CHANCE News 13.06
November 2, 2004 to December 31, 2004
Prepared by J. Laurie Snell, Bill Peterson, Jeanne Albert, and Charles
Grinstead with help from Fuxing Hou and Joan Snell. We are now using a
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If it moves, it’s biology; if it changes
color, it’s chemistry; if it breaks, it’s physics; if it puts
you to sleep, it’s statistics.
Bob Hogg, University of Iowa
Contents of Chance News 13.06
(2) Catastrophe: risk and analysis.
(3) Using a risk thermometer to sentence the guilty.
(4) Miracle on probability street.
(5) Who are the nation's 'cheapskates'? Try the blue
(6) Misleading numbers in the news.
(7) Counting the casualties; the Iraq war.
(8) Regression to the mean in the stock market.
(9) Getting statistics out of the hands of politicians.
(10) Lies and statistics.
(11) Measuring productivity.
(12) Deaths from natural causes spike during the holidays.
(13) Holiday death statistics: Bah, humbug!
(14) Using graphics to show election results.
(15) How did the polls do?
(16) Understanding the polls.
(17) How did the political markets do?
(18) Using meta-studies to predict the electoral vote.
(19) A great book and a statistics Blog.
(20) Special issue of the Statistics Research Journal
on variability and variation.
(21) The origin of "There are three kinds of:lies,damned
lies, and statistic."
(22) A christmas version of the last passenger problem.
Peter Doyle suggested the following forsooth:
I went back last night and I looked at the exit
polls from 2000, and it was uncanny how they were all off anywhere from
two to three percent.
November 2, 2004
This Forsooth is from the December RSS News.
Paxman: 'Your bonuses are the basic statistics of
the Normal distribution.
What name is given to the root mean square deviation from the mean of
Answer: 'the error?'
Paxman: 'no it's the variance, or simple (sic) variance."
University Challenge (BBC TV)
4 October 2004
And this one is from the January RSS News.
God and sex there is a moral divide between Britain and US.
The Times (London), 11 November 2004
(1) How should this table be interpreted?
(2) The article reports "British and American voters have sharply
different attitudes to churchgoing and abortion."
Once you interpret the table correctly what differences do you see?
Here is a Forsooth from the New York Times:
From the Drudge Report to Wonkette to DailyKos, Web sites
were often reporting the survey data in its pure form -- Kerry 50; Bush
49 in Ohio -- without explaining in depth important caveats, such as that
the results fell within a margin of error. So in Ohio, for instance, the
first report fell with a margin of error of plus or minus five percentage
points, meaning a candidate would have to have a lead of more than 10
points to have a statistically significant lead.
Survey experts cite problems with
data and interpretation.
New York Times 4 Nov.,2004, Sec. P p.5
And here is another one from the New York Times taken from our
The expected costs of a future event are the
costs of that event, if it should happen, divided by the probability that
it will happen. Thus if I offer you $1,00o if a tossed coin turns up heads,
the expected cost of my offer is $500.
New York Times, Book Reviews, 2 Jan, 2005,p. 12
New York Times, 2 Jan 2005, Book reviews, p.12
This is a review of a new book: Catastrophe: Risk and Response
by Richard Posner published by Oxford University Press, November 2004.
Richard Posner is a judge on the United States Court of Appeals from the
Seventh Circuit, and a senior lecturer at the University of Chicago Law
Posner feels that we often do not take seriously low probability, high
risk, events such as Global Warming, biodiversity, asteroid collisions,
and terrorism. He asks us to consider the expected value of the cost of
such an event. The reviewer Peter Singer remarks that most of us would
asses large risks differently than small risks, remarking:
We may pay a steep price to reduce a risk of one in a thousand
to one in ten thousand, but we are not much concerned about reducing a
risk of one in a million to one in a billion.
Posner... suggests that the value of a human life actually
varies in accordance with the degree of risk we are considering -- so
that the loss of each human life in a highly improbable catastrophe should
be valued only at $50,000 instead of the $5 million that it would be valued
at if we were considering a more likely disaster. This is bizarre. The
real worth of our lives has nothing to do with the probability of a particular
cause of death.
Frank Duckworth, the editor of RSS News, and other members of the Royal
Statistical Society attempted to develop a "Richter scale" that
might used to indicate the degree of a risk (See
Chance News 7.11). They proposed that the expected value be used for
monetary risks but proposed a more complicated method of evaluating risks
involving a change in quality of life or deaths.
Posner suggests possible practical recommendations for responding to
catastrophic risks which the review says "seem calculated to parcel
out irritation to everyone." But despite his concerns Singer concludes
Still, we would be well advised to set aside such minor
discontents and take the message of this book seriously. We ignore it
at (a small risk of) our (very great ) peril.
Do you think it is reasonable to use only expected value to assess the
cost of catastrophic events?
New York Times Magazine, 2 Jan. 2005, p. 18
This article describes a risk scale that is actually being used. In 1994
the Virginia state sentencing commission carried out a study to determine
which nonviolent offenders could be kept out of prison without posing
a risk of committing new crimes. They followed 1,500 nonviolent drug,
larceny and fraud offenders for three years after release from prison.
