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“Teams that touch more at the beginning of the season win more over the course of the entire season. The two touchiest teams in the study, the Boston Celtics and Los Angeles Lakers, finished the season with two of the NBA's top three records, and the Celtics Kevin Garnett was the touchiest player in the league by at least a 15% margin, said … one of the study's authors.” | “Teams that touch more at the beginning of the season win more over the course of the entire season. The two touchiest teams in the study, the Boston Celtics and Los Angeles Lakers, finished the season with two of the NBA's top three records, and the Celtics Kevin Garnett was the touchiest player in the league by at least a 15% margin, said … one of the study's authors.” | ||
<div align=right>[http://test.causeweb.org/wiki/chance/index.php/Chance_News_87#Forsooth Chance News 87]</div> | <div align=right>[http://test.causeweb.org/wiki/chance/index.php/Chance_News_87#Forsooth Chance News 87]</div> | ||
“At issue was how highly correlated the prices of various subprime mortgage bonds inside a CDO might be. Possible answers ranged from 0 percent (their prices had nothing to do with each other) to 100 percent (their prices moved in lockstep with each other). Moody’s and Standard & Poor’s judged the pools of triple-B-rated bonds to have a correlation of around 30 percent, which did not mean anything like what it sounds. It does not mean, for example, that if one goes bad, there is a 30 percent chance that the others will go bad too. It means that if one bond goes bad, the others experience very little decline at all.” | |||
<div align=right>[https://www.causeweb.org/wiki/chance/index.php/Chance_News_100 Chance News 100]</div> | |||
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Revision as of 21:56, 30 January 2016
The newsletter of Royal Statistics Society included a regular column entitled "Forsooth!" highlighting statistical gaffes from media reports (here is their installment from May 2013). Laurie Snell obtained permission from longtime RSS News editor Frank Duckworth to reproduce some of their entries in Chance News.
When Chance News became a Wiki in 2005, readers continued the tradition by submitting their own Forsooths. Appearing below is a compilation of Favorite Forsooths, 2005-February 2014. We are very grateful to Margaret Cibes for extracting these and carefully organizing them by topic, providing a ready resource for instructors who wish to include them in their classes. Margaret would like to dedicate this project to the memory of Laurie, who passed away in 2011.
In keeping with that dedication, here is a link to One in a Million— Remembrances of Laurie Snell (1925–2011) , written by Dan Rockmore for the Notices of the AMS, October 2012. In a passage that seems especially appropriate here, Dan quotes Claudia Henrion, who co-taught several Chance courses with Laurie at Dartmouth:
Many people think of mathematics as something done alone, tucked away in an office with pen, paper, and now computer. But as Laurie Snell exemplified, it can also be a life filled with community, friendships, generosity and playfulness. These qualities all came together in his development of the Chance course, where he combined the theory of mathematics with people’s everyday lives: events in the news, sports, gambling, and medicine.
Resource for Instructors
Chance News 1 – Chance News 97
Within each category, Forsooths are listed in chronological order, as submitted.
(Links to the original Chance Wiki issues provide citation details.)
PERCENTS
Basic arithmetic
Ambassador Newton: “Well, so far, six candidates out of 6,000 have been killed. That's .001 percent, and it's not at all clear that all of those cases involved the election.”
Ad for Peperami sausage: “Ingredients: Pork (108%), Pork Fat, Salt, Spices, Glucose, ....”
Company’s response to an inquiry: “The weight of the raw meat going into Peperami exceeds the weight of the end product because the recipe loses moisture, and therefore loses weight, during the fermentation, drying and smoking process.”
“Four million ... heard it. Ten percent remember it. One percent of those matter. One percent of those do something about it. That's still - he does the math - four people."
“The waitress coyly asked if they wanted change of the two twenties Kiley laid down on a thirty-two-dollar tab.
‘No, we’re fine.’
‘That’s a twenty percent tip, Mom.’
‘I’m feeling generous.’"
“Clearly, any product with a large user base is going to throw up some problems. Dell, for example, is shipping almost 40m PCs a year, so even if 95% of its users are happy, there could still be 6m or so with significant gripes.”
“USA Today has come out with a new survey: Apparently three out of four people make up 75 percent of the population.”
“France. The state statistics agency estimates that there are 3.8 million employed workers of foreign origin in France, representing 8.4 per cent of the total workforce of 25.4 million.”
"[A] Public Policy Polling survey released Thursday found that Gingrich's favorable rating with GOP voters has dropped 27 points in the last month--from 52 percent to 38 percent."
“In 1998 there were 361 fatal accidents out of 39 million flights. The ‘risk’ of a fatal accident is only 0.000009 percent.”
"Gates...found his ratio. 'In general,' he concluded, 'best results are obtained by introducing recitation after devoting about 40 percent of the time to reading. Introducing recitation too early or too late leads to poorer results.' The quickest way to master that Shakespearean sonnet, in other words, is to spend the first third of your time memorizing it and the remaining two-thirds of the time trying to recite it from memory."
"Our investigation of government spending in the 24 states that dedicate lottery funds for education yields a stunningly bad report card: the percentage of state spending on education is down or flat in 21 of those states from coast to coast. Lotteries provide no additional funding for education in 21 out of 24 states. As math students in one of those places would put it, that is nearly 50%."
"The 2012 agriculture appropriations bill that the … Committee approved … includes large cuts in [the WIC program]. …. One of the … justifications … is its claim that over 40 percent of WIC expenditures go for program administration. …. In coming up with the 40 percent figure, the Committee apparently misunderstood a finding in a USDA report that for every $1 in federal WIC funds spent for WIC foods in 2006, 41 cents in federal funds went for administrative costs plus WIC nutrition services. The Committee evidently used this statement to come up with its assertion … that ‘administrative costs of operating WIC are well above 40 percent.’ But 41 cents out of $1.41 in expenditures equals 29 percent, not 41 percent ….” (original emphasis)
100 percent
“Thursday is the least productive day for finance workers, research has found. The start of the week is the best time with 18 per cent claiming they were most productive on a Monday.”
“The BBC remains just ahead of commercial radio in the UK, with a 67% share of all listeners compared with 64%.”
“In terms of platform use trends among the respondents, 53% cited Windows as their primary technical computing platform, with Linux following closely at 51%.”
