Journalists love to use anecdotes to enliven otherwise dry stories. Here's one from an article about a new drug:
Patient Barbara Moss, 55, was given just three months to live in November 2006 when doctors discovered her bowel cancer had spread to her liver. She did not respond to chemotherapy but after two treatments of Avastin, her grapefruit-sized tumour shrank to half its size and she was operated on by surgeons. Mrs Moss, a former teacher from Worcester, said: "…I am still here―alive. I am living proof that Avastin works."
Anecdotes are logically weak, but often psychologically compelling, and they can have the effect of slanting an otherwise neutral story. In this case, the anecdote livens up a story about a bureaucratic decision not to fund a new drug, but it's likely to influence the way the reader evaluates that decision. It's hard to read the anecdote without wondering how Britain's National Institute for Health and Clinical Excellence―"NICE"―could be so mean. Even when the same article tells you that the average lifespan of a patient taking Avastin is only six weeks longer than that of a control, the story of Mrs. Moss is what impresses us.
An additional fallacy is lurking here: How do we know that Avastin was responsible for the tumor shrinking? How does Mrs. Moss know that it "works"? All that the anecdote tells us is that the tumor shrank after―post hoc―the Avastin treatments. Perhaps the tumor spontaneously shrank, or the chemotherapy had a delayed reaction, or Mrs. Moss took an alternative medicine not mentioned in the article.
Finally, I wonder whether those who named NICE had read C.S. Lewis' That Hideous Strength. Even if they hadn't, didn't it occur to them that the acronym would sound ironic every time the institute has to make an unpopular decision?
Source: Jo Couzens, "Watchdog Says No To Costly Cancer Drug", Sky News Online, 8/24/2010
Resource: Name that Fallacy, Too!, 6/25/2010
Via: Ben Goldacre, "The Power of Anecdotes", Bad Science, 8/28/2010
New Book: Proofiness
Scientific American has a brief excerpt (see the Source, below) in its current issue from the new book Proofiness: The Dark Arts of Mathematical Deception, by Charles Seife. "Proofiness", which is clearly related to the term "truthiness" popularized by comedian Stephen Colbert, supposedly means "the art of using bad math to prove bogus arguments".
The excerpt provides an opportunity to play "name that fallacy" twice, so read the whole thing―it's short!―see whether you can recognize the two fallacies described, and then check your answers by clicking on the links below:
Source: Kate Wong, "Recommended: The 50 Most Extreme Places in Our Solar System", Scientific American, September, 2010, p. 102
Update (8/27/2010): Check out liberal pundit Eleanor Clift's column from the beginning of the month on the book. The book's title made me expect that it would have something to do with failed or bogus mathematical proofs, which would be a fascinating topic. However, Clift's column and the short excerpt suggest that it's more in the mold of Joel Best's books, or the recent Sex, Drugs, and Body Counts, which I'll be reviewing here soon. Nonetheless, math abuse is a rich topic, and here's an interesting example from Clift's column:
There are plenty of fun examples and brain teasers in this highly readable book. A 2004 paper in the journal "Nature" analyzed athletes' Olympic performances in the 100-meter dash and found that male sprinters and female sprinters were getting faster. By charting each group's progress on a line, at some point the two lines would cross―with women matching and then surpassing men around the year 2156. Women hadn't been racing competitively as long, and so their progress was greater. And if you kept stretching the lines, eventually women would be sprinting at about 60 miles per hour, and in roughly the year 2600, they would break the sound barrier. Absurd, yes, but a computer simulation done by the team of experts added heft to the paper, concluding the "momentous" day when women beat men in the 100-meter dash could come as early as 2064 or as late as 2788. Don't hold your breath.