They found that men were 55% more likely to be rearrested than women,
and offenders in the 20's were a much higher risk than offenders older
than 40. Also being unemployed made offenders more likely to carry out
another crime. The same was true for being single.
This study led the commission's director, Richard Kern, to design a simple
7-point scale of risk assessment to aid judges in their sentencing. If
an offender has a score of 35 or less, probation or house arrest is suggested
rather than jail. A score higher than 35 suggests a jail sentence.
This model was tested on prisoners released five years earlier. Of those
who scored below 35, 12 percent committed new crimes as compared to 38%
for those who scored higher.
These are only suggestions, so Judges are not required to use this risk
scale. However, the scale is being used and has solved some of the overcrowded
problems Virginia had for its jails.
(1) The article states that while Virginia is pleased with the results
of using this scale, legal experts and others have serious concerns with
it. What do you think these concerns are?
(2) How might drug dealers and others try to take advantage of this kind
Pat Philips, a student in Bill Peterson's probability
class, suggested the first of these two articles which led to the second
on probability street.
The Law of Large Numbers guarantees that one-in-a-million miracles happen
295 times a day in America.
Scientific American, 26 August, 2004.
By Michael Shermer
One in a million.
The New York Review of Books, 25 March, 2004
Freeman J. Dyson
Michael Shermer is publisher of the magazine Skeptics and Director
of the Skeptics Society. He writes a monthly column for the Scientific
American. Freeman Dyson is famous physicist and interpreter of science
for the general public. These two articles provide an interesting story
with a surprising ending.
In the first article Shermer provides two probability calculations to
show that events that might be considered as supernatural events can be
shown to be not at all surprising. The first calculation is from a recent
book that Dyson is reviewing in our second article. Sherman writes:
In their delightful book Debunked! (Johns Hopkins
University Press, 2004), CERN physicist Georges Charpak and University
of Nice physicist Henri Broch show how the application of probability
theory to such events (events of low probability) is enlightening. In
the case of death premonitions, suppose that you know of 10 people a year
who die and that you think about each of those people once a year. One
year contains 105,120 five-minute intervals during which you might think
about each of the 10 people, a probability of one out of 10,512--certainly
an improbable event. Yet there are 295 million Americans. Assume, for
the sake of our calculation, that they think like you. That makes 1/10,512
X 295,000,000 = 28,063 people a year, or 77 people a day for whom this
improbable premonition becomes probable. With the well-known cognitive
phenomenon of confirmation bias firmly in force (where we notice the hits
and ignore the misses in support of our favorite beliefs), if just a couple
of these people recount their miraculous tales in a public forum (next
on Oprah!), the paranormal seems vindicated. In fact, they are merely
demonstrating the laws of probability writ large.
His second example is taken from Dyson's review of Charpak and Broch's
book Debunked. Dyson writes:
The book also has a good chapter on "Amazing Coincidences."
These are strange events which appear to give evidence of supernatural
influences operating in everyday life. They are not the result of deliberate
fraud or trickery, but only of the laws of probability. The paradoxical
feature of the laws of probability is that they make unlikely events happen
unexpectedly often. A simple way to state the paradox is Littlewood's
Law of Miracles. Littlewood was a famous mathematician who was teaching
at Cambridge University when I was a student. Being a professional mathematician,
he defined miracles precisely before stating his law about them. He defined
a miracle as an event that has special significance when it occurs, but
occurs with a probability of one in a million. This definition agrees
with our common-sense understanding of the word "miracle."
Littlewood's Law of Miracles states that in the course of any normal person's
life, miracles happen at a rate of roughly one per month. The proof of
the law is simple. During the time that we are awake and actively engaged
in living our lives, roughly for eight hours each day, we see and hear
things happening at a rate of about one per second. So the total number
of events that happen to us is about thirty thousand per day, or about
a million per month. With few exceptions, these events are not miracles
because they are insignificant. The chance of a miracle is about one per
million events. Therefore we should expect about one miracle to happen,
on the average, every month. Broch tells stories of some amazing coincidences
that happened to him and his friends, all of them easily explained as
consequences of Littlewood's Law.
While Dysen agrees with Sherman and Chapak and Broch that such calculations
and magician's tricks can be used to debunk much of what is called paranormal
behavior, he does not believe that it rules out the all of paranormal
behavior. After an interesting discussion of the nature of science Dysen
The hypothesis that paranormal phenomena are real but lie
outside the limits of science is supported by a great mass of evidence.
The evidence has been collected by the Society for Psychical Research
in Britain and by similar organizations in other countries. The journal
of the London society is full of stories of remarkable events in which
ordinary people appear to possess paranormal abilities. The evidence is
entirely anecdotal. It has nothing to do with science, since it cannot
be reproduced under controlled conditions. But the evidence is there.
