Chance News 104: Difference between revisions
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# In baseball, [an analysis] from the ''American Statistician'' of a year of batting data from the New York Yankees showed that the number triples hit by a player correlated positively with the number of base hits he had, which in turn correlated positively with the number of home runs he hit; however, the number of triples a player hit correlated negatively with the number of home runs he hit. As John explains, good hitters get base hits of all kinds, so it is not surprising that home runs an triples are positively correlated with total hits. But triples tend to be the result of speed, while home runs require power, and stronger players tend to be less speedy. | # In baseball, [an analysis] from the ''American Statistician'' of a year of batting data from the New York Yankees showed that the number triples hit by a player correlated positively with the number of base hits he had, which in turn correlated positively with the number of home runs he hit; however, the number of triples a player hit correlated negatively with the number of home runs he hit. As John explains, good hitters get base hits of all kinds, so it is not surprising that home runs an triples are positively correlated with total hits. But triples tend to be the result of speed, while home runs require power, and stronger players tend to be less speedy. | ||
# The Alaska election for US Senate in 2010 was [http://www.nytimes.com/2010/11/18/us/politics/18alaska.html?_r=0 won by Lisa Murawski] | # The Alaska election for US Senate in 2010 was [http://www.nytimes.com/2010/11/18/us/politics/18alaska.html?_r=0 won by Lisa Murawski] | ||
Revision as of 20:24, 22 March 2015
Quotations
Forsooth
Transitivity, Correlation and Causation
Theorem 1 of the article cited by Paul Alper in the previous issue, "Is the Property of Being Positively Correlated Transitive?" (The American Statistician, Vol. 55, No. 4, November, 2001), depends on the existence of non-observed independent random variables U, V, and W which cause the correlations between X=U+V, Y=W+V, and Z=W-U to be non-transitive. An interesting question is whether this relates back to the difference between causation and correlation.
The answer turns out to be no, we can get the same sort of result even in the presence of causative relationships between X, Y and Z. Here’s an example:
- X is N(0,1);
- Y = X + U, where U is N(0,1) and independent of X;
- Z = Y - 1.5*X.
The correlation coefficients between X and Y and between Y and Z are both positive but the correlation coefficient between X and Z is negative.
Stan Lipopvetsky’s follow-up letter (The American Statistician, 56:4, 341-342, 2002) hints at this but does not include an actual example.
Submitted by Emil M Friedman
Followup
Thanks to John Allen Paulos, who sent the following link:
Who's Counting: Non-transitivity in baseball, medicine, gambling and politics
by John Allen Paulos, ABCNews.com, 5 December 2010
This installment from the john's "Who's Counting" column describes several real world illustrations of non transitivity in correlation. Among these:
- In baseball, [an analysis] from the American Statistician of a year of batting data from the New York Yankees showed that the number triples hit by a player correlated positively with the number of base hits he had, which in turn correlated positively with the number of home runs he hit; however, the number of triples a player hit correlated negatively with the number of home runs he hit. As John explains, good hitters get base hits of all kinds, so it is not surprising that home runs an triples are positively correlated with total hits. But triples tend to be the result of speed, while home runs require power, and stronger players tend to be less speedy.
- The Alaska election for US Senate in 2010 was won by Lisa Murawski
See the article for further discussion.