Regular readers of this weblog may recall that last month I answered an email from a reader who suggested adding an entry to the files for the etymological fallacy. At the time, I was doubtful whether this type of mistake was common enough to be worth including, but since then I've found an excellent example in the wild. The short time it took to find one suggests to me that it is a fairly common error. Also, it's worth noting that I found it because the reader's suggestion had sensitized me to it, so that my fallacy antennae were raised when I came across the example. If not for the suggestion, I probably wouldn't have spotted it. So, keep up the good work, readers! I've now added an entry for this fallacy, which can be found via the index to your left.
Source: The Etymological Fallacy, Fallacy Files Weblog, 6/12/2006
Check it Out
The latest issue of Skeptical Inquirer, which is in the stores but not yet available online, has a favorable review of Jamie Whyte's book Crimes Against Logic.
The ABCs of Reporting
ABC News seems to be trying to take the place that Fox used to have as the American television network with the most gullible coverage of pseudoscience. I've previously noted their reporting of Noah's ark spottings. Now, here's what I've gleaned about how to report from their latest article:
- Anecdotes: Use anecdotes. Anecdotes provide drama and interest, and people remember them better than dry statistics. If you're reporting on a faith healer, then the report should consist primarily of stories from people who claim that either they or their loved ones were healed. Any "healer" will get such testimonials through a combination of regression to the mean and coincidence. Someone is bound to get better, and they are almost bound to credit the "healer" for it through fallacious post hoc reasoning. So, you can count on getting at least three for your story. The anecdotes may sound exaggerated, but whatever you do, don't check them out!
- Balderdash: In addition to the testimonials, throw in some gibberish about quantum mechanics. Quantum mechanics is a highly mathematical and notoriously counterintuitive theory in physics, and even most educated people know almost nothing about it. Specifically, mention quantum holograms. There is such a thing, at least in theory, though it has nothing to do with faith healing or whatever you're reporting on, but your readers won't know that. The only reason to mention it is because it sounds scientific and intimidates those who don't understand it, which is almost everyone!
- Call in the Token Skeptic: In order not to appear completely one-sided, you have to question at least one skeptic. But only use one or two sentences at most, and put them down near the end of the article. Also, you might want to throw in one brief anecdote in which the faith healer, psychic, medium, or whatever, failed. That's enough balance!
- John Quinones, Geoff Martz & Kim Launier, "Adam the Healer: Nineteen-Year-Old Says His Touch Can Cure Diseases", ABC News, 7/13/2006
- Phil Schewe, James Riordon & Ben Stein, "Hidden Objects Revealed With Quantum Holography", Physics News Update, 11/21/2006
Via: Bob Park, "ABC Primetime: Wake Up ABC, It's the Twenty First Century!", What's New?, 7/14/2006
Update (7/29/2006): Benjamin Radford, the managing editor of The Skeptical Inquirer, has done a thorough debunking of this episode of Primetime.
Source: Benjamin Radford, "Medical 'Miracles' Not Supported by Evidence", Live Science, 7/29/2006
|Drama pricing/energy pricing||Lowering prices|
"Home sellers are learning what any retailer, from Wal-Mart to the owner of the corner gas station, already knows: Low prices are one of the surest ways to beat the competition. Coldwell Banker Residential Brokerage, Massachusetts' largest real estate firm with more than 3,500 agents, is coaching agents on how to persuade clients to list their homes at an asking price that undercuts those of comparable ones on the market. The hope is low prices will attract more prospective buyers, leading to faster sales. Other real estate agents in the Boston area report success with similar strategies in a housing market with an unprecedented glut of properties for sale. Called 'drama pricing' or 'energy pricing,' it is a drastic measure for difficult times. And it seems to run counter to the conventional strategy of selling your home for the highest price possible."
What I learned from this article:
- If the price is too high, no one will buy it.
- If you lower the price, it will sell faster.
- If you give something a new name, reporters will write articles about it as if it's a new invention.