"Two years ago the sausage roll was the number one snack, but is now in second place with 53% of sales."
“I think we’re in trouble. …. Look at the difference between the top 1 percent and the bottom 95.”
News alert (corrected 20 minutes later): "With just under 40 percent of the precincts reporting, Romney was leading with 78 percent of the vote, followed by Gingrich with 31 percent, Rick Santorum with 13 percent and Ron Paul with 7 percent."
“I wonder if when you [Nate Silver] get up in the morning you open your kitchen cabinet and go, I’m feeling 18.5% Rice Chex and 27.9% Frosted Mini-Wheats and 32% one of those whole-grain Kashi cereals .... And then I wonder if you think, But I’m really feeling 58.3% like having a cupcake for breakfast ....”
"Doctors were on board and volunteered to help in 48 percent of cases; nurses and other health workers were available in another 28 percent. Only one-third of cases had to be handled by flight attendants alone."
Percent change
“Waiting time for foot surgery down by 500%.”
“Alcohol is now 49% more affordable than it was in 1978.”
“The All England Club said yesterday the men's champion will receive $1.170 million and the women's winner $1.117 million -- a 4 percent increase for both in British currency.”
”At St John's Wood station alone, the number of CCTV cameras has jumped from 20 to 57, an increase of 300 per cent.”
“NOAA's heating degree day forecast for December, January and February projects a 2 percent warmer winter than the 30 year average.”
“The car population went up 10 per cent over the 1997-2004 period, while daily car trips more than doubled, rising 23 percent.”
“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.”
"The Times' leader of 28 February tells us that taking regular doses of certain vitamins 'can actually increase the risk of mortality by five per cent.' Since the ‘risk of mortality' is already 100 percent this is very worrying."
A 2008 table showed a student:faculty ratio falling from 10:1 to 8:1 during the period Fall 1998 to Fall 2006, with a stated percent change of -25%.
"In the last five months, according to the Federal Reserve Board, the money supply in the United States has increased by 271 percent. It has almost tripled."
“Duke Energy customers voiced their concerns on Thursday night about a planned 13.5 percent rate increase. Under the plan, people with an average monthly bill of 100 dollars a month would go up about 18 dollars.”
“I must write again about the misleading adverts by GMPTE in the papers re the Congestion Charge. In their latest round of propaganda they state there will be a 10 per cent increase in bus services. With 10 councils in Greater Manchester this works out at a one percent increase per council. If Stockport’s bus companies run 200 buses in the morning peak, a one per cent increase will give two extra buses; is that what you want?”
"In a computer simulation of human behaviour in the layouts exited most swiftly by ants ..., evacuation times were reduced by up to 160 per cent."
"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."
Other comparisons
“Of the US Fortune 500 companies, 84 percent now have women on their boards: in the UK among the directors of companies in the FTSE 100, only 9 percent are women.”
(Hint: If every FTSE 100 company had 11 board members, one of whom was female, what percent of these companies would have a female board member? What percent of all board members would be women? On the other hand, if 84% of F500 companies had a female board member, and every board had 20 members, what percent of all board members would be women?)
“The number of motorists willing to pay to travel on Britain's roads is falling, a survey out today reveals. More than one in four drivers were will to pay to use city centre roads in 2002, but that figure fell to just 36 per cent in 2005, a study for the RAC said.”
“The IOC Coordination Commission were told that 80 per cent of the land had already been acquired. London Mayor Ken Livingstone added that he was hoping that, by the time the public enquiry starts at the end of next month, four-fifths of the land would have been acquired.”
“Now 78% of female veterinary medicine students are women, almost a complete turn-around from the previous situation.”
“We were eleven people obtaining those 30.000 millions. I want the 11% that corresponds to me.”
"[W]hile the majority of students who enter doctoral programs have the academic ability to complete the degree, on average only 50-60 percent of those who enter doctoral programs in the United States complete their degrees."
“Brian Kelly, the editor of U.S. News, said more than 50 percent of the presidents, provosts and admission deans who were sent the annual survey of colleges’ reputations continued to fill it out. ‘We think the vast majority of presidents and academics are still supporting the survey,’ he said.”
“Strokes have tripled in recent years among middle-aged women in the U.S., an alarming trend doctors blame on the obesity epidemic. Nearly 2-percent of women ages 35 to 54 reported suffering a stroke in the most recent federal health survey, from 1999 to 2004. Only about half a percent did in the previous survey, from 1988 to 1994.”
“Roughly one-third of all eligible Americans, 64 million people, are not registered to vote. This percentage is even higher for African-Americans (30 percent) and Hispanics (40 percent).”
Source 1: “[P]eople with gum disease have a 25 percent greater risk of heart disease than those with healthy gums.”
Source 2: “Researchers have found that people with periodontal disease are almost twice as likely to suffer from coronary artery disease as those without periodontal disease.”
"The New England Common Assessment Program (NECAP) is probably one the most challenging. The NY Regents might be a little bit more challenging; Massachusetts, the MCAS, may also be. But [the NECAP] is in the top 2 or 3% of the most challenging state assessments."
Logic
“The AMA is for Obama’s health plan, but only 29% of doctors belong to the AMA, so 71% are opposed to Obama’s health plan.”
"About 21% of American Children will see at least two live-in partners of their mothers by the time they're 15. And an additional 8% will see three or more."
Factoids
“12%: The percentage higher for searches of the word ‘guacamole’ in Wisconsin than in Pennsylvania.
“5%: The percentage higher for ‘baba ganoush’ searches in Pennsylvania than in Wisconsin.”
PROBABILITY
General probability
“In theory, if you were to buy 50 tickets and your neighbor bought one, neither of you would have a better or worse chance of winning, We like to say it only takes one ticket to win."
“In addition, a person's odds of becoming obese increased by 57 percent if he or she had a friend who became obese over a certain time interval. If the two people were mutual friends, the odds increased to 171 percent.”
Presenter [University Challenge, BBC2]: "In statistics, in data which are binomially distributed, individual values may be placed in one of two mutually exclusive categories such that the sum of the probabilities of occurring in the categories is what value?"
Answer given: "Unity"
Presenter: "No, it's one, or a hundred percent."
"Probability -- the chance, or likelihood, of a certain/particular event occurring which can be expressed as a quantitative description, often ranging from 0 (rare event) to 1 (common event)."