The members of the society took great trouble to interview first-hand
witnesses as soon as possible after the events, and to document the stories
carefully. One fact that emerges clearly from the stories is that paranormal
events occur, if they occur at all, only when people are under stress
and experiencing strong emotion. This fact would immediately explain why
paranormal phenomena are not observable under the conditions of a well-controlled
scientific experiment. Strong emotion and stress are inherently incompatible
with controlled scientific procedures. In a typical card-guessing experiment,
the participants may begin the session in a high state of excitement and
record a few high scores, but as the hours pass, and boredom replaces
excitement, the scores decline to the 20 percent expected from random
Michel Shermer ends his article with:
Freeman Dyson is one of the great minds of our time, and
I admire him immensely. But even genius of this magnitude cannot override
the cognitive biases that favor anecdotal thinking. The only way to find
out if anecdotes represent real phenomena is controlled tests. Either
people can read other people's minds (or ESP cards), or they can't. Science
has unequivocally demonstrated that they can't--QED.
(1) How does Shermer get his headline: The Law of Large Numbers
guarantees that one-in-a-million miracles happen 295 times a day in America?
(2) Does it surprise you that a famous scientist would support the existence
of paranormal behavior?
are the nation's 'cheapskates'? Try the blue ones.
Christian Science Monitor, 22 December 2004
G. Jeffrey MacDonald
A Massachusetts organization called the Catalogue
for Philanthropy uses Internal Revenue Service data to compute an
Index of Generosity, which compares each state's average itemized
charitable deduction to it's average adjusted gross income. Mississippi
is the poorest state in terms of average income, but it ranks first in
charitable giving as a proportion of income. By contrast, Connecticut,
which has the highest average income, ranks 44th in charitable giving
as a proportion of income. This inverse relationship between income and
proportion of giving appears to be the general trend.
George McCully, president of the organization, sees religion as a key
factor in the lower income states. By contrast, in the Northeast, he says
that "religion doesn't help our giving. I wouldn't say it hurts,
but it doesn't help either." Others see a difference between "old
money" and new, noting that during the late 1990s technology boom,
when many new fortunes were created, private giving doubled in Massachusetts.
The article provides the following warnings about interpreting the results.
Researchers admit tax return data reveal only so
much. Better analysis is needed to account for the fact that high earners
tend to itemize deductions more often than low earners, and high-tax states
also produce more itemizations than low-tax states - both factors that
can skew study results.
(1) In what direction would the factors noted above skew the results?
(2) The article notes that:
What puzzles some researchers is not just the parsimony
of the wealthy states, but also the pattern. The same Northeastern "blue"
states - those labeled Democratic at election time - have appeared near
the bottom of the list in every year since the index began keeping track
in 1997. And the same "red" - or Republican - states are always near the
top. Does this mean that Democrats contribute a smaller proportion of
their incomes than do Republicans?
numbers in the news.
A look at numbers behind Social Security, illegal immigrants and Iraqi civilians
ABCNews.com, 5 December 2004
John Allen Paulos
In this installment of his Who's Counting
column, Paulos takes a closer look at some widely quoted statements from
current news stories.
The first concerns the Bush Administration's proposal to partially privatize
Social Security. Many news stories have stated that the proposal would
redirect 2% of current social security taxes into private accounts, a
figure that makes the change sound small. In fact, Paulos explains that
American taxpayers now contribute an average of 6.2% of their taxable
income to Social Security, which would be reduced to 4.2% under the new
proposal. The cut is two percentage points, but it amounts to a 32% reduction
Time magazine reports that 3 million illegal immigrants enter
the US annually from Mexico. Paulos cites two problems with this figure.
First, it is based on border agents' reports of 1 million arrests each
year. But this ignores the facts that the same individuals get multiply
counted if they fail on repeated attempts to enter the US. The 1 million
is then inflated to 3 million based on agents' guesstimates that three
times as many illegal immigrants elude capture as are caught. The softness
of the estimates gets left out of the sound bites, and Paulos observes
that the 3 million figure has "now attained a life of its own."
Paulos' final example concerns estimates of civilian casualties in Iraq.
The journal Lancet recently published research estimating that
100,000 Iraqi civilians had lost their lives in the war, with most deaths
presumably attributable to the aerial bombing campaign. The figure is
based on a cluster sample, involving 33 clusters of 30 households. The
clusters were randomly selected from around the country, not including
Fallujah, which because of its central role in the insurgency is an obvious
outlier. The Lancet figure is substantially higher than the 15,000
deaths included in the Iraq Body Count (IBC), a list of names compiled
by British researchers from published accounts. While Paulos concedes
that the actual number is most likely higher than the IBC, he notes that
the margin of sampling error for the cluster sample is plus or minus 93,000,
so the interval estimate is 8,000 to 194,000! He cites a number of other
potential difficulties with the survey, none of which tend to receive
attention in news reports.
The next five items were suggested by John Gavin. The first one discusses
the estimation of the casualties in Iraq mentioned in Paulos' column.
the casualties; the Iraq war.
The Economist, 6 November,2004
Gavin remarked that this article is unusual in that it includes a detailed
account of how the authors of the Lancet
article made their estimate for the number of casualties in the Iraq
war.The article also describes possible problems with the estimation,
including comments on the study from experts.
