Chance News 56
Quotations
I can calculate the motion of heavenly
bodies but not the madness of people
After losing a fortune in the
South Sea Company bubble of 1720
Trying is the first step towards failure. -- Homer Simpson
Forsooths
This forsooth is from the October 2009 RSS Forsooth.
Of course in those days we worked on the assumption that everything was normally distributed and we have seen in the last few months that there is no such thing as a normal distribution.
Scientific Computing World
February/March 2009
You can see the context of this comment here.
University of North Dakota researchers found that pilots who ate the fattiest foods such as butter or gravy had the quickest response times in mental tests and made fewer mistakes when flying in tricky cloud conditions.
According to a New Yorker (October 12, 2009) review of Matthew Stewart's The Management Myth: Why the Experts Keep Getting It Wrong, Stewart tells a story about how "his boss taught his twenty-something[-old] trainees ... how to conduct a 'two-handed regression'":
"When a scatter plot failed to show the signifiant correlation between two variables that we all knew was there, he would place a pair of meaty hands over the offending clouds of data points and thereby reveal the straight line hiding from conventional mathematics." Management consulting isn't a science, Stewart says; it's a party trick.
Minimizing the number of coins jingling in your pocket
Do We Need a 37-Cent Coin? Steven d. Levitt, October 6, 2009, Freakonomics Blog, The New York Times.
The current system of coins in the United States is inefficient. Patrick DeJarnette studied this problem and his work was highlighted in the Freakonomics blog. Dr. DeJarnette makes two assumptions.
1. Some combination of coins must reach every integer value in [0,99].
2. Probability of a transaction resulting in value v is uniform from [0,99].
Under this system, the average number of coins that you would receive in change during a random transaction would be 4.7. The system that would work better is rather bizzarre.
The most efficient systems? The penny, 3-cent piece, 11-cent piece, 37-cent piece, and (1,3,11,38) are tied at 4.10 coins per transaction.
Such a set of coins would be evocative of the monetary system in the Harry Potter books.
The article goes on to discuss systems where the coins are more conveniently priced and which single change in coins would lead to the greatest savings.
Submitted by Steve Simon
Lack of transparency in reporting study results
“Data Call Into Question HIV Study Results”
by Gautam Naik and Mark Schoofs, The Wall Street Journal, October 10, 2009
Researchers from the U.S. Army and Thailand failed to disclose that trial results of a potential HIV vaccine were not statistically significant, although they had this information when they announced the discovery.
"We thought very hard about how to provide the clearest, most honest message," [one researcher] said. "We stand by the fact that this is a vaccine with a modest protective effect." He called the trial results "complex."
The first analysis, a “modified intent-to-treat” analysis, included “virtually everyone who enrolled in the study, regardless of whether they ended up getting the full course of the vaccine. …. By this measure, the vaccine tested in Thailand reduced by 31% the chance of infection with HIV ….”
New infections occurred in 51 of the 8,197 people who got the vaccine, compared with 74 of the 8,198 volunteers who got placebo shots. Statistical calculations showed there was a 3.9% probability that chance accounted for the difference. In drug and vaccine trials, anything above a 5% probability of a chance result is deemed statistically insignificant.
The second analysis, a “per protocol” analysis, included only the “study participants who got the full regimen of vaccine shots at the right time.” Apparently, for this group, in which 86 people were infected, there is a “16% chance the study results were a fluke.” It reduced by 26% the chance of infection with HIV.
The article’s authors comment:
It isn't clear why the vaccine was seemingly ineffective among participants who followed the guidelines to the letter.
Submitted by Margaret Cibes
Questions
1. Minimizing the number of coins received in change is not the only criteria for a set of coin denominations. What other criteria make sense.
2. Is it logical to assume a uniform distribution in this problem?
3. What coin could be added to the current mix of coins to minimize the number of coins given in change.