This is an example of the dangers of straight-line extrapolation, that is, graphing data that approximates a straight line and extending the line out beyond the limits of the data. Here's a classic example from Mark Twain:
…[T]he Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago. It was eleven hundred and eighty after the cut-off of 1722. It was one thousand and forty after the American Bend cut-off. It has lost sixty-seven miles since. Consequently, its length is only nine hundred and seventy-three miles at present. Now, if I wanted to be one of those ponderous scientific people, and "let on" to prove what had occurred in the remote past by what had occurred in a given time in the recent past, or what will occur in the far future by what has occurred in late years, what an opportunity is here! … Please observe: In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
- Eleanor Clift, "Proofiness: Using Numbers to Fool People and Shape Political Debate", Politics Daily, 8/1/2010
- David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought (1970), pp. 120-122. Fischer is the only writer on fallacies that I know of to discuss a "fallacy of false extrapolation".
- Mark Twain, Life on the Mississippi, ch. 17.
Check it Out
The latest issue of The Skeptical Inquirer, available on the magazine racks but not yet on the web, is a tribute to the late Martin Gardner, which includes reminiscences by John Allen Paulos, James Randi, and others. It also includes what I presume is Gardner's last column, the topic of which is another of Oprah Winfrey's protégés, Dr. Oz, who apparently endorses homeopathy. I liked this comment:
Mainstream doctors like to tell of the homeopath who forgot to take his daily pill and died of an overdose.
There's also a long article on Nostradamus that I didn't have a chance to read, but which looks interesting.
Source: Martin Gardner, "Swedenborg and Dr. Oz", The Skeptical Inquirer, September/October, 2010, pp. 10-11
- Bad Science Theatre 2005, 11/26/2005
- Through the Looking Glass, Darkly, 2/7/2009
- Check 'Em Out, 6/2/2009
Where's the harm?
California is in the midst of its worst outbreak of whooping cough in a half-century. More than 2,700 cases have been reported so far this year―eight times last year's number at this point. Seven of the victims, all infants, have died. … Doctors thought they wiped out whooping cough when they developed vaccines decades ago. The disease hits young children hardest, especially ones who are not vaccinated or who have not yet built up full immunity. … The California epidemic has raised plenty of questions about the role of vaccination and the increasing numbers of parents who decide not to vaccinate their children. California's Department of Public Health cites three schools in the state where 80 percent of parents have signed a "personal belief exemption" to keep their children from being vaccinated.
Source: "Deadly Whooping Cough, Once Wiped Out, Is Back", NPR, 8/14/2010
Some people wonder: what's the harm of a little illogic in life? This is an occasional series of entries aimed at answering that question. Fallacious reasoning can be deadly. These are reminders that it's not all fun and games.
Rep. Maxine Waters Refutes Ethics Charges
If you read the article beneath this headline, you'll see that Waters did not "refute" the charges, but merely denied them. "To refute" a charge means not merely to deny it, but to disprove or rebut it. As a part of logical literacy, it's important to understand some basic logical terminology. I don't mean technical vocabulary, but the common vocabulary of reasoning and argument, which includes such words and phrases as "premiss", "begging the question", and "refute".
This is not the first time I've seen "refute" used to mean "deny", and it appears to be a common type of illogicality, as well as one that has been around for awhile. Kingsley Amis included it in his The King's English:
This word once had the useful meaning of proving falsity or error by argument and/or recital of facts; it was not a mere synonym of reject…. Then, some time in the 1960s, it began to be used to mean deny,…a mere declaration that something was untrue. And yet, with the old basic sense of the word still hanging about in the public mind, it did sort of mean more than just deny, it implied too that there were or might be facts around that would back up the denial if they were produced. … No wonder that an American president said he categorically refuted the accusation that he had abused his powers, or that a local authority should refute without satisfactory argument the idea that their proposals were wasteful.
Presumably because misuse of the word has become so common, some recent dictionaries include "deny" as a secondary meaning of "refute". However, it's misleading to use the word in that sense, since the primary meaning is still "disprove", and the unambiguous "deny" is always available. I've been told that correcting the journalistic abuse of "begging the question" is a lost cause, but perhaps it's not too late to do something about "refute".
