated, and asks for a heuristic for the general case.


In the present essay, he laments the enthusiasm that governments have for lotteries as revenue generators. His historical references range from the 1530 ''La Lotto de Firenze''
Later he cites a careful reader's correction of his initial solution in the B=2 case: the optimal strategy is to continue until each bin has at least one ball, for an expected winning of 1.25With B=3,  
to the Irish Sweepstakes.  Indeed, he reports that even Continental Congress flirted with the idea of a lottery to fund the Revolutionary War. He criticizes modern-day advertising campaigns that entice citizens to play, with tales of imagined winnings and promises that the funds go to support various public worksInstead, he concludes, lottery tickets might include printed warnings like those required for cigarettes: “Playing lotteries decreases your chances of saving” or “Player not likely to win in 10,000 lifetimes.”


==Cancer and luck==
Thanks to Henk Tijms for sending this link, along another balls and urns story, this one about drawings for the the schedule of European soccer tournaments. He adds that many fans are suspicious of the governing organization FIFA (Fédération Internationale de Football Association).
[http://www.nytimes.com/2015/01/06/health/cancers-random-assault.html?action=click&contentCollection=U.S.&module=MostEmailed&version=Full&region=Marginalia&src=me&pgtype=article Cancer’s random assault]<br>
By Denise Grady, ''New York Times'', 5 January 2015


The article concerns a recent research paper,  [http://www.sciencemag.org/content/347/6217/78 Variation in cancer risk among tissues can be explained by the number of stem cell divisions] (''Science'' 2 January 2015).  From the abstract
:[http://wmbriggs.com/post/8782/ Was the UEFA Champions League draw rigged?—Bayesian analysis by Henk Tijms]<br>
<blockquote>
:William M. Briggs statistics blog, 5 April 2013
Here, we show that the lifetime risk of cancers of many different types is strongly correlated (0.81) with the total number of divisions of the normal self-renewing cells maintaining that tissue’s homeostasis. These results suggest that only a third of the variation in cancer risk among tissues is attributable to environmental factors or inherited predispositions.
</blockquote>


News coverage has created controversy by summarizing the findings in more colloquial terms, similar to this from the NYT article:
For an accessible general introduction to the theory of optimal stopping see:
<blockquote>
:[http://www.americanscientist.org/issues/pub/knowing-when-to-stop Knowing when to stop]<br>
Random mutations may account for two-thirds of the risk of getting many types of cancer, leaving the usual suspects — heredity and environmental factors — to account for only one-third, say the authors, Cristian Tomasetti and Dr. Bert Vogelstein, of Johns Hopkins University School of Medicine.
:by Theodore Hill, ''American Scientist'', March-April 2009
</blockquote>


Of course, saying that two-thirds of the variation among cancer types is "explained" by the rate of cell division is not the same thing as saying that two-thirds of risk of a particular cancer is can be accounted for by chance, or that two-thirds of all cancer cases are attributable to bad luck. But versions of these latter interpretations have in appeared in various responses to the article. For example, one [http://www.nytimes.com/2015/01/13/science/your-letters-cancers-luck-earth-like-planets-and-protecting-pedestrians.html letter to the NYT] commented, "If their conclusion is correct, that two-thirds of many cancer types are caused by random mutations, then we have a long road ahead."  Or consider this headline from ''Forbes'': [http://www.forbes.com/sites/geoffreykabat/2015/01/04/most-cancers-may-simply-be-due-to-bad-luck/ Most cancers may simply be due to bad luck].
Hill's discussion includes variations on the classical Secretary (a.k.a. Marriage or Dowry) Problem, the Chow-Robbins game, and more.


The resulting confusion is addressed in
Submitted by Bill Peterson
:[http://news.sciencemag.org/biology/2015/01/bad-luck-and-cancer-science-reporter-s-reflections-controversial-story Bad luck and cancer: A science reporter’s reflections on a controversial story]<br>
:by Jennifer Couzin-Frankel, ''Science Insider'', 13 January 2015
This article presents the following data graphic of the relationship
<center>
[[File:Sn-cancer.png | 500px]]
</center>
We now see where the two-thirds comes from:  if the correlation coefficient <math>r = 0.81</math>, as noted in the abstract above,  then <math>R^2=0.66</math>.


In response to the controversy, Drs. Tomasetti and Vogelstein (the study's authors), offered some clarifying remarks in an addendum to the original [http://www.hopkinsmedicine.org/news/media/releases/bad_luck_of_random_mutations_plays_predominant_role_in_cancer_study_shows Johns Hopkins news release].  In particular, they construct the following extended analogy with driving a car:  the road conditions correspond to environmental factors;  the condition of your car corresponds to hereditary factors;  the length of the trip corresponds to the number of cell divisions;  and the risk of having an a accident corresponds to the risk of getting cancer.  It makes sense that for any combination of car and road conditions, your risk of an accident increases with the length of the trip.  Nevertheless, this does not suggest that you should routinely neglect to service your vehicle or or to intelligently plan your routes.
==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>


'''Discussion'''


1. The original headline of the news release for the study was "Bad Luck of Random Mutations Plays Predominant Role in Cancer, Study Shows." Do you think this could have contributed to the misinterpretationsCan you suggest another wording?
==KinTape==
[http://well.blogs.nytimes.com/2015/03/27/ask-well-does-kinesiology-tape-really-work/?hp&action=click&pgtype=Homepage&module=second-column-region&region=top-news&WT.nav=top-news Ask Well: Does kinesiology tape really work?]<br>
by Gretchen Reynolds, "Well" blog, ''New York Times'', 27 March 2015


