MONT 105Q -- Class March 14, 2016

A.  Misconceptions about probability

Independence is subtle(!)

(1) The "gambler's fallacy" -- I just tossed a coin and heads came up 10 times
in a row.  That coin is "due for a tail"  (independent events perceived as
not independent).

(2) The probability of a jet engine failing in flight is .000001.  So on a two-engine
jet the probability of both engines failing is (.000001)^2   (perhaps not-independent
events treated as independent. For instance, a major cause of failure is bird strikes
and it's often the case that birds could get sucked into both engines.)

B.  How data is gathered matters -- GIGO(!)

(1) From a web page for a stats class taught by D. Deturck at U Penn:

In 1936 Alfred Landon, the Republican governor of Kansas, ran against the FDR, the incumbent Democratic President. The Literary Digest was one of the most respected magazines and had
conducted polls and accurately predicted the winners of presidential elections dating back 
to 1916. For the 1936 election, the Literary Digest prediction was that Landon would get 57% 
of the vote against Roosevelt's 43%. On election day, 62% voted for Roosevelt against 38% 
for Landon, and error of 19% points(!)

The irony of the situation was that the Literary Digest poll was also one of the largest and 
most expensive polls ever conducted, with a sample size of around 2.4 million people!
The Literary Digest's method for choosing its sample was as follows: Based on every 
telephone directory in the United States, lists of magazine subscribers, rosters of clubs 
and associations, and other sources, a mailing list of about 10 million names was created. 
Every name on this list was mailed a mock ballot and asked to return the marked ballot to 
the magazine.

One cannot help but be impressed by the sheer ambition of such a project. Nor is is 
surprising that the magazine's optimism and confidence were closely tied to the magnitude of 
its effort. In its August 22, 1936 issue, the Literary Digest published this:

    "Once again, [we are] asking more than ten million voters -- one out of four, 
representing every county in the United States -- to settle November's election in October.

    Next week, the first answers from these ten million will begin the incoming tide of 
marked ballots, to be triple-checked, verified, five-times cross-classified and totaled. 
When the last figure has been totted and checked, if past experience is a criterion, the 
country will know to within a fraction of 1 percent the actual popular vote of forty 
million [voters]." 

Problems:  

(a)  selection bias: methods of selecting poll recipients (esp. telephone, club memberships, 
etc.) slanted toward middle- and upper-class voters, excluded lower-income 
voters (more likely to vote Democratic; more supportive of New Deal policies to combat
effects of the Depression).  

(b)  self-selection (nonresponse) bias:  Only about 2.4 million of those polled 
responded to the survey.  Possible interpretation: The ones who did were disproportionately 
angry at Roosevelt's New Deal programs(!)


(2) "More Is More or More Is Less? Parental Financial Investments During College," 
Laura T. Hamilton of the University of California-Merced, American Sociological Review.

From a report on this study "Parents' financial support may not help college grades" 
by Tamar Levin, NYT 15 January 2013:

http://www.nytimes.com/2013/01/15/education/parents-financial-support-linked-to-college-grades.html

"Parents saving for college costs, take heed: A new national study has found that the more 
college money parents provide — whether in absolute terms or as a share of total costs — the 
lower their children’s college grades."

Along with the headline, this invites readers to leap to causal conclusions. Maybe students 
who pay their own way are more motivated and study harder. A "dose-response" effect is even 
suggested: the more money parents put up, the worse students performed.

"Rather than strategically using resources in accordance with parental goals, or maximizing 
on their ability to avoid academic work, students are [just getting by]...[S]tudents with 
parental funding often perform well enough to stay in school but dial down their academic 
efforts."

A survivorship bias effect?? (Might students who are paying their own way be more
likely to drop out if they are not doing well?)

Also discuss graph of model results(!) -- GIGO?

C. A study found that the average life expectancy of famous orchestral conductors was 
73.4 years, significantly higher than the life expectancy for males, 68.5, at the time 
of the study.  Jane Brody in her NYT Health column reported that this was 
thought to be due to the arm exercise conductors got by virtue of their jobs. 

J. D Caroll gave an alternative suggestion, remarking that it was reasonable to assume 
that a famous orchestra conductor was at least 32 years old. The life expectancy for a 
32 year old male was 72 years making the 73.4 average not at all surprising. 

- Another sort of survivorship bias!

D.  Oscar season just came around again and, if you're a film fan, you'll were 
following the proceedings with interest. But did you know there is a health benefit to 
winning an Oscar? Doctors at Harvard Medical School say that a study of actors and actresses 
shows that winners live, on average, for four years more than losers. And winning directors 
live longer than non-winners. Source: "Harvard Health Letter" March 2006.
The assertion that Oscar winners live longer was based on an article by Donald Redelmeier, 
and Sheldon Singh: "Survival in Academy Award-winning actors and actresses". Annals of 
Internal medicine, 15 May, 2001, Vol. 134, No. 10, 955-962.

Not so easy to explain this away since the Oscar winners are compared with other 
actors, not with general population(!)