Chance News 104
Quotations
"Regression to the mean is so powerful that once-in-a-generation talent basically never sires once-in-a-generation talent. It explains why Michael Jordan’s sons were middling college basketball players and Jakob Dylan wrote two good songs....
"The Bush family’s dominance would be the basketball equivalent of Michael Jordan being the father of LeBron James and Kevin Durant — and of Michael Jordan’s father being Walt Frazier....In other words, it is virtually impossible, statistically speaking, that Bushes are consistently the most talented people to lead our country. Same for Chelsea Clinton or any other member of a political dynasty thought to be possible presidential timber."
Submitted by Bill Peterson
“You can often see error bars in public opinion polls .... Imagine a society in which every speech in the Congressional Record, every television commercial, every sermon had an accompanying error bar or its equivalent.”
Submitted by Margaret Cibes
Forsooth
From a Vancouver demographer commenting, tongue-in-cheek, on the result of making Canada’s census long form voluntary in 2010:
“Because of the move to the voluntary NHS, Canada is a richer, whiter, more educated country now.”
Note that the response rate dropped from 98.5 percent in 2006 to 68.6 in 2011.
Submitted by Margaret Cibes
"The percentage of students scoring at/above Proficient in 3rd grade math increased .... Curiale posted the highest gain ..., improving from 27.0 percent to 51.9 percent, an increase of 24.9% percent. …. In 6th grade, the percentage of students scoring at/above Goal ... increased from 28.0 percent to 39.4 percent, a gain of 11.4 percent."
CT State Department of Education CSDE News, August 13, 2013
Submitted by Margaret Cibes
“I just bought jumbo rolls of toilet paper--big bargain. It says on label: 12 mega rolls equals 48 regular rolls. On the other side of the label it says: use four times less.”
Submitted by Margaret Cibes at the suggestion of Howard Mayer
“Why are governments so eager to protect their citizens against dread risks, from cows to swine, and so hesitant to protect the very same people against the risk of financial disaster from investment banking?”
Submitted by Margaret Cibes
“.... President Dwight Eisenhower express[ed] astonishment and alarm on discovering that fully half of all Americans have below average intelligence ....”
Submitted by Margaret Cibes
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 for sending 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 is an analysis from the aforementioned American Statistician article. Looking at the 2000 batting data from the New York Yankees, it was found that the number of 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, so the powerful physique typical of home run hitters makes them less likely to get triples.
See the column for further discussion, including an example of non-transitive dice, the potential for non-transitive preferences in three way elections, and the potential pitfalls resulting from the large number of correlations in medical data.
TED Talk: Mathematics of Love
“The Mathematics of Love”, by Hannah Fry, April 2014
(17 min video, transcript provided)
Fry, an aerodynamicist, discusses three topics related to mating, based on recent statistical studies:
Topic #1: How to win at online dating (presenting oneself on social media in order to be popular)
Topic #2: How to pick the perfect partner (timing one’s choice)
Topic #3: How to avoid divorce (analogy to nations headed for war)
One study she refers to is “Why I Don’t Have a Girlfriend”, by economist Peter Backus, who uses the Drake equation to estimate the number of potential girlfriends for him.
Submitted by Margaret Cibes