Difference between revisions of "Sandbox"

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==Smile Intensity and Divorce==
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Elections
  
Is there a connection between positive expressive behavior, as seen by facial photographs, and success in avoiding divorce?  According to http://www.livescience.com/culture/090414-smile-marriage.html Moskowitz], “If you want to know whether your marriage will survive, look at your spouse's yearbook photos.  Psychologists have found that how much people smile in old photographs can predict their later success in marriage.”  This claim is based on a study headed by Matthew Hertenstein detailed in the April 5 issue of the journal Motivation and Emotion and is entitled “Smile intensity in photographs predicts divorce later in life.
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[http://www.fivethirtyeight.com/2009/04/national-elections-getting-closer.html Andrew Gelman] has an interesting article regarding the statistics of elections. He starts with
  
The table below is taken from Hertenstein’s publication. Study 1, Sample 1 involves alumni who were psychology majors at a particular university; Study 1, Sample 2 involves alumni from the same university who were not psychology majors. In each instance, the participants submitted yearbook photos which were judged for smile intensity and whether or not the participants were divorced or still married. Study 2 is similar but involved older members of the community who submitted photos from decades past.
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“Presidential elections have been closer in the past few decades than they were for most of American history. Here's a list of all the U.S. presidential elections that were decided by less than 1% of the vote:
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http://www.dartmouth.edu/~chance/forwiki/smilingtable.gif
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1880
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1884
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1888
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1960
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1968
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2000
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Funny, huh? Other close ones were 1844 (decided by 1.5% of the vote), 1876 (3%), 1916 (3%), 1976 (2%), 2004 (2.5%).
  
Discussion
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Four straight close elections in the 1870s-80s, five close elections since 1960, and almost none at any other time.”
  
1. In the above table, a two sample t-test of means (“M”) is carried out for each row.  Pick a row and verify degrees of freedom (“df”), the value of t and the p-value (“p”).  Note that “p values are one-tailed given the directional hypothesis of the studies.”
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Perhaps more interesting is his take on House and Senate elections:
  
2. While p-value is useful to some extent, “effect size” may be of more interest.  The last column, “r” signifies that some sort of correlation is taking place; it is sometimes called the point-biserial correlation coefficient.  This correlation is between the independent dichotomous variable and the dependent variable (smile intensity).  According to the psychology literature, it is given by
 
  
http://www.dartmouth.edu/~chance/forwiki/smilemath.gif
 
 
   
 
   
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[http://www.nytimes.com/2009/04/19/opinion/19silver.html?_r=1&ref=opinion In the companion piece] written with Nate Silver, the graphic concerning the House is made more evident
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[http://www.nytimes.com/imagepages/2009/04/19/opinion/19chart_ready.html here].
  
  
Use this formula and Pick a row to verify the value in the table for “r”—ignore the sign.
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3.  Clearly, these results are for a sample. Speculate on what you would need to know of the characteristics of the participants in order to infer to a larger population.
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From the graph, “the rate of close elections in the House has declined steadily over the century. If you count closeness in terms of absolute votes rather than percentages, then close elections become even rarer, due to the increasing population. In the first few decades of the twentieth century, there were typically over thirty House seats each election year that were decided by less than 1000 votes; in recent decades it's only been about five in each election year.
  
4.  Although the table is informative as to means and standard deviations, why would boxplots for each row be useful?
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Another way of putting it: “Consider that, in the past decade, there were 2,175 elections to the United States House of Representatives held on Election Days 2000, 2002, 2004, 2006 and 2008. Among these, there were 41 instances — about 1.9 percent — in which the Democratic and Republican candidates each received 49 percent to 51 percent of the vote (our calculations exclude votes cast for minor parties). In the 1990s, by contrast, there were 65 such close elections. And their number increases the further one goes back in time: 88 examples in the 1950s, 108 in the 1930s, 129 in the 1910s.”
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Discussion
  
5According to Moskowitz, but not mentioned in the paper itself by Hertenstein, “Overall, the results indicate that people who frown in photos are five times more likely to get a divorce than people who smile.”  This comes about by looking at the highest scorers--who turn out to be mostly still married--compared to the lowest scorers who turn out usually to be those who are divorced. Why is this quotation featured rather than the above table?
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1A contention mentioned in the NYT article for this bifurcation of opinion is: “as the economy has become more virtual, individuals can now choose where to live on an ideological rather than an occupational basis: a liberal computer programmer in Texas can settle in blue Austin, and a conservative one in the ruby-red suburbs of Houston.“ Argue for and against this assertion coupling ideology and occupational mobility.
  