“Up to 69 you have a one in six chance of getting cancer. After 70 it drops to one in three.”
Interviewer: “You told these men in Houston that a cure was, in a memorable phrase, 100% possible.”
Response: “Possible. Is that a guarantee?”
Denmark politician: “Don’t provide us with too many moving targets, because it is already a very very complicated process. I need fixed targets, and figures that are certain, and not too many considerations of uncertainty and risk and things like that.”
”One can't really say anything meaningful about probability without actual data.”
“It is Friday 13th today and though it is still only ten in the morning some awfully unlucky things have happened. I stubbed my toe; the cat caught a shrew and left it in the middle of the kitchen floor, which was unlucky for me because I almost stepped on it, and was even more unlucky for the shrew. It is a black cat too. Clear evidence that superstition works, even for small rodents. Or perhaps not. Yesterday I broke my fingernail, but it wasn’t Friday 13th then, so that wasn’t the fates being lined up against me, it was just an accident.”
"Is there one New Yorker in a hundred who knows what the morning line is? (It’s the track oddsmaker’s estimate of how the public will bet each horse in a race, expressed in probabilities like 3/1 or 7/2.)"
"Did you hear about the statistician who took a bomb with him whenever he got on an airplane? He did this as a safeguard against terrorism, reasoning that although the chance is low that a terrorist will bring a bomb onto a particular airplane, the chance is really low that two people will bring bombs onto the same plane."
Newspaper report: “Statistically, there's a 1 in 3,200 chance someone could be hit by one of the 26 objects...expected to crash into Earth's surface [in September].”
Headline: "NASA warns: Look out below! There's a 1 in 3,200 chance a piece of satellite will hit you.”
“Strangely, DNA experts are required to give probabilities for their evidence of matching; fingerprint expert[s] are forbidden to.”
“Odds of becoming a top ranked NASCAR driver: 1 in 125 billion.”
(Check out the world population.)
"Picture yourself behind the wheel on a dark and shadowy night, watching the windshield wipers bat away the rain and wondering, 'What are the odds I’m going to hit a deer?' The answer would be one in 102 if you live in Virginia."
See also Drivers_beware_of_deer “Drivers beware of deer” in this issue.
"The forecasters were predicting only a 10% or 20% chance of rain in Dunedin yesterday, but it turned out to be 100%."
"There’s still time to vote, but with forecasters giving Republicans anywhere from a 75% to 113% chance of capturing a Senate majority, it isn’t too early to explain the result."
Conditional probability
“Texas beats Ohio State in their opening game of the season [Saturday Sept 10 2002]. The sportscasters … observed that of the 14 teams who have previously played in the championship game [at the end of each season] 5 have suffered an earlier defeat. ‘Thus,’ they conclude, ‘Ohio State can still make it to the championship game, but their chances are now less than 50%.’"
“Thomas Bayes … was … the mathematician who formulated a probability theorem that can be used to solve problems that stymie conventional statistics. The crux of his theorem can be stated as follows: “The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening.”
“British experts studied more than 17,000 children born in 1970 for about four decades. Of the children who ate candies or chocolates daily at age 10, 69 percent were later arrested for a violent offence by the age of 34. Of those who didn't have any violent clashes, 42 per cent ate sweets daily.”
“Here is the rub: Apple is so big, it’s running up against the law of large numbers. Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.”
"It is ridiculous to believe that the legal profession has to get involved with the complex parts of statistics. The statistics of gambling uses the frequency approach to statistics, and that is straightforward. The reasoning involved with Bayes is more complex and we cannot expect juries to accept it."
Weather
“Glasgow's odds [on a white Christmas] had come in at 8-11, while Aberdeen was at 5-6, meaning snow in both cities is considered almost certain.”
“[Researchers at the University of Washington] found people in Seattle didn't have much of a grasp for what the probability forecast [of rain] really means, but found the numbers helpful in planning their day.”
“In Minnesota the temperature was predicted to reach -31F (-35C) but meteorologists warned that accompanying wind chill could make it feel twice as cold.”
“Environment Canada is predicting the vast majority of the country will see below-normal temperatures — and snowfall — through March. In Thunder Bay and the Northwest, the probability of this is seen as between 50 and 60 per cent. Which means the weather office could be only half-right."
Unlikely events
“He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date -- March 2. But Casey-James was delivered at 12.04 am on March 3 ....”
“The English language currently comprises roughly a million words. Discounting new words that are added every day, and those occasionally lost to posterity, the possibility of forming a three-word combination is therefore a million cubed, or a quadrillion--that's followed by 216 zeros.”
“Everybody trips on stairs at some time or other. It has been calculated that you are likely to miss a step once every 2,222 occasions you use stairs, suffer a minor accident once in every 63,000 uses, suffer a painful accident once in every 734,000, and need hospital attention once every 3,616,667 uses.”
Risk of dying
“In the US, those in the poorest households have nearly four times the risk of death of those in the richest.”
“You’re more likely to die in a fire in Strathclyde than anywhere else in the country.”
“HIV patients in low socio-economic classes are 89 per cent more likely to die than better-off people with the infection, claims a study of 2684 adults in the Journal of Health Care for the Poor and Underserved."
“A ten-year study of men in Wales found that those who had sex twice or more a week were 50% less likely to have died than those who had it less than once a month.”
“Long-term, serious smokers have a 50% chance of dying.”
"The Times' leader of 28 February tells us that taking regular dose of certain vitamins 'can actually increase the risk of mortality by five per cent.' Since the 'risk of mortality' is already 100 percent this is very worrying.”
"People who were given a vitamin D supplement had a 7-per-cent lower risk of premature death than those who were not. …. It appears to be a life extender."
“Individuals who are 50-59 years-old and from the poorest fifth of the population are over ten times more likely to die than their peers from the richest fifth.”
“Last week, a formatting error led to us inadvertently suggesting that there was a one in 1,019 chance of the world ending before this edition. That should have read, er, one in 10^1 – rather less likely. Sorry. Feel free to remove the crash helmet.”
“HIV patients in low socio-economic classes are 89 per cent more likely to die than better-off people with the infection, claims a study of 2684 adults in the Journal of Health Care for the Poor and Underserved (Nov).”
“Of the 29,000 people who may get cancer from CT scans done in 2007, about 50 percent will die, the researchers estimated.”