There is also an interesting discussion of why the estimate of 100,000
is so much larger than the 15,000 estimate based on the media accounts
referred to by Paulos.
Mean question about the stock market returns.
Financial Times, Weekend edition Oct. 30/31, 2004
and forecasts of equity returns.
SafeHaven, 16 January, 2004,artical-1232
A case of
panic now not later.
SafeHaven, 17 September, 2004, article-1972
The Financial Times article begins with the following remarks:
Are stock market returns random or do they revert to the
This is an extremely important question for investors. If the former is
the case, then history is irrelevant. But if the latter, then the high
returns of the 1980s and 1990s have an inevitable consequence; low returns
for the foreseeable future.
Most analysis of the data has found little evidence of any reversion to
the mean over the short term.
Smithers says that the best argument for regression to the mean can be
found by looking at the longer term. In his 17 September article we find
the following graphic:
Smithers claims that this question is important for investors. If returns
are random, history is irrelevant but if they revert to the mean, the
high returns of the 1980s and 1990s imply low returns for the future.
Currently many US pension funds assume future returns of 9-10% even though
government bonds are at 4-5%. If returns do not match expectations, deficits
Andrew Smithers started Smithers
& Co. Ltd. in 1989 with 12 clients. It now provides advice on
international asset allocation to about 100 clients spread over many countries.
His articles are frequently discussed in the news media.
How would you test Smither's hypothesis that the stock returns revert
to the mean?
Less state control of statistics urged.
The Times (London), 14 October, 2004, Business p.63
Letwin pledges independent and impartial statistical service.
Financial Times, 9 December 2004, National News Business and
The UK government's Office of
National Statistics (ONS) is described
here as follows:
The Office for National Statistics (ONS) is the government
department that provides UK statistical and registration services. ONS
is responsible for producing a wide range of key economic and social statistics
which are used by policy makers across government to create evidence-based
policies and monitor performance against them.
The UK Statistics Commission
is described here
as a watchdog, helping to ensure that National Statistics are trustworthy
and responsive to public needs.
The Times article reported:
The Royal Statistical Society endorsed a recent report
by the Statistics Commission, the government watchdog, that said the current
Code of Practice should be made legally binding. The RSS said the privilege
by which ministers received advance copies of statistics must end because
persistent leakage of data was undermining public faith in its objectivity.
Andy Grieve, the RSS president, said that legislation should give statutory
roles to the Office of National Statistics and its director, the National
Two weeks ago the Royal Statistics Society said it supported the Commission's
stance. Michael Howard, leader of the Conservative party said that on
winning the next election "within the first hour, (he would) remove
political advisers' power over civil servants and make the Office of National
Oliver Letwin is a member of Parliament and the shadow Secretary of State
for Economic Affairs & shadow Chancellor of the Exchequer. In his
Financial Times article Briscoe writes:
The shadow chancellor attacked the government for having
"a track record of using statistics to mislead rather than inform
people", and said he wanted the potential for political interference
of data removed.
The government's performance should be assessed on the basis of "reliable
and impartial statistics", Mr Letwin said. He proposed an independent
regulator, charged with ensuring compliance with statistical best practice
in all government departments.
Britain would then have "the most independent and transparent statistical
framework in the world, putting it at the forefront of professional and
international best practice", he said. The reputation of government
statisticians has been damaged by a blunders and instances of suspected
manipulation by politicians.
The Statistic Commission has supported
this proposal in principle but refers us to its own
proposal. More information about the position of the RSS can be found
(1) Do you think the problems addressed could also occur in the U. S.?
(2) Does the U. S. have anything like the UK Statistics Commission? If
not should they?
Lies and Statistics.
Financial Times, Editorial comment, 23 Dec, 2004
This article discusses a similar problem in the European Union, but first
some terminology from the free encyclopedia
The European Union is a supranational organization of 25
European states. The European Commission is the executive of the European
Union. Its primary roles are to propose and enact legislation, and to
act as 'guardian of the treaties' which provide the legal basis for the
EU. The Statistical Office of the European Communities (Eurostat) is the
statistical arm of the European Commission,producing data for the European
Union and promoting harmonization of statistical methods across the member
states. The Eurozone is the subset of European Union member states which
have adopted the Euro currency, creating a currency union.
The issue is the same as in the previous UK discussion. According to
this article it is believed that the previous Greek government persistently
under-reported budget deficits in order to qualify to join the Eurozone
The Commission now wants to give Eurostat the the right to check national
accounts including having its employees turn up to check data in an attempt
to secure the independence of national statistics offices from political
While the editorial supports the idea of independence it is skeptical
that Eurostat can act as a statistics police officer while it is still
tarnished by charges of its own corruption. In addition Eurostat would
need more qualified economists and statisticians it has now.
primer; economic focus.
The Economist, 6 Nov. 2004, Finance and Economics.
