Chance News 104: Difference between revisions
| Line 24: | Line 24: | ||
Thanks to John Allen Paulos, who sent the following link: | Thanks to John Allen Paulos, who sent the following link: | ||
[http://abcnews.go.com/Technology/WhosCounting/counting-transitivity-baseball-medicine-gambling-politics/story?id=12304772&singlePage=true Non-transitivity in baseball, medicine, gambling and politics]<br> | [http://abcnews.go.com/Technology/WhosCounting/counting-transitivity-baseball-medicine-gambling-politics/story?id=12304772&singlePage=true Who's Counting: Non-transitivity in baseball, medicine, gambling and politics]<br> | ||
by John Allen Paulos, ABCNews.com, 5 December 2010 | 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 | 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 tend to get a lot of 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 tend to get a lot of hits. But triples tend to be the result of speed, while home runs require power, and stronger players tend to be less speedy. | ||
# The 2010 Alaska | |||
See the article for further discussion. | |||
==Item 2== | ==Item 2== | ||
Revision as of 20:16, 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 tend to get a lot of hits. But triples tend to be the result of speed, while home runs require power, and stronger players tend to be less speedy.
- The 2010 Alaska
See the article for further discussion.