"[Psychologist Carolyn] Aldwin …used data from a huge, long-term study of male veterans enrolled in the VA health care system. She focused in on older men - average age 65 - who said they suffered stress. She found it didn't matter whether it was caused by a major life event or by day-to-day problems. The harmful effect was the same. 'These stressed-out men had a 32 percent increased risk of dying.'"
Fifty-fifty chances
“This summer there's about a 50 per cent probability that there will be above normal temperatures for much of Britain and Europe.”
“’I realize I don't have a chance, but nobody's got a chance. So the way I look at it, I have a 50-50 chance -- either I win it or someone else wins it,’ reasoned Barrie Green, 60, after buying a single ticket Monday afternoon ….”
“Europe's particle physics lab, CERN is losing ground rapidly in the race to discover the elusive Higgs boson, or 'God particle', its US rival claims ... the US Fermilab says the odds of its Tefatron accelerator detecting the famed particle first are now 50-50 at worst and up to 96% at best.”
“It’s only fifty-fifty you’ll get him back if you pay it,” he said factually …. I tried to smile. “Two to one, not bad odds at the track.”
The New York Times has printed two alternative covers of the Sunday Times magazine, for random distribution to subscribers around the country. That explains a headline that appeared in the week preceding the Super Bowl: "This Week's Cover Accurately Predicts the Super Bowl Winner (Half of the Time)"
Perfect predictions
“Events like this send a shiver down the spine, but the math behind strange coincidences shows that most people simply have a poor grasp of statistics. The odds against meeting someone else at a party with your birthday are not 365 to 1. In a room with just 23 people, the chances that two of them will share the same birthday are better than even.”
“[Persi Diaconis] proved that it takes seven shuffles to perfectly randomize a pack of cards.”
“[T]here is a reasonable chance—not a certainty, mind you, but a reasonable chance—that the second half of 2009 will surprise us on the upside. …. [T]his seemingly high growth scenario … [would follow] directly from the arithmetic of hitting bottom. …. Eventually those huge negative numbers [associated with the decline of some GDP components] must turn into (at least) zeroes … [and] … almost certainly do better. …. None of these events are probabilities; they are all certainties. The only issue is timing, about which we can only guess.”
“Hey, how many people do you need to have in a room to guarantee the chance that at least two of them would have the same birthday?”
“I don’t know. Three hundred sixty-four.”
“Hah! Twenty-three. At least two out of every twenty-three people will have exactly the same birthday. Statistical odds. A lot of life is coincidence.”
Gambling
“Well, fairer in the sense that everyone's got an equal chance, but not fair in the sense that, well, it is literally a lottery.”
“We cannot increase the probability of winning a [lottery] prize as this is fixed. However, we can increase the amount we can expect to win if we do strike [it] lucky …. [C]hoosing popular combinations of numbers decreases the expected value of your ticket as you have a higher probability of having to share your prize if you win. …. [W]hen you select your numbers, you may as well try to choose a less popular combination that might increase your expected value. Unfortunately, it is not possible to determine what exactly the unpopular combinations are: there is not enough data.”
Expected value
"So for a company that thought there was a 60 percent chance that it would have to pay $1,000 on a claim, and a 40 percent chance it would have to pay $2,000, its required reserve would rise from $1,000, the most probable number, to $1,400 — the average of the probabilities."
STATISTICS
Statistical measures
“There are now more overweight people in America than average-weight people. So overweight people are now average. Which means you've met your New Year's resolution.”
“Ministers define child poverty as children living on less than 60% of median income, adjusted for composition of the household. The median is the halfway point between the nation's highest and lowest income.”
“Two quantities were almost equal on average, according to … the study’s lead author: the fraction of MHC genes shared, and the woman’s number of extra partners. In other words, if the man and woman had half the genes in common, the woman would have on average nearly half a lover on the side.”
“The other kind of variable is called a quantitative variable in which numbers are used to order or to represent increasing levels of that variable. The simplest example of a quantitative variable is a dichotomous variable such as sex or genre, where one category is seen as representing more of that quality than the other. For example, if females are coded as 1 and males as 2, then this variable may be seen as reflecting maleness in which the higher score indicates maleness. The next simplest example is a variable consisting of three categories such as social class, which may comprise the three categories of upper, middle and lower. Upper class may be coded as 1, middle as 2 and lower as 3, in which case lower values represent higher social statuses. These numbers may be treated as a ratio measure or scale. Someone who is coded as 1 is ranked twice as high as someone who is coded as 2 giving a ratio of 1 to 2.”
“A separate opinion poll yesterday suggested that 50% of obese people earn less than the national average income.”
"The Bureau of Labor Statistics (BLS) projects that the U.S. will add 15.3 million new jobs between 2008 and 2018, and a whopping 15 out of 30 jobs with the most projected openings and vacancies will pay wages that are above the national median wage for all workers in the United States."
“The most important statistics in football are wins and losses and whether or not a team can outscore his opponent.”
“Let's start with T. Rowe Price's U.S. stock fund lineup. I have plugged in 15 of its largest actively managed U.S. equity funds. Let's start at the top with T. Rowe Price Blue Chip Growth. [Note] that T. Rowe Price Growth Stock is a tight fit with a 1.00 correlation--the highest it can get. So, we know that owning those two large-growth funds is rather redundant. [Note] that Small-Cap Value has the lowest correlation at 0.91 – thus, it's a good choice for diversification purposes.”
"The main philosophical question is, how should [the recession] be treated? … Should it be treated as an outlier and done away with?"
“Resolved Question: What is the definition for zero correlation?”
“Best Answer - Chosen by Voters: .... Therefore, the closer the score is to 1, the stronger the correlation (or the closer the link between 2 things) and the closer the score is to 0, the weaker the correlation (or the more distant the link between 2 things). …. In summary, a zero correlation is a score which shows that there is no relationship/link between 2 things. .... “
"Oh, aren't people stupid! Do you know the average IQ is only 100? That's terribly low, isn't it? One hundred. It's no wonder the world's in such a mess."
"Chi-squared was calculated as 18 995 and was significant at both the 95% and 99% significance levels."
"The UK mean income in 2011 was £27,000, but the median income was £21,500. This means that 50 per cent of people earned less than £27,000."