Productivity growth is probably the single most important indicator of
an economy's health. This article compares two methods to measure productivity:
labour productivity, output per man-hour in the non-farm business sector,
multi-factor productivity, which tries to capture the efficiency with
which inputs of capital as well as labour are used. The article states:
One virtue of multi-factor productivity over labour
productivity is that comparisons between countries may be less distorted
by national differences in the way real output is measured. For example,
many economists suspect that the growth in America's GDP, and hence its
labour productivity, is overstated relative to Europe's because American
statisticians make a much bigger adjustment for improvements in the quality
of goods, notably computers. In addition, American statisticians count
firms' spending on software as investment, but in much of Europe it counts
as a business expense, and so is excluded from final output.
The article goes into greater details on some the issues involved in
having different ways to measure productivity.
You can learn more about these choices in the US from the US
Bureau of Labor Statistics website. You will find Mutifactor Productivity
described here, and about
labour productivity described here.
See if you can learn enough , from the references we provided, about
how these measures are computed to explain them to your Uncle George.
Here are two holiday news stories. Alas, they
are less than cheerful!
from natural causes spike during the holidays. Whether sparked by
unhealthy eating or ignoring symptoms, the 'holiday effect' is real, a
study says. Best to heed the warning signs.
Los Angeles Times, 20 December 2004, F5
The first story comes with a warning. Researchers at Tufts University
and the University of California at San Diego have found more evidence
for the so-called "holiday effect": the highest risk days for
death from heart attack and other natural causes are Christmas, the day
after Christmas, and New Years Day. Examining death certificates from
1973-2001, the researchers focused on the two weeks from December 25 to
January 7. They identified 53 million deaths from natural causes. Overall
the holidays were found to have 12% excess mortality over the other days
in the period.
The researchers suggested several possible explanations for the findings.
People may postpone needed care until after the holidays, or else have
less access to their usual care because they are traveling. Previous research
had cited cold weather as a contributor, but this would not explain the
specific holiday effect.
The study appeared in the journal Circulation, which is published
by the American Heart Association. You can find more information on the
Association's web page, including a link to a video news release.
death statistics: Bah, humbug!
Los Angeles Times, 22 December 2004
Research does not support the popular belief that people can postpone
their deaths until after holidays, birthdays or other personal milestones.
Donn Young of Ohio State University's Comprehensive Cancer Center examined
death certificates of patients who died of cancer from 1989-2000, focusing
on the pattern around Thanksgiving, Christmas and the patients' birthdays.
Young found no significant difference between the proportion of patients
dying right before these dates compared with after.
Dr. Daniel Loiterstein, a geriatric psychiatrist, was dismayed by the
timing of the publication. He said, "I cant believe they'd put this out
just before Christmas. It's like telling people there's no Santa Claus."
Election results using graphics.
The U.S. presidential election suggests interesting discussions for statistics
classes. Here is a graphic example. ( A color printer will be required
to understand these graphics).
Many of the news reports used only a graphic like the following
New York Times graphic to show the final results for the
electoral college votes:
This graph suggests a major victory by Bush. However, unlike many other
news services, the New York Times also provided a graphic with
the size of the states scaled by the number of electoral votes that the
states provides (in the previous map choose "View map according to
Electoral Votes"). This provides a more realistic picture of the
relative electoral votes won by Bush and Kerry.
The ESRI used its Geographic Information
System, worked with CBC to provide demographic maps to help analyze the
election on election night. You can see some of the results here.
Here is our favorite graphic suggested by Bob Drake showing, rather dramatically,
the popular vote by county:
What do you think the heights of the bars in the ESRI graphic represent?
How did the polls do?
Despite the continually decreasing response rate, the standard polls
did pretty well for in their final polls before the election. Recall that
Bush received 51.1% of the popular vote and Kerry received 48% . PollingReport.com
provides the following results for several final vote projections:
It is pretty clear from this that the
election was too close to call. The results given here for Harris was
their final telephone poll. They also do an on-line poll and the final
result was 50% Kerry and 47% Bush which is not very good.
she said, nobody knew.
The Economist, November 18, 2004
This article discusses problems with
modern traditional polls in the context of the U.S. presidential election.
We discussed these problems also in Chance
News 13.05. In this Economist article we read:
In this election, the biggest polling problem was how to
identify likely voters. Because turnout in America is below 60%, pollsters
adjust their raw numbers to screen out people deemed unlikely to vote
and also to ensure that their sample properly represents ethnic minorities,
women, registered Democrats and Republicans, and so on.
The trouble is that, by reducing the size of the sample, screening produced
implausible volatility in the middle of the campaign. Frequently, half
the polls would show Mr Bush's vote rising while the other half showed
it falling. Jon Krosnick of Stanford University also points out that screening
produced an illusory “bounce” after each convention. The screen
let through a disproportionate number of Democrats after the Democratic
convention, and Republicans after the Republican convention. But no one
had really changed their mind.