2. Consider the same questions for the ''NYT'' headline, "Cancer's random assault."
The technical paper referred to is
:[http://www.manualtherapyjournal.com/article/S1356-689X%2814%2900141-6/fulltext Kinesiology tape does not facilitate muscle performance: A deceptive controlled trial]<br>
:by K.Y. Poon, et.al., ''Manual Therapy'', February 2015 (Vol 20, Issue 1, pp. 130–133)


Submitted by Bill Peterson
The sample size started at 46, eventually 30 completed the study;  each was blindfolded so that the subjects could not see what kind of taping was done: "Thirty healthy participants performed isokinetic testing of three taping conditions: true facilitative KinTape, sham KinTape, and no KinTape."  Here are the ANOVA results for Normalized Peak Torque (NPT), Normalized Total Work (NTW), and Time to Peak Torque (TPT):


===Followup===
<blockquote>
<center> [[File:LeadingCancer2015.png|650px]]</center>
All the participants were confirmed to be ignorant about KinTape at the debriefing after the experiment. None of them used KinTape prior to the study and they had never heard of the application of KinTape in any circumstances. NPT, NTW, and TPT in different conditions were shown in Table 1. There was no significant difference in NPT between all three taping conditions at 60° (F(2,87) = 0.05, p = 0.96) and 180°/s (F(2,87) = 0.41, p = 0.66). Similar results were found in NTW (F(2,87) = 0.27, p = 0.76; F(2,87) = 0.53, p = 0.59) and TPT (F(2,87) = 0.03, p = 0.98; F(2,87) = 0.32, p = 0.73) at slow and fast contraction speed respectively.
 
</blockquote>
==Some math doodles==
With such enormously high p-values (correspondingly low F-values) the conclusion is
<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>
<blockquote>
The present study demonstrated that the KinTape application did not generate higher peak torque, yield greater total work, or shorten time to peak torque in healthy young adults. Positive results in the previous studies of KinTape may be attributed to the placebo effects.
</blockquote>


Submitted by Paul Alper


==Accidental insights==
==Accidental insights==
Line 94: Line 92:


Submitted by William Montante
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

Revision as of 21:23, 5 April 2015

A stopping problem

Henk Tijms: Dropping balls Into bins
By Gary Antonick, "Numberplay" blog, New York Times, 9 February 2015

Here is the puzzle, as posed by Prof Tijms:

A game machine is used to drop balls into four bins. The balls are dropped one at a time and any ball will land at random into one of the bins. You can turn off the machine whenever you wish. At the end of the game you win a dollar for every bin containing exactly one ball and you lose half a dollar for every bin containing two or more balls. What stopping rule will maximize your expected gain? In other words, when should you turn off the machine?

He notes that B=4 bins is the first case that gets very complicated, and asks for a heuristic for the general case.

Later he cites a careful reader's correction of his initial solution in the B=2 case: the optimal strategy is to continue until each bin has at least one ball, for an expected winning of 1.25. With B=3,

Thanks to Henk Tijms for sending this link, along another balls and urns story, this one about drawings for the the schedule of European soccer tournaments. He adds that many fans are suspicious of the governing organization FIFA (Fédération Internationale de Football Association).

Was the UEFA Champions League draw rigged?—Bayesian analysis by Henk Tijms
William M. Briggs statistics blog, 5 April 2013

For an accessible general introduction to the theory of optimal stopping see:

Knowing when to stop
by Theodore Hill, American Scientist, March-April 2009

Hill's discussion includes variations on the classical Secretary (a.k.a. Marriage or Dowry) Problem, the Chow-Robbins game, and more.

Submitted by Bill Peterson

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>


KinTape

Ask Well: Does kinesiology tape really work?
by Gretchen Reynolds, "Well" blog, New York Times, 27 March 2015

The technical paper referred to is

Kinesiology tape does not facilitate muscle performance: A deceptive controlled trial
by K.Y. Poon, et.al., Manual Therapy, February 2015 (Vol 20, Issue 1, pp. 130–133)

The sample size started at 46, eventually 30 completed the study; each was blindfolded so that the subjects could not see what kind of taping was done: "Thirty healthy participants performed isokinetic testing of three taping conditions: true facilitative KinTape, sham KinTape, and no KinTape." Here are the ANOVA results for Normalized Peak Torque (NPT), Normalized Total Work (NTW), and Time to Peak Torque (TPT):

All the participants were confirmed to be ignorant about KinTape at the debriefing after the experiment. None of them used KinTape prior to the study and they had never heard of the application of KinTape in any circumstances. NPT, NTW, and TPT in different conditions were shown in Table 1. There was no significant difference in NPT between all three taping conditions at 60° (F(2,87) = 0.05, p = 0.96) and 180°/s (F(2,87) = 0.41, p = 0.66). Similar results were found in NTW (F(2,87) = 0.27, p = 0.76; F(2,87) = 0.53, p = 0.59) and TPT (F(2,87) = 0.03, p = 0.98; F(2,87) = 0.32, p = 0.73) at slow and fast contraction speed respectively.

With such enormously high p-values (correspondingly low F-values) the conclusion is

The present study demonstrated that the KinTape application did not generate higher peak torque, yield greater total work, or shorten time to peak torque in healthy young adults. Positive results in the previous studies of KinTape may be attributed to the placebo effects.

Submitted by Paul Alper

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