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==Demystifying conditional probability?==
Lucky Charms and Disappointing Journalism
[http://opinionator.blogs.nytimes.com/2010/04/25/chances-are/ Chances are]<br>
by Steven Strogatz, ''New York Times'', Opinionator blog, 25 April 2010


Steven Strogatz, an applied mathematics professor at Cornell University, has been writing engaging weekly installments about mathematics for the Opinionator.  His post this week is about probability;  more specifically, it focuses on conditional probability.  Of course, this topic is a notorious source of confusion. (Indeed, this edition of Chance News includes [http://www.causeweb.org/wiki/chance/index.php/Chance_News_63#Bird_brains_vs._birdbrains another appearance of the Monty Hall problem], which refuses to stay solved!)  
The headline of the WSJ article [http://online.wsj.com/article/SB10001424052748703648304575212361800043460.html The Power of Lucky Charms New Research Suggests How They Really Make Us Perform Better] is eye catching. The descriptions of the success or failure of the lucky charms is, however, an indictment of the way the journalism profession discusses statistics.  Especially because the author, Carl Bialik, unlike most journalists, knows better.  In fact, while his first paragraph tries to draw the reader in with “Can luck really influence the outcome of events,” his second paragraph begins with “They [lucky charms] do (sometimes)” as a means of absolving himself from taking the material seriously.


The article presents several famous examples, including the false positive problem in diagnostic medical screening, and the conflicting arguments over spousal abuse and murder at the the O.J. Simpson trial.  Strogatz expresses enthusiasm for the approach of Gerd Gigerenzer, a psychologist who has argued that describing such problems in terms of &quot;natural frequencies&quot; rather than conditional probabilities helps people reason more clearly (see, for example, Gigerenzer's article [http://www.bmj.com/cgi/content/full/327/7417/741 Simple tools for understanding risks: from innumeracy to insight], British Medical Journal  2003; 327:741-744).  Essentially, this approach amounts to thinking about the problem in terms of a hypothetical cohort large enough to clear the denominators from the fractions, so one is talking about whole numbers of cases and the ratios become easier to visualize.   
In silly instance after silly unreplicated instance, the article tells us that averages improve or don’t improve with lucky charms present, but never once do we know anything about the variability between the charm holders and those deprived of the lucky charms.   


For another recent discussion see the section on Probabilities vs. Frequencies in John Allen Paulos's ''Who's Counting'' column from January, [http://abcnews.go.com/Technology/WhosCounting/medical-statistics/story?id=9460557&page=3 Medical statistics don't always mean what they seem to mean].
'''Discussion Questions'''
 
Submitted by Bill Peterson, based on a suggestion from Dan Bent (an intro statistics student)
1.  The first example referred to will be published in the June issue of Psychological Science; the study involves 28 German college students whose putting with a “lucky ball” sank “6.4 putts out of 10, nearly two more putts, on average, than those who weren’t told the ball was lucky.”  Evaluate the comment, “but the effect was big enough to be statistically significant.”  What additional statistical information would be necessary to view this study as worthwhile?
 
2. A well known quotation in the field of statistics is “The plural of anecdote is not evidence.”  Read the article and evaluate the anecdotes.
 
3.  Superstition plays a vital part of this article: a motorcyclist who wears “gremlin balls” to “help ward off accidents”; a lucky brown suit “to help the horse he co-owns, Always a Party, win the second race”; after an eclipse, “major  U.S. stock-market indexes typically fall.”  Compare those superstitions with the reading of tea leaves and goat entrails of the middle ages.
 
Submitted by Paul Alper


==Tea party graphics==
==Tea party graphics==

Revision as of 00:47, 30 April 2010

Lucky Charms and Disappointing Journalism

The headline of the WSJ article The Power of Lucky Charms New Research Suggests How They Really Make Us Perform Better is eye catching. The descriptions of the success or failure of the lucky charms is, however, an indictment of the way the journalism profession discusses statistics. Especially because the author, Carl Bialik, unlike most journalists, knows better. In fact, while his first paragraph tries to draw the reader in with “Can luck really influence the outcome of events,” his second paragraph begins with “They [lucky charms] do (sometimes)” as a means of absolving himself from taking the material seriously.

In silly instance after silly unreplicated instance, the article tells us that averages improve or don’t improve with lucky charms present, but never once do we know anything about the variability between the charm holders and those deprived of the lucky charms.

Discussion Questions

1. The first example referred to will be published in the June issue of Psychological Science; the study involves 28 German college students whose putting with a “lucky ball” sank “6.4 putts out of 10, nearly two more putts, on average, than those who weren’t told the ball was lucky.” Evaluate the comment, “but the effect was big enough to be statistically significant.” What additional statistical information would be necessary to view this study as worthwhile?

2. A well known quotation in the field of statistics is “The plural of anecdote is not evidence.” Read the article and evaluate the anecdotes.

3. Superstition plays a vital part of this article: a motorcyclist who wears “gremlin balls” to “help ward off accidents”; a lucky brown suit “to help the horse he co-owns, Always a Party, win the second race”; after an eclipse, “major U.S. stock-market indexes typically fall.” Compare those superstitions with the reading of tea leaves and goat entrails of the middle ages.

Submitted by Paul Alper

Tea party graphics

A mighty pale tea
by Charles M. Blow, New York Times, 16 April 2010

This article recounts Blow's experience visiting a Tea Party rally as a self-identified "infiltrator." He was interested in assessing the group's diversity. Reproduced below is a portion of a graphic, entitled The many shades of whites, that accompanied the article.

Shades.png

The data are from a recent NYT/CBS Poll.

Submitted by Paul Alper