Chance News 24
Quotations
Paul Alper suggested the following quotations from "Sense and Nonsense of Statistical Inference" by Chamont Wang, Marcel Decker, 1993.
As a rule of thumb, often the more computer printouts empirical studies produce, the less intellectual content they have." [Page 84]
In brief, the previous design (the two-sample comparison) had three problems: (1) not scientific, (2) not ethical, and (3) not effective. Other than that, everything was fine." [Page 106]
In comparison to engineering measurements, most modern-day psychometric instruments are still in the stone age." [Page 129]
Forsooths
These Forsooths are from the Feb. 2007 RSS News.
The car poplation went up 10 per cent over the 1997-2004 period, while daily car trips more than doubled, rising 23 percent.
The Straits Times (Singapore)
24 November 2006
Online banking fraud up 8000%
The UK has seen an 8000% increase in fake internet banking scams in the past two years, the government's financial watchdog has warned...The amount stolen is still relatively small but it is set to go up by 90% for the second year running.
BBC Ceefax
213 December 2006
The danger of providing expert witness testimony when you are not an expert
Expert witness guidance: Likely implications of Professor Sir Roy Meadow’s GMC case
Sir Roy Meadow is an expert on child abuse, having published a landmark paper in 1977 on a condition known as Munchausen Syndrome by Proxy. An observation of his
one sudden infant death in a family is a tragedy, two is suspicious and three is murder, unless proven otherwise.
became knows as "Meadow's Law".
In testimony at the trial of a woman, Sally Clark, who had two children who died from SIDS, Sir Meadow tried to quantify this statement by arguing that the chances of observing two SIDS deaths would be 73 million to one. He arrived at this figure by squaring the probability of one SIDS death (8.5 thousand to one). Sally Clark was convicted of murder, but her conviction was overturned on appeal.
Dr. Meadow's testimony came under criticism, because squaring the probability only makes sense under independence. If there are genetic or environmental risk factors that influence SIDS deaths, then the probability estimate could be wrong. Not just wrong, but spectacularly wrong. It's an error that (hopefully) no statistician would make, but Dr. Meadow is not a statistician.
The General Medical Council reviewed this case and found Dr. Meadow to be guilty of serious professional misconduct and erased his name from the medical register. This action, which would prevent Dr. Meadow from practicing medicine, was still largely symbolic since Dr. Meadow is currently retired from medical practice.
Dr. Meadows appealed this decision in the British Courts which ruled that the actions of the General Medical Council should be overturned because expert witnesses will refuse to testify if they believe that their testimony, if shown later to be invalid, could lead to sanctions.
Submitted by Steve Simon.
Questions
1. What is the proper course of action if an expert witness is asked questions outside his/her area of expertise?
2. Do Sir Meadow's actions constitute an honest mistake or serious professional misconduct?
3. Do expert witnesses need immunity from recrimination if their testimony is found to be in error?
Additional readings
(1) Royal Statistical Society, [RSS%20Statement%20regarding%20statistical%20issues%20in%20the%20Sally%20Clark%20case,%20October%2023rd%202001.pdf Statement regarding statiscal issues in the Sally Clark case,
Press Release, October 23, 201.
(2) Ray Hill, Multiple suddent infant deaths--coicidence or beyond coicidence?, Paediatric and Perinatal Epidemiology, 18 (2004), 320-326.
Unrandomizing a Walk
America is a wealthy country. At times too wealthy. According to a New York Times article of February 10, 2007 by Benedict Carey, "James S. McDonnell, a founder of the McDonnell Douglas Corporation" donated "more that $10 million over the years" to Robert G. Jahn of Princeton University whose Princeton Engineering Anomalies Research Laboratory [PEAR] "has conducted studies on extrasensory perception and telekinesis." For 28 years Jahn has employed random number generators and other devices in order to show that the output could be influenced merely by thinking.
More specifically, according to the article, "Analyzing data from such trials, the PEAR team concluded that people could alter the behavior of these machines very slightly, changing about 2 or 3 flips out of 10,000." So to speak, unrandomizing a walk. From this meager beginning it supposedly follows that "thought could bring about changes in many other areas of life--helping to heal disease, for instance, in oneself and others." The beginning is meager because there is a suspicion that random number generators aren't all that accurate. An even larger suspicion that pervades all such ESP investigations is that the data may be unconsciously or otherwise manipulated.