From testimony by Michael Gove, British Secretary of State for Education, before their Education Committee:
"Q98 Chair: [I]f 'good' requires pupil performance to exceed the national average, and if all schools must be good, how is this mathematically possible?
"Michael Gove: By getting better all the time.
"Q99 Chair: So it is possible, is it?
"Michael Gove: It is possible to get better all the time.
"Q100 Chair: Were you better at literacy than numeracy, Secretary of State?
"Michael Gove: I cannot remember."
"So, all you've gotta do is set up a null hypothesis and try and prove it.
And when you can't prove it, well that means your original hypothesis must be true. …. You said you believe Cassius returns to the scene of the crimes. And you've got photos of every murder. So set up a hypothesis of, say, Stephen Hawking is Cassius... which gives you a null hypothesis of Stephen Hawking is not Cassius. So, go through the photos and try and prove the null... that Rolling Thunder is not Cassius. If you can, that means your hypothesis is incorrect. If you can't... then depending on your 'P' value of course... you've statistically proven your hypothesis must be true. Or that Stephen Hawking is Cassius. Yeah. Some of us didn't sleep our way through Logic and Stats at Harvard."
"A survey was conducted, taking a single image from each of 323 user ids. 23 (7.1%) of those images contained undesirable nudity. From this we can infer that the true proportion of undesirable images in Yahoo webcam is 7.1% ± 3.7% with confidence 95%."
“A few years ago I performed surgery to correct a displaced abomasums ... in a dairy cow .... Ben, the owner of the farm, asked how likely the cow was to have problems after the surgery. Trying to put it in terms that he could relate to I said, ‘If we did this procedure on 100 cows, I expect about 10 to 15 would not completely recover within a few weeks of surgery.’ He paused a moment and said, ‘Well that’s good because I only have 35 cows.’’”
".... President Dwight Eisenhower express[ed] astonishment and alarm on discovering that fully half of all Americans have below average intelligence ....”
"Statistical Significance."
"Definition: A mathematical technique to measure whether the results of a study are likely to be true. Statistical significance is calculated as the probability that an effect observed in a research study is occurring because of chance."
Surveys
Survey question: “Is Snape good or bad? Yes or No?" As of June 7, there were 33 (29%) votes for "No."
“’Only 2% of the people we interviewed said they didn't believe in God,’ says Ali Carkoglu, co-author of a 2006 study of religious attitudes. ‘Given that we had a 2% margin of error that could mean nobody,’ he added. ‘In any case it takes considerable courage for a Turk to admit to a stranger that they [sic] are atheists.’"
“Having a husband creates an extra seven hours a week of housework for women, according to a University of Michigan study of a nationally representative sample of U.S. families. For men, the picture is very different: A wife saves men from about an hour of housework a week.”
“Researchers at Cardiff University School of Social Science claim errors made by the Hawk-Eye line-calling technology can be greater than 3.6 mm – the average error quoted by the manufacturers.”
“Women are more likely than men to have academic partners (40% of female faculty in our sample versus 34% of male faculty). In fact, rates of dual hiring are higher among women respondents than among men respondents (13% versus 7%). This means that couple hiring becomes a particularly relevant strategy for the recruitment and retention of female faculty.”
"Responses (29,760) to a survey of American public and private high-school students:
- "30 percent said that they had stolen from a store within the past year.
- "42 percent said that they sometimes lie to save money.
- "64 percent said that they had cheated on a test during the past year.
- "26 percent admitted that they had lied on at least one or two questions on the survey.
- "93 percent said that they were satisfied with their personal ethics and character.
- "77 percent said that when it comes to doing what is right, I am better than most people I know.”
"On another occasion, Bailey and other staffers spent hours voting repeatedly to manipulate a television opinion poll on Palin’s decision to reject part of the federal government’s economic stimulus funding."
“In a study involving 11,000 patients hospitalized for nearly four dozen ailments, researchers found that, across the board, women reported suffering pain more acutely than men did. …. The patients were asked to self-report their pain – in most cases to a female nurse.”
“This past week, Obama sports a 53-44 [favorable/unfavorable] rating among women, but 43-54 among men. That's a whopping 20-point gender gap. .... In 2008, President Barack Obama won women 56-43, while narrowly edging out John McCain among men 49-48. That 12-point gender gap appeared massive at the time, but it appears that we're headed toward an even bigger margin in 2012.”
"We're spending $70 per person to fill this [the American Community Survey] out. That’s just not cost effective," he continued, "especially since in the end this is not a scientific survey. It’s a random survey."
“While the study tracked just under 400 babies, the researchers said the results were statistically significant because it relied on weekly questionnaires filled out by parents.”
“I remember a few years ago looking at peer rankings of graduate departments and being delighted to discover that among statistics departments my own alma mater was in the top ten (although my trust in the process was tempered by the knowledge that, despite its lofty ranking, Princeton’s statistics department had been disbanded decades earlier.)”
“As they do on many obscure policy issues, Americans polarize sharply along partisan lines when they learn that President Barack Obama supports a repeal of the 1975 Public Affairs Act. …. There's one striking problem here: The 1975 Public Affairs Act does not exist. …. In a series of surveys that polled national samples about similarly fictitious or otherwise unknown legislation, [pollsters] found 20 to 40 percent of Americans were willing to offer opinions on laws they have never heard of.”
“Most uses of the classical tools of statistics have been, are, and will be, made by those who know not what they do.”
A Vancouver demographer comments, 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.
Sample size
“'There's virtually nothing or any conclusion that anyone could draw from 500 samples,' said a USDA spokesman.”
“The methodology behind the ICS survey is flawed. There were only 2000 respondents, a small number for any statistical survey, who were asked to nominate which firms of services they used and how that rated them.”
"You can prove any silly hypothesis by running a statistical test on tons of data."
“A somewhat comic, though not necessarily typical reaction to the use of sampling by a Federal agency occurred in 1936 when the National Resources Planning Board published its report Consumer Incomes in the United States, …. It showed a highly skewed distribution of income, with the top 10 per cent of the families and single individuals receiving 36 per cent of the income. …. [T]his was the first time that a Federal agency had published such data, and it was based on a sample. The U.S. Chamber of Commerce issued a blast against this report, which it considered it to be socialistic propaganda. It said that the estimates were based on ‘less than a 1 per cent sample, and a random sample at that!’”