6For those who would like to improve their “smile intensity” of their photos, here is what the paper itself says the measurement process is:
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2Gelman and Silver end their NYT article with “Elections like those in New York’s 20th district or in Minnesota, as contentious as they are, actually hark back to a less divisive era in American politics.”  Explain the seeming paradox of a close race indicating less divisiveness.
  
“two muscle action units, AU6 and AU12, were analyzed for each photoThe combination of these actions units are used to reflect positive facial expression because AU6 (orbicularis oculi) causes one’s cheeks to raise as well as bagging around the eyes while AU12 (zygomatic major) causes the corners of the mouth to move upward forming a smile. The intensity of each action unit was scored utilizing a 5-point intensity scale (ranging from a 1-minimal to 5-extreme).  A smile intensity score was created by adding together the scores of Action Unit 12 and Action Unit 6 (2 meaning no smile and 10 being the highest smile intensity score available…Once all photos for an individual subject were scored, all of the that participant’s smile intensity scores were averaged to provide a total smile intensity score.
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3. As of this posting, the Minnesota senate seat is unfilled despite a manual recount, a canvassing board followed by a so-called election contest and awaits an appeal to the Minnesota Supreme Court—possibly furtherSee [http://www.fivethirtyeight.com/2009/04/when-does-close-become-too-close-to.html When Does ‘Close Become Too-Close-to-Call?] for an analysis of error rates and how likely it is that the real winner would be Norm Coleman instead of Al Franken who currently leads by 312 votes out of about 2.9 million cast.

Revision as of 13:34, 23 April 2009

Elections

Andrew Gelman has an interesting article regarding the statistics of elections. He starts with

“Presidential elections have been closer in the past few decades than they were for most of American history. Here's a list of all the U.S. presidential elections that were decided by less than 1% of the vote:

1880 1884 1888 1960 1968 2000

Funny, huh? Other close ones were 1844 (decided by 1.5% of the vote), 1876 (3%), 1916 (3%), 1976 (2%), 2004 (2.5%).

Four straight close elections in the 1870s-80s, five close elections since 1960, and almost none at any other time.”

Perhaps more interesting is his take on House and Senate elections:


In the companion piece written with Nate Silver, the graphic concerning the House is made more evident

here.



From the graph, “the rate of close elections in the House has declined steadily over the century. If you count closeness in terms of absolute votes rather than percentages, then close elections become even rarer, due to the increasing population. In the first few decades of the twentieth century, there were typically over thirty House seats each election year that were decided by less than 1000 votes; in recent decades it's only been about five in each election year.”

Another way of putting it: “Consider that, in the past decade, there were 2,175 elections to the United States House of Representatives held on Election Days 2000, 2002, 2004, 2006 and 2008. Among these, there were 41 instances — about 1.9 percent — in which the Democratic and Republican candidates each received 49 percent to 51 percent of the vote (our calculations exclude votes cast for minor parties). In the 1990s, by contrast, there were 65 such close elections. And their number increases the further one goes back in time: 88 examples in the 1950s, 108 in the 1930s, 129 in the 1910s.”

Discussion

1. A contention mentioned in the NYT article for this bifurcation of opinion is: “as the economy has become more virtual, individuals can now choose where to live on an ideological rather than an occupational basis: a liberal computer programmer in Texas can settle in blue Austin, and a conservative one in the ruby-red suburbs of Houston.“ Argue for and against this assertion coupling ideology and occupational mobility.

2. Gelman and Silver end their NYT article with “Elections like those in New York’s 20th district or in Minnesota, as contentious as they are, actually hark back to a less divisive era in American politics.” Explain the seeming paradox of a close race indicating less divisiveness.

3. As of this posting, the Minnesota senate seat is unfilled despite a manual recount, a canvassing board followed by a so-called election contest and awaits an appeal to the Minnesota Supreme Court—possibly further. See When Does ‘Close Become Too-Close-to-Call? for an analysis of error rates and how likely it is that the real winner would be Norm Coleman instead of Al Franken who currently leads by 312 votes out of about 2.9 million cast.