On the other hand, not having a tough enough screen can be worse than
having one. And here The Economist has to own up to problems
of our own. YouGov, a firm that has used internet polling successfully
in Britain and Australia, polled for us in America without sufficiently
seeking to gauge respondents' likelihood to vote. Its final poll showed
Mr Kerry up by three points among registered voters. Interestingly, YouGov
says that if you recalibrate its final poll to reflect the demography
of the voters who actually showed up on November 2nd, its panel showed
a Bush lead (fewer blacks and poor people actually voted than YouGov researchers
In the last chance news we mentioned
that The Economist and a leading British pollster, YouGov, had
a joint venture to provide an online poll to track the progress of this
year's presidential election. At the YouGov
website we read:
YouGov is a research company using online
panels to provide research for public policy, market research, and stakeholder
YouGov has a track record as the UK's most accurate pollster. In all five
of the YouGov polls where data could be compared to actual outcomes (including
the UK general election, the Australian election, the Pop Idol contest),
we were within 1% of the actual result.
Unfortunately this record was broken
by this U.S. presidential election. From YouGov's
analysis of The Economist/YouGov poll we read:
YouGov questioned 2,903 American electors between Friday
October 29 and Monday
November 1. Of these, 2,164 either had already voted (294) or were certain
even if there were “a long line of people waiting to vote”
(1,870). Excluding the 20
respondents who refused to say who they supported, or were still making
minds, support was divided among the main candidates as follows:
So, together with the poor result for the Harris on-line poll, it would
suggest that such polls did not do so well for this presidential election.
This article discusses the fate of the political futures markets as polls.
Political futures markets claim they're more accurate than opinion polls.
So, how'd they do yesterday?
Slate Magazine, Wednesday, Nov. 3, 2004
The article states that the two best known political markets are the
Iowa Electronic Markets at
the University of Iowa which has been running since 1988 and TradeSports,
a three year-old Dublin, Ireland-based exchange. In either of these you
could bet on Bush or Kerry to win the presidential election. We discussed
these markets in
Chance News 12.02. For TradeSports, those participating in the presidential
betting had a choice of offering to buy or sell k units of stock on a
candidate at a price they specify. For example on October 24 one bettor
offered Kerry shares at 41 cents. If you buy some of these shares and
Kerry wins, you are paid $1 per share and if he loses you are paid nothing.
Since we thought Kerry had better than a 41% chance of winning, we happily
bought 50 Kerry Shares for $41 and with Kerry losing the election and
trading fees, we lost $41.80.
The Iowa Electronic Market's "winner-take-all" market works
in the same way. Here we could have bought Kerry shares on October 24
for 38.8 cents a share and again would have been paid $1 a share if Kerry
won and nothing if Bush won. The closing price of a Kerry share on November
1 was 48.5 cents and for Bush 51.2 cents. Thus using this as a poll would
give a good prediction for the popular vote which was 48.2% for Kerry
and 51.2% for Bush. The following graph shows how the price varied through
time. Note that Bush was almost always ahead.
In his article Gross points out that, for both the Iowa Electronic Market
and TradeSports, share prices were strongly influenced by the leaking
of the exit poll reports the afternoon of election day. These reports
showed surprising strength for Kerry. The Iowa Electronic Market Kerry
shares rose from below 50 in the morning to above 70 by 4:30 ET. Similarly
the TradeSports traders bid the Kerry shares up to 67.
(1) The Iowa Electronic Market gives the following comparison of a number
of market election poll and traditional election polls.
Does this convince you that Markets give better prediction that polls.
(2) We asked David Moore of Gallup if he felt that on-line polling would
become as good as traditional polling. He remarked that, in general it
would compare favorably but would be more subject to significant errors
in some elections. Why do you think he said this? Would you expect the
same to be true for Election Market predictions? Is this born out in the
comparison provided by the Iowa Electronic Market?
For math whizzes, the election means a
quadrillion options--close race has programmers predicting the outcomes.
Wall Street Journal, 26 Oct. 2004, A1
Entertainment: winner at picking electoral vote.
Wall Sreet Journal, 4 Nov. 2004, D9
These articles discuss a number of attempts to use serious math and statistics
to develop a meta-analysis to predict the electoral vote in this years
presidential election. The meta-analysis carried out by Samuel Wang at
Princeton was acknowledged by many to be the inspiration for their studies
and it also attracted the greatest interest in the media and on the web
so we restrict our discussion to this study. However readers will enjoy
looking at some of the other studies (see links below).
Sam Wang is Assistant Professor of Molecular Biology at Princeton and
director of a lab titled; Design principles and learning in neural circuits.
Sam was a great help to us in writing this, and readers will enjoy looking
at his Electoral College Meta-Analysis
web site where you will find the history of his study and comments
on other events related to the election.
The first step in Wang's Electoral College Meta-Analysis was to estimate
the probability that each of the candidates will win the 23 states that
he felt the outcome was in doubt, using the results of the state polls
over about a week's time period. Wang assumes that the true value of the
Bush-Kerry margin (number of Bush votes - number of Kerry votes) is a
random variable normally distributed with mean and standard deviation
estimated from the state polls. From this he estimates the probability
that each candidate will win.