Correlation/Causation
“If you play golf, you could be adding five years to your life. A new study shows that the death rate for Scandanavian golfers is 40% lower than for those who don't golf. The reason may be simple: Golfers walk, spend time outdoors, and developing social relationships. …. Researchers have not ruled out the possibility that golfers simply live healthy lives in general, but they believe that the game itself does have health benefits.”
“Let’s look at basketball …. The 1993 college basketball playoffs started with 64 teams. Of these, 15 were from schools with accredited library education programs. That’s an amazing statistic by itself, when you consider that there are only slightly more than three times that many library education programs in the United States, and that some of these don’t compete athletically in Division I. However, those 15 schools also went on to win 28 of the 63 games played, while losing only 14. The reason that there were only 14 losses is that the championship school has a library education program. So does the runnerup. Indeed, what sportswriters call the Final Four included three schools with accredited library education programs. …. Do I believe a single word of what I have just written? Of course not, although I have seen ‘research’ studies … for which the hypotheses were no more credible.”
“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.”
“[The researcher] said the familiar LSU fight song… slowed down their decision-making performance for a longer time than even a standard ringtone."
“I can show you a bar graph where free and reduced lunch has the worst test scores in the state of South Carolina .... You show me the school that has the highest free and reduced lunch, and I'll show you the worst test scores, folks. It's there, period.”
“Last year, nearly 5,000 teens died in car crashes. Making it safer for a teen to be in a war zone than on a highway.”
“When the average age of the halftime act [at the Superbowl] is older than 47, the NFC team, the New Orleans Saints this year [2010], has won nearly two-thirds of the time, and the games are about three times as likely to be blowouts.”
An article describes two brands of athletic wear that are claimed to optimize performance: “A lot of these products are a sort of merchandized superstition. …. [A French surfer states,] ‘But if wearing the thing makes you think you feel or perform better, who cares?’”
"The relationship between an area's income and mortality is so striking," the report says, "that on average, every $10,000 increase in an area's median income appears to buy its residents another year of life."
"[A] former Colorado Springs state senator ... once claimed, 'I don’t know whether we need a bill on teen pregnancy because statistics show teen pregnancy drops off significantly after age 25.'”
“[The] ballad ‘Someone Like you’ … has risen to near-iconic status recently, due in large part to its uncanny power to elicit tears and chills from listeners. …. Last year, [scientists] at McGill University reported that emotionally intense music releases dopamine in the pleasure and reward centers of the brain, similar to the effects of food, sex and drugs. …. Measuring listeners' responses, [the] team found that the number of goose bumps observed correlated with the amount of dopamine released, even when the music was extremely sad.”
Cleveland Clinic doctors Marc Gillinov and Steven Nissen describe a study by Wayne State University researchers who rated the smiles of 230 baseball players who played before 1950 based on pictures in the Baseball Register. Then they looked to see how long the players lived on average: No smile, age 73; partial smile, 75. Those with a full smile made it to 80.
"Teams that touch more at the beginning of the season win more over the course of the entire season. The two touchiest teams in the study, the Boston Celtics and Los Angeles Lakers, finished the season with two of the NBA's top three records, and the Celtics Kevin Garnett was the touchiest player in the league by at least a 15% margin, said … one of the study's authors."
“Teams that touch more at the beginning of the season win more over the course of the entire season. The two touchiest teams in the study, the Boston Celtics and Los Angeles Lakers, finished the season with two of the NBA's top three records, and the Celtics Kevin Garnett was the touchiest player in the league by at least a 15% margin, said … one of the study's authors.”
“At issue was how highly correlated the prices of various subprime mortgage bonds inside a CDO might be. Possible answers ranged from 0 percent (their prices had nothing to do with each other) to 100 percent (their prices moved in lockstep with each other). Moody’s and Standard & Poor’s judged the pools of triple-B-rated bonds to have a correlation of around 30 percent, which did not mean anything like what it sounds. It does not mean, for example, that if one goes bad, there is a 30 percent chance that the others will go bad too. It means that if one bond goes bad, the others experience very little decline at all.”
Correlation/Regression/Extrapolation
"[A] boss taught his twenty-something[-old] trainees ... how to conduct a 'two-handed regression'": "When a scatter plot failed to show the significant 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."
"If you took the CEOs with the best track records and brought them in to run the businesses with the worst performance, how often would those companies become more profitable? According to [an MIT] economist …, who has studied the effects of hundreds of management changes, the answer is roughly 60%. That isn't much better than the flip of a coin. …. The real force in corporate performance isn't the boss, but regression to the mean: Periods of good returns are highly likely to be followed by poor results, and vice versa."
"Here is the rub: Apple is so big, it’s running up against the law of large numbers. Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger."
“The quants have arrived at the Academy [of Motion Picture Arts and Sciences]. …. The goals in making ... predictions extend beyond [Oscar night]. Dr. Rothschild [Microsoft Research economist] is testing whether surveying people online about Oscar patterns—for example, does winning best-adapted screenplay correspond with winning best picture?—is a method that can be translated to forecasting in other areas. If it works, ‘We can apply it to all sorts of other things we don't have data for,’ Dr. Rothschild said."
“At issue was how highly correlated the prices of various subprime mortgage bonds inside a CDO might be. Possible answers ranged from 0 percent (their prices had nothing to do with each other) to 100 percent (their prices moved in lockstep with each other). Moody’s and Standard & Poor’s judged the pools of triple-B-rated bonds to have a correlation of around 30 percent, which did not mean anything like what it sounds. It does not mean, for example, that if one goes bad, there is a 30 percent chance that the others will go bad too. It means that if one bond goes bad, the others experience very little decline at all.”
Contradictory results
British Medical Journal, v. 336, p. 244: "Much of the data on overweight people and obesity are limited, equivocal and compromised."
British Medical Journal, v. 336, p. 245: "The adverse effects of obesity on health are well established, serious, and causal."
A1. "Most Trials are unethical because they are too large."
A2. "Small Trial are unethical."
B1. "A significant result is more meaningful if obtained from a large trial."
B2. "A given significant P-value is more indicative of the efficacy of a treatment if obtained from a small trial."
B3. "For a given P-value, the evidence against the null hypothesis is the same whatever the size of the trial."
"The potential public health benefits are huge" according to Dr. Paul M. Ridker, lead author of a controlled study of Crestor versus, a statin drug used to lower the risk of heart disease, versus a placebo.
