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===Discussion===
<blockquote>In other words, the population of a city is [according to Zipf's law], to a good approximation, inversely proportional to its rank [within its country]. Why this should be true, no one knows. </blockquote>
===Discussion===


1. Parker-Pope also mentioned researchers [http://www.psy.plymouth.ac.uk/research/ece/publications/pdf/Social-Support-and-Slant.pdf here] who “studied 34 students at the University of Virginia, taking them to the base of a steep hill and fitting them with a weighted backpack. They were then asked to estimate the steepness of the hill. Some participants stood next to friends during the exercise, while others were alone.  The students who stood with friends gave lower estimates of the steepness of the hill. And the longer the friends had known each other, the less steep the hill appeared.”  In fact, three of the 34 were excluded because they were deemed outliers.  The participants estimated the slant via three different methods as can be seen in the figure below:
<div align=right>
Steven Strogatz.<br>
Guest Column <br>
[http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/?em The New York Times] <br>May 29 2009<br>
</div align=right>


<center> http://www.dartmouth.edu/~chance/forwiki/Fig.3.jpg</center>
Submitted by Paul Albert
 
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The haptic measurement "required adjusting a tilt board with a palm rest to be parallel to the hill, importantly, without looking at one's hand."  As can seen from the above figure, it appears to more accurate than either the verbal, merely a guess, or the visual? which a (presumably crude) disk-like device acted as an aide.
The researchers performed a two-way ANOVA (sex and social support) separately for each of the three measuring methods.  They reported the value of each F(1,27) to determine a p-value for each method to see if Friend compared to Alone is statistically significant.  So, why the number ?27??  From merely looking at the figure, which of the three methods for determining slant would appear to be unrelated to friendship?
2.  The above study took place in Virginia.  In Plymouth, England the researchers did a similar slant study but this time instead of friendship directly, imagining of support was tested as can be seen from the following figure:
<center> http://www.dartmouth.edu/~chance/forwiki/Fig.4.jpg </center>
 
This study had 36 participants and similarly to the first study, they did a two-way ANOVA (sex and imagery of support) leading to F(2,30) for each slant measuring technique.  So, why the ?2? and the ?30??  From merely looking at the figure, which of the three methods for determining slant would appear to be unrelated to imagery of support?
3. In either study, ?visual? or ?verbal? on average markedly overstate the slant of the hill.  What does that suggest about people?s ability to judge a task?
4.  The researchers admit that for either study, ?"Participants in this study were not randomly assigned."?  Why would this pose a problem?
5. To give Voltaire his due, Parker-Pope points out that  [http://content.nejm.org/cgi/content/full/357/4/370 "?A large 2007 study] showed an increase of nearly 60 percent in the risk for obesity among people whose friends gained weight."?
 
Submitted by Paul Alper

Revision as of 16:10, 21 May 2009

Friendship

In other words, the population of a city is [according to Zipf's law], to a good approximation, inversely proportional to its rank [within its country]. Why this should be true, no one knows.

Steven Strogatz.
Guest Column
The New York Times
May 29 2009

Submitted by Paul Albert

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