Wang remarks that he feels now that he should have used a t-distribution
instead of the normal distribution since the number of polls available
per state was small (between 3 and 15). He also points out that a more
elaborate procedure could be used in which the reported sampling margins
of error were used to calculate an overall confidence interval. However,
such a procedure would not take into account variation in methods or biases
among polling organizations. Therefore he chose the simpler procedure.
Wang then uses his estimated probabilities that each candidate will win
to calculate the probability of each sequence of possible winners for
the 23 states. Here he assumes independence. There are 2^23 = 8,388,608
such possibilities. Using these results Wang calculates the distribution
for the number of electoral votes Bush will win. He chooses the median
distribution for his estimate for the number of electoral votes Bush will
win. His final estimate, based based on the state polls the week before
the election, estimated 286 votes for Bush and hence 252 for Kerry. This
turned out to be exactly the numbers the two candidates won. Wang remarks
that the margin of error for his prediction was quite large, +/-39 electoral
votes for the 95% confidence interval. Averaging over longer time periods
would have given a more precise snapshot, and he is now interested in
determining what a suitable time period would be.
A snapshot of polls is not the same as a prediction, and Wang attempted
to control for biases coming, for example, from the fact that most of
the polls were restricted to decided voters (and the undecided voters
might vote differently). In an interesting interview the day before the
election, on the radio program The Wall Street Journal this Morning,
Wang was asked for his prediction. He replied that the race was close
enough to make prediction difficult but then went on to give his opinion
that Kerry would win based on the historical pattern that undecided voters
break for the challenger. You can listen to this interview here.
However, this pattern appears not to have held this year. Instead, pre-election
polls gave margins that closely reflected the final outcomes. Therefore
the raw decided-voters calculation, based on polls alone, was the most
Wang points out that his method provides a tool for reducing the large
number of polls reported in the mainstream press to a more easily digestible
statistic. Properly applied, he thinks that this can improve the statistical
rigor of horserace political reporting. This would reduce confusion, noise
reduction in both a statistical and a mass-media sense.
You can see other similar attempts to predict the electoral vote here:
A bag of tricks.
Oxford University Press, 2002
Andrew Gelman and Deborah Nolan
Gelman's BLog: Statistics Modeling, Causal Inference and Social Science
Berkeley study scrutinizes Florida tally for Bush
San Francisco Chronicle,19 Nov.2004, B3
For some time we have been intending to mention the book Teaching
statistics: a bag of tricks written by Andrew Gelman (Columbia University)
and Deborah Nolan (University of California, Berkeley). This is a wonderful
book that provides many ways to enhance a statistics course with tried
and true tricks used by the authors of the book in their classes. You
will find excerpts from several reviews at the book's web
site. Here is a comment by George Cobb, the father of the current
statistics teaching reform:
Anyone who cares about teaching statistics should own this
book. It is the fruit of years of collecting, inventing, experimenting,
and hard thinking by two classroom veterans who are also leading statisticians.
Buy it, read it, use it: if your reaction is like mine, you'll find lots
of things that you want to try.
George Cobb, Mt Holyoke College
Andrew Gelman has also started a statistics Blog. Surprisingly, this
is the first statistics Blog that we have seen. We found it useful in
understanding another election discussion reported in the San Francisco
Chronicle article. This article discusses a study carried out by
Michael Hout, Professor of Sociology at Berkeley and three graduate students
from the university's Survey Research Center. The authors were interested
in seeing if the use of electronic voting machines in Florida had any
effect on the Bush vote in the 2004 election. The Chronicle article reports:
In the statewide study, researchers used a technique called
multiple regression analysis to account for differences in county size,
change in overall voter turnout (not by party), past voting history of
residents and demographic factors of income and race.
They also looked at whether a county used an electronic voting machine
or another ballot counting system. That distinction was the only one of
the six factors that showed a statistically significant relationship with
the increase in the Bush vote from the 2000 election, Hout said.
The article reports that the researchers concluded that their study
shows that President Bush may have received at least 130,000 extra and
unexplained votes in the Florida counties that used electronic voting
In his November 19 Blog posting, Gelman remarks:
Before getting to a discussion of this paper, let me show
you a few pictures (adapted from an analysis performed by Bruce Shaw here
First, a scatterplot of the counties in Florida, displaying the change
in the Republican vote percentage from 2000 to 2004, plotting vs. the
Republican vote percentage in 2000 (in both cases, using the Republican
% of the two-party vote). Red circles indicate the counties that used
e-voting in 2000, and black circles used optical scans. The radius of
each circle is roughly proportional to the log of the #votes in the county.
There are three obvious patterns in the figure:
1. The e-voting counties, especially the largest of them, were more Democrat-leaning.
2. For the optical scan counties, there was a consistent trend that the
counties that favored Bush more in 2000, tended to move even more toward
Bush in 2004.
3. For the e-voting counties, no such trend is apparent. In particular,
the two large red circles on the left of the plot (Broward and Palm Beach)
moved strongly toward the Republicans.
Gelman then provides similar graphics for previous elections and concludes
It would make sense to look further at Broward and
Palm Beach counties, where swings happened which look unexpected compared
to the other counties and compared to 2000, 1996, and 1992. But lots of
unexpected things happen in elections, so we shouldn't jump to the conclusion
that e-voting is related to these particular surprises.