One doctor’s reaction: "It's a breakthrough study. It's a blockbuster. It's absolutely paradigm-shifting."
Another doctor’s reaction: Crestor "can cause potentially serious kidney toxicity that is not seen with other cholesterol-lowering drugs, and it is the only drug of its type that caused rhabdomyolysis, a life-threatening adverse muscle reaction...there is no medical reason for you to be taking Crestor when there are three safer drugs on the market for reducing cardiovascular events."
"Experts disagree over the issue, with some saying there is no proof light drinking harms the baby, while others believe the evidence is inconclusive."
Ethics
"[My kids' science-fair] experiments never turned out the way they were supposed to, and so we were always having to fudge the results so that the projects wouldn't be screwy. I always felt guilty about that dishonesty ... but now I feel like we were doing real science."
"The mechanics of the ghostwriter’s job are fairly simple, [an anonymous ghostwriter] says. Early on, a medical-communications agency and its pharmaceutical-company sponsors will agree on a title for an article and a potential author, usually an academic physician with a reputation as a 'thought leader.' The agency will ask the thought leader to 'author' the article, sometimes in exchange for a fee. The ghostwriter will write the article, or perhaps an extended outline containing the message the company wants to transmit, and send it along to the physician, who may make some changes or simply sign it as written and submit it to a journal, usually scrubbed of any mention of the ghostwriter, the agency, or the pharmaceutical company. [The ghostwriter] says he rarely even sees the published articles he writes."
"When I was in NYC I went to this party by group of Japanese bio-scientists. There, one guy told me about how the biggest pharmaceutical company in Japan did their statistics. They ran 100 different tests and reported the most significant one. (This was in 2006 and he said they stopped doing this few years back so they were doing this until pretty recently…) I’m not sure if this was 100 multiple comparison or 100 different kinds of test but I’m sure they wouldn’t want to disclose their data…"
"[A researcher] has been funded in part by the U.S. government’s Monty Python-esquely named Office of Research Integrity’s Research on Research Integrity Program."
Studies
"I study the case histories of all lightning fatalities. Often, if people had gotten inside 5 or 10 minutes earlier, they would be alive."
"People who have personalised number plates on their cars are most likely to live in Scotland, a survey has found."
"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."
"[M]ale participants tended to perform worse on a cognitive task …following the mixed-sex interaction compared to the same-sex interaction. …. Also, this effect was even stronger when the male participant reported higher attraction to the opposite-sex person they [sic] were interacting with. …. It should be noted that there was evidence that women's cognitive performance did tend to decline after mixed-sex interactions if they reported having a relatively strong goal to impress the opposite-sex other."
"There has always been a question about just how much of a forecasting mechanism markets are. Hence the saying that stocks have correctly predicted 15 of the past nine recessions."
An article describes two brands of athletic wear that are claimed to optimize performance: “A lot of these products are a sort of merchandized superstition. …. [A French surfer states,] ‘But if wearing the thing makes you think you feel or perform better, who cares?’”
"Persons with higher numeracy rely more on the numerical information depicted in the graph, whereas persons with lower numeracy seem to be confused when they are guided towards these numbers."
"[A] recent peer-reviewed study found that early-voting states received more federal dollars after a competitive election — so long as they supported the winning candidate."
"Biostatistics vs. Lab Research" (3.5 minute cartoon video depicts conversation between biostatistician and lab scientist).
"[A] political science professor at Southern Connecticut State University … has developed a mathematical formula to assess presidential success. … Her model, she said, 'explains 50 percent in the variance in the quality of the president, which is awfully good ….'"
Charts
Nicholas Taleb wrote, "My classical metaphor: A Turkey is fed for 1000 days—every day confirms to its statistical department that the human race cares about its welfare 'with increased statistical significance'. On the 1001st day, the turkey has a surprise."
Rachel Maddow commented, "Why even bother making a graph? [Laughing] I'm sorry. It looks like that is what, a third of 12,000? Not to scale….. The worst bar graph in the history of cable news."
Article states, "Drivers 85 and older still have a higher rate of deadly crashes than any other age group except teenagers."
Online blog provided "Patience of Mobile Web Users" chart.
Check out the NOV point. See also Freethought blogs and Simply Statistics blog
“The difference in mortality rates [in deaths per 100,000 women] between black women [top curve] and white women [bottom curve] with breast cancer has widened since 1975, in part because black women have not benefited as much from improvements in screening and treatment. Among the states with available data, Tennessee has the largest gap—with nearly 14 black women dying for every one white woman.” (emphasis added)
"Chi-squared was calculated as 18 995 and was significant at both the 95% and 99% significance levels."
"The UK mean income in 2011 was £27,000, but the median income was £21,500. This means that 50 per cent of people earned less than £27,000."
From testimony by Michael Gove, British Secretary of State for Education, before their Education Committee:
"Q98 Chair: [I]f 'good' requires pupil performance to exceed the national average, and if all schools must be good, how is this mathematically possible?
"Michael Gove: By getting better all the time.
"Q99 Chair: So it is possible, is it?
"Michael Gove: It is possible to get better all the time.
"Q100 Chair: Were you better at literacy than numeracy, Secretary of State?
"Michael Gove: I cannot remember."
"So, all you've gotta do is set up a null hypothesis and try and prove it.
And when you can't prove it, well that means your original hypothesis must be true. …. You said you believe Cassius returns to the scene of the crimes. And you've got photos of every murder. So set up a hypothesis of, say, Stephen Hawking is Cassius... which gives you a null hypothesis of Stephen Hawking is not Cassius. So, go through the photos and try and prove the null... that Rolling Thunder is not Cassius. If you can, that means your hypothesis is incorrect. If you can't... then depending on your 'P' value of course... you've statistically proven your hypothesis must be true. Or that Stephen Hawking is Cassius. Yeah. Some of us didn't sleep our way through Logic and Stats at Harvard."
"A survey was conducted, taking a single image from each of 323 user ids. 23 (7.1%) of those images contained undesirable nudity. From this we can infer that the true proportion of undesirable images in Yahoo webcam is 7.1% ± 3.7% with confidence 95%."