- Kingsley Amis, The King's English: A Guide to Modern Usage (1997), p. 158
- Matthew Jaffe, "Rep. Maxine Waters Refutes Ethics Charges", ABC News, 8/13/2010
Via: Eugene Volokh, "'Refutes'?", 8/13/2010
Millions face 25% cut in pensions as inflation rules for final salary schemes are changed
Despite the headline, the story from which it is taken is not about a "cut" in pensions, but about using a different index to figure inflation adjustments, which by the nature of things are always increases. In other words, there are two ways of adjusting the pensions for inflation, both of which will result in future increases in the pensions, but one of which will be 25% lower than the other. Naturally, those who have to pay the pensions would like to use the index that produces 25% lower future pensions; and, just as naturally, those who will receive the pensions would prefer the index that produces higher pensions. But no pensions are actually going to be "cut".
Usually, the notion that an increase which isn't as big as some benchmark is actually a "cut" is political doublespeak, as I've documented in the past (see the Resource, below). For instance, when government spending is increased less than expected this is frequently trumpeted by politicians as a "cut" in spending. In this case, we have a news outlet perpetrating the doublespeak, though the Daily Mail may have been channeling some interest group.
The first sentence of the article says: "Plans to shake up final salary pension schemes will cut payouts by up to 25 per cent, it has been claimed." So, some unidentified person or group made the claim, but why was it repeated in the headline without even anonymous attribution?
Later in the article we read: "Dawid Konotey-Ahulu, of the Mallowstreet group, said: ‘Pensions linked to CPI [the Consumer Prices Index] will be lower over time―some estimates put the drop as high as 25 per cent.’" Did the editor who wrote the headline simply misunderstand this to mean that the pensions would actually be 25% lower than they are today, as opposed to 25% lower than they would be under the Retail Prices Index?
Source: Jason Groves, "Millions face 25% cut in pensions as inflation rules for final salary schemes are changed", Mail Online, 8/11/2010
Resource: Political Doublespeak Dictionary, 9/25/2008
Belief in "nature" and what is "natural" is a source of many errors. It used to be, and to some extent still is, powerfully operative in medicine. The human body, left to itself, has a certain power of curing itself; small cuts usually heal, colds pass off, and even serious diseases sometimes disappear without medical treatment. But aids to nature are very desirable, even in these cases. Cuts may turn septic if not disinfected, colds may turn to pneumonia, and serious diseases are only left without treatment by explorers and travelers in remote regions, who have no option. Many practices which have come to seem "natural" were originally "unnatural," for instance clothing and washing. Before men adopted clothing they must have found it impossible to live in cold climates. Where there is not a modicum of cleanliness, populations suffer from various diseases, such as typhus, from which western nations have become exempt. Vaccination was (and by some still is) objected to as "unnatural." But there is no consistency in such objections, for no one supposes that a broken bone can be mended by "natural" behavior. Eating cooked food is "unnatural"; so is heating our houses. The Chinese philosopher Lao-tse, whose traditional date is about 600 B.C., objected to roads and bridges and boats as "unnatural," and in his disgust at such mechanistic devices left China and went to live among the Western barbarians. Every advance in civilization has been denounced as unnatural while it was recent. The commonest objection to birth control is that it is against "nature." (For some reason we are not allowed to say that celibacy is against nature; the only reason I can think of is that it is not new.)
Source: Bertrand Russell, "An Outline of Intellectual Rubbish", Unpopular Essays (1950)
In the Mail
The new book Sex, Drugs, and Body Counts: The Politics of Numbers in Global Crime and Conflict by Peter Andreas and Kelly M. Greenhill. Jack Shafer had an enthusiastic plug of it in Slate (see the Source, below). I'll post a review as soon as I've had a chance to read it.
Source: Jack Shafer, "By the Numbers", Slate, 7/14/2010
Update (8/7/2010): Check out an interview of one of the editors of the book, Peter Andreas, from the NPR radio show On the Media:
Source: "Sex, Drugs, and Body Counts", On the Media, 7/30/2010