Readers will find many other interesting statistical topics discussed
on Gelman's Blog.
At a meeting to honor Bobb Hogg that we attended
some years ago, Bobb asked each of us to write down the concept they most
wanted students in an introductory statistics course to understand. The
winner by far was "variation."
The current issue of Statistics
Education Research Journal
(SERJ) , published jointly by the International Association for Statistical
Education and the International Statistical Institute, is a special issue
on reasoning about variability and variation. A PDF version of the entire
issue can be freely downloaded from the journal's website. PDF versions
of individual papers are available from the following table of contents
for this issue.
Dani Ben-Zvi and Joan Garfield (Invited). Research on Reasoning about Variability: A Forward
Rob Gould (Invited). Variability: One Statistician's View
James Hammerman and Andee Rubin. Strategies for Managing Statistical Complexity with New Software Tools
Dani Ben-Zvi. Reasoning about Variability in Comparing Distributions
Arthur Bakker. Resoning about Shape as a Pattern in Variability
Chris Reading. Student Description of Variation while Working with Weather Data
Forthcoming IASE Conferences
Other Forthcoming Conferences
What is the origin of the famous quotation: There
are three kinds of lies: lies,damned lies, and statistics?
In the the November issue of RSS News, in a letter to the editor from
Peter M Lee, we read that the mystery of the originator of the famous
quotation 'There are three kinds of lies: lies, damned lies, and statistics",
often attributed to Mark Twain or to Disraeli has been solved. Lee says
that it is "almost certainly due to Leonard Henry Courtney, Lord
Courtney (1832-1918)." You can find his case for this here
on the Materials
for the History of Statistics web page that Lee maintains.
Read Lee's explanation for why he believes the mystery is solved
and Courtney's speech
(the quotation is on page 4). Are you convinced that Cortney originated
the famous quotation?
News 13.05 we discussed the "Lost boarding pass" problem
that appeared on the the Oct. 4 Car Talk program. Jerry Grossman wrote
us about the history of this problem:
There is a much richer history to the boarding pass
problem than you suggest in CHANCE News 13.05. Please see The College
Math Journal, vol 34, no 4, Sept 2003, pages 332-333.
The"Lost boarding pass problem" is number 735 in the College
Math Journal and was proposed by two readers one of whom was Jerry.
The problem described here is the same as the car talk problem discussed
in Chance News 13.05 except that it occurs on a tour bus with n > 1
seats. A large number of people provided solutions and the Problem Editor
describes two of the solutions.
The editor remarks that The Con Amore Problem Group pointed out that
this problem, with a different setting, appeared in the December 2001,
(vol 15, no2) issue of the journal FAMØS published by
the University of Copenhagen. Solutions and a generalization appeared
in the March and May, 2002 issues of FAMØS. These issues
are available in pdf format on the
FAMØS website. They are in Danish but Peter Doyle
and Lise Richardson (our Danish member of our Bach Study Group) provided
us with a translation of the articles. Here is the version of the problem
provided in FAMØS and appropriate for the Holiday period
when this Chance News was written:
There are n nisses (a type of gnome or elf associated with Danish Christmas)
who have their beds in a big common dormitory. Nisses are normally very
disciplined, so they go to bed one by one. Last year's Christmas party
caused nisse # l to have too much to drink, and as he was going to bed
(as the first one) he chose a random bed instead of his own. The rest
of the nisses took their own beds, but if the bed had already been taken,
they took a random one. What is the probability that nisse # n gets his
The problem was solved by Henning Makholm in the March 2002 issue of
FAMØS who also proposed as a bonus problem to find the
probability that the kth nisse gets his own bed. This problem was solved
by Rolf Dyre Svvegstrup who showed that the answer is:
Note that when k = n, the answer is 1/2 in agreement with the original
problem. Rolf's proof is very short and as usual we had trouble being
convinced without working an example. So here is our example which we
convinces us, but is probably more complicated than what Rolf had in mind.
We assume that the nisses beds are number according to the order that
they come in. Assume that there are 7 nisses and we want to find the probability
that the 5th nisse gets his own bed. The first nisse chooses randomly
from all the 7 beds. If he chooses bed 1,5,6, or 7, nisse 5's fate is
settled and he gets his own bed with probability 3/4. If not he chooses
from 2,3,4. Suppose he chooses bed 3. Then the 3rd nisse must make a random
choice from 1,5,6,7 or 4. Again if he chooses from 1,5,6,7, nisse 5's
fate is settled and he gets his own bed with probability 3/4. His only
other choice is 4, but if he chooses this, nesse 4 has no choice but to
choose from 1,5,6,7 and again nesse 5 will get his own bed probability
Copyright (c) 2004 Laurie Snell
This work is freely redistributable under the terms of the GNU General
Public License published by the Free
Software Foundation. This work comes with ABSOLUTELY NO WARRANTY.
CHANCE News 13.06
November 2, 2004 to December 31, 2004