“A few years ago I performed surgery to correct a displaced abomasums ... in a dairy cow .... Ben, the owner of the farm, asked how likely the cow was to have problems after the surgery. Trying to put it in terms that he could relate to I said, ‘If we did this procedure on 100 cows, I expect about 10 to 15 would not completely recover within a few weeks of surgery.’ He paused a moment and said, ‘Well that’s good because I only have 35 cows.’’”
“.... President Dwight Eisenhower express[ed] astonishment and alarm on discovering that fully half of all Americans have below average intelligence ....”
Statistical Significance.
Definition: A mathematical technique to measure whether the results of a study are likely to be true. Statistical significance is calculated as the probability that an effect observed in a research study is occurring because of chance.
GENERAL QUANTITATIVE REASONING
Arithmetic
“Of Italy's 151 Series A players, 52 are non-white, with Inter fielding 19, Juventus 12, AC Milan 13, AS Roma 12 and Udinese 10. Messina has eight.”
“Twenty-six new cases of the inflammatory lung disease sarcoidosis [were seen amongst rescuers] in the first five years after 9/11. [Only f]ive or fewer rescuers got sarcoidosis annually before 9/11.”
“With the [CT] state economy in the tank, this is the year of givebacks. .... [S]tate Rep. Terry Backer ... says the general public often is not aware that state legislators earn a base salary of 28,000 dollars per year for a part-time job with a pay rate that has been frozen for nine years.
"On principle, Backer says he does not want to give up a day's pay to be in solidarity with the state employee unions. 'I would rather take the 40 dollars and donate it to the food pantry in my town than do some baloney solidarity thing,' Backer said."
"According to the World Bank, $1.3 billion in remittances is sent each year to Kenya, a process that costs about $110 million in fees. By using bitcoin’s peer-to-peer technology to avoid banks and wire-transfer companies like Western Union, BitPesa hopes to reduce these fees by a third, saving ordinary Africans $74 million annually." (emphasis added)
Logic
“Q. How many punnets [a small light basket or other container for fruit or vegetables] of strawberries are eaten each day during the Wimbledon tournament? Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?”
“In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.”
“Fewer names appear in the top 100 than ten years ago.”
“[Hanson is the l]argest aggregates producer in the world and 3rd largest in the USA.”
“Mr Davis was forced out after his division showed flat revenue growth.”
“Michael Ballack's heart must have skipped a beat for a microsecond.”
“The RSS [Royal Statistical Society] has global standing. Of its 7000 members, about one in four is drawn from over 50 countries.”
“By 2023, more than half of all American children will be minority, the Census Bureau projects.”
"Connecticut has the 2nd highest incidence of breast cancer in the U.S. Connecticut. DON'T settle for second place!"
Big numbers
On the subject of congestion on the London Underground, “last year 976 million of us used the tube."
"A Malaysian man was speechless when he received a $218 trillion phone bill and was ordered to pay up within 10 days or face prosecution."
In a restroom in the Administration Building of the Arizona State Government complex there is a sign that says: "Everyday each person in this building uses an average of 15 gallons of our precious water."
"This costs about a billion dollars. I'm not going to say how many zeros after it, but it's a lot."
Newspaper report: "Irene's bill in Vermont could top half-billion dollars."
Headline: “COST: Irene repairs could top 500,000 dollars."
Twice and other factors
"Britain has been basking in the early onset of spring with temperatures almost twice as warm as the same time last year."
"Phew! Twice as warm as Corfu … It's not often we put Corfu in the shade weatherwise, especially at this time of the year. But while the Greek holiday spot could only manage a paltry 8C [46F] yesterday, Britons basked in the sun as temperatures reached 16C [60F] yesterday."
"'We're off by a factor of a lot.'--Tony Miller, founder of Carol.com a company that hoped to sell about 200 healthcare policies a month but after eight months sold but a total of 160."
"If you do not have so many players, what can you do? There are 95 registered Brazilian players in the Championship League, 94 French players and 45 English players. When you have twice as few players as other countries it is difficult."
"Retail sales figures in the US on Wednesday were almost twice as bad as had been expected."
“Retail sales figures in the US on Wednesday were almost twice as bad as had been expected.”
Units of measure
"One primary school in East London has a catchment area of 110 metres."
"To convert kilometres to miles multiply by .6214; kilometres/hour to miles/hour multiply by .6117.”
"Despite the ceaseless terrorist attacks on the country's infrastructure and particularly the oil industry, the value of the Iraqi dinar has continued to rise-in November, from D1,410 to the dollar to D1,480. That is obviously good for the vast majority of people whose pay comes in dinars."
"If we can increase IQ by three to four points in the whole population, we can have fewer children at the low end and more Einsteins at the high end."
“The afternoon wave of [U.S. Open] starters began their first round Thursday in hot, sticky conditions and finished in cool, breezy weather on Friday. Luke Donald described the difference as ‘180 degrees’ ….”
"Only 18 percent of American adults can calculate how much a carpet will cost if they know the size of the room and the per yard price of the carpet, according to a federal survey." (emphasis added)
Extrapolation and trends
“The current rate of shrinkage [in 2005] they calculate at 8% per decade; at this rate there may be no ice at all during the summer of 2060.”
“Mr. Romney started Bain Capital in 1984 with an initial fund of about $40 million. During the fourteen years he ran it, Bain Capital's investments reportedly earned an annual rate of return of over 100 percent, potentially turning an initial investment of $1 million dollars into more than $14 million by the time he left in 1998.”
"The population of the USA has topped 300 million for the first time. It reached the figure sometime in October [2006]. It passed the 200 million mark in 1967. The U.S. census bureau, which reports the figure, calculates that, if current trends continue, it is expected to reach 400 billion by 2043."
Mathematics
"The explanation rests in a mathematical formula created by the baseball analyst Bill James and introduced in the 1980 Baseball Abstract. James determined that the record of a baseball team could be approximated by taking the square of team runs scored and dividing it by the square of team runs scored plus the square of team runs allowed. Because of its similarity to the geometric method for determining the sum of the angles in a right triangle, he called it the Pythagorean theorem."
"When do you draw the line? When do you take action to avoid that logarithmic point where things take off exponentially?"
"Their visual acuity is only fractionally – not geometrically – better than that of the common primates from which they were engineered."
“After two months of trying to crack the code – a process that involved factoring two huge prime numbers – Mr. Moody says he succeeded in July.”
"The money involved in big-time college sports is staggering, and it grows almost exponentially every couple of years."