In his 2000 book, Voodoo Science: The Road from Foolishness to Fraud, Robert L. Park wrote of Jahn's results, "a large number of trials with a tiny statistical deviation from pure chance, and apparently no way to increase the strength of the effect." Park suggested that "Why not just use your psychokinetic powers to deflect a microbalance?...The reason, of course, is that the microbalance stubbornly refuses to budge. That may explain why statistical studies are so popular in parapsychological research: they introduce all sorts of opportunities for uncertainty and error."
Jahn is finally packing it in, realizing that no respectable journal will publish his assertions; "If people don't believe us after the results we've produced, then they never will." According to the NYT, "One editor famously told Dr. Jahn that he would consider a paper 'if you can telepathically communicate it to me.'"
Discussion
1. According to the NYT, "Princeton made no official comment" concerning the closing of PEAR. Speculate why Princeton issued no statement.
2. According to the NYT, "The culture of science at its purest, is one of freedom in which any idea can be tested regardless of how far-fetched it might seem." Why then does Park say, "Science has a substantial amount of credibility, but this is the kind of thing that squanders it."
3. A theme running throughout Park's book is that even though the scientific community is overwhelming united regarding ESP, astrology, divining rods, the second law of thermodynamic, etc., the media often presents an issue as if there were a legitimate disagreement among equals. Relate this to how global warming is portrayed.
Submitted by Paul Alper
A Stirling Approach to the Central Limit Theorem (CLT)
A Stirling Approach to the Central Limit Theorem (CLT) By Bill Roach and Robert Kerchner Washburn University Topeka, KS 66621
Key words:
Central Limit Theorem, LaPlace, Stirling’s Approximation, error propagation, Excel, De Moivre
Abstract: Many applied statistics courses do not review a proof of the Central Limit Theorem; they rely on simulations like Galton’s Quincunx, and / or sampling distributions to acquaint the students with the Bell Curve. The Bell Curve is there, but students are left asking: 1. where did the π come from? 2. how did a power function based on e get into the formula? The short answer to that question is “Stirling’s Formula for n!.” Looking at the accuracy of Stirling’s Formula can give students some useful insights into the DeMoivre-LaPlace (binomial distribution) version of the Central Limit Theorem (CLT).
How to detect voting fiddles
Election forensics, The Economist, Feb 22nd 2007
Walter Mebane and his team at Cornell University claim to have devised a new method to detect fraud by using statistics. It is based on a mathematical curiosity known as Benford's law.
(This topic has been discussed previously in Chance News: Following Benford's law, or looking out for No. 1, in Chance News 7.07, Benford's distribution in the Dow-Jones, in Chance News 6.01 and Chance News 4.10. However, those articles deal with the first significant digit only.)
This law states that in certain long lists of numbers, such as tables of logarithms or the lengths of rivers, the first digit of each number is unevenly distributed between one and nine. Instead, there are far more numbers beginning with one—about a third of the total—and far fewer starting with nine. For example, a 2km stream is twice as long as a 1km stream; by contrast, a 10km stream is only 11% longer than a 9km stream. So you will find more streams measuring between 1km and 2km than between 9km and 10km.
Dr Mebane is concerned with the second, rather than the first, digit of lists of election results from different precincts of a constituency, where he also observes a non-uniform distribution of possible digits. The effect is far more subtle, with zero occurring about 12% of the time and nine turning up on 9% of occasions.
A quoted example concerns an analysis of the last three elections in Bangladesh.
The 1991 election showed no strange results. For the 1996 election some 2% of results were problematic. And fully 9% of the results in 2001 failed the test. The 2001 election was fiercely contested. Yet monitors from the Carter Centre and the European Union found the election to be acceptably, if not entirely, free and fair. Tests like Dr Mebane's one could provide monitors with quantitative estimates of exactly how free and fair an election has been, on which to base their qualitative judgment of whether that is indeed acceptable.
It is a very simple but not foolproof test for fraud, that can be easily applied to data. The author admits that his method sometimes fails to detect a discrepancy in a vote that is known to have been problematic, and occasionally detects fiddling where there was none.
The author claims to have developed a mathematical model that explains the distribution of the second digits, putting what might appear to be a statistical oddity on a more solid footing.
Questions
- Why do you think the author foccuses on the second digit rather than the first digit, when anomolies in the distribution of the second digit relative to the first are more difficult to detect?
- Do you think similar results might hold for the third or fourth significant digits?
Further reading
- Election Forensics: Vote Counts and Benford's Law, Walter Mebane Jr., 2006.
- Benford's Law and Zipf's Law.
- SigFigDistbGen, repeatedly mutiplies a number of your choice by a factor of your choice and plots the significant figure.
Submitted by John Gavin.