Source: Kimberly Blanton, "To fight the glut, home sellers push their prices down", Boston Globe, 7/17/2006
Via: David Bernstein, "Drama Pricing", The Volokh Conspiracy, 7/17/2006
In Woodpecker Forest, there are only two types of woodpecker: red-headed and white-headed. 85% of the birds in the forest have red heads and the rest have white ones. An experienced birdwatcher is able to identify the color of woodpecker heads correctly 80% of the time. A woodpecker flies past such a birder, who identifies it as white-headed. What is the probability that the bird actually has a white head?
Will eating unsmoked fish work?
Blurb Watch: The Devil Wears Prada
|…Meryl Streep is scarily sensational as magazine editor Miranda Priestly, the tyrannical, all-powerful arbiter of New York fashion. When the satire stays focused on Streep or her snooty Brit assistant…, "Prada" is malicious fun. But the central story about how smart, idealistic Anne Hathaway, as Miranda's drably dressed new assistant, loses her soul…in pursuit of success and great shoes is dramatically anorexic.|
|Source: Go!, 7/7/2006, p. 6||Source: David Ansen, "Snap Judgment: Movies", Newsweek, 7/3-10/2006|
"Why Do They Do It?"
Asks David Post:
Pretty much every day, in pretty much every newspaper in the country, there is a story that goes something like this…: "Yesterday, the Dow Jones industrials fell xxx points to yyyy on new concerns about interest rates and anxiety over North Korea's missile tests." Or the Dow rose, due to "increasing optimism about prospects for peace in the Mideast." Or whatever. It's complete and utter nonsense.
It's the post hoc fallacy! That's why.
Source: David Post, "Why Do They Do It?", Volokh Conspiracy, 7/5/2006
Resource: How to be a Stock Market Reporter, 12/19/2003
Why is ABC News obsessed with Noah's ark? Just a few months ago, they published a story about a lawyer who claimed to see the ark in blurry satellite photographs. Now, they have another story about a group of "archaeologists" who have supposedly found the actual ark, and brought back samples of it. The current story mentions in passing the previous story: "As recently as March, researcher [sic] claimed to have satellite photos that proved the presence of Ark remains." What they don't tell you is that the satellite photos were of Mount Ararat in Turkey, the traditional site of Noah's landfall, whereas the current claim is to have found the ark in the Elburz mountain range in Iran, over 350 miles distant from Ararat! In other words, these cannot both be the ark unless it broke in two and sank.
My main criticism of the first story was that it treated the lawyer as if he were some kind of expert in photographic analysis. The current story begins: "A team of Texas archaeologists believe they may have located the remains of Noah's Ark in Iran's Elburz mountain range." However, if you define an "archaeologist" as someone with at least a bachelor's degree in archaeology from an accredited institution, there doesn't appear to have been a single archaeologist on the team. Bob Cornuke, the president of the B.A.S.E. (Bible Archaeology Search and Exploration) Institute, and leader of the expedition, is a former police officer; no credentials in archaeology are listed on his B.A.S.E. Institute biography page. In an article on the expedition linked to from the B.A.S.E. Institute website, the other team members are described as: "Some of America’s leading businessmen, an attorney who has argued several cases before the U.S. Supreme Court, and two leading [Christian] apologists…." Where are the archaeologists?
- "Bob Cornuke, President of BASE Institute", B.A.S.E. Institute
- "Has Noah's Ark Been Found?", ABC News, 6/29/2006
- Brannon S. Howse, "Noah’s Ark? For Real", Christian Worldview Network, 6/16/2006
Resource: Some Experts, 3/15/2006
At Risk for Doublespeak
Here're a couple of new entries for the Doublespeak Dictionary, and they have the imprimatur―at least for now―of the government:
- At risk for overweight = overweight
- Overweight = obese
Source: Lindsey Tanner, "Experts Debate Labeling Children Obese", Washington Post, 7/2/2006
The easiest way to see that this is correct is to suppose that the birdwatcher, while on a bird counting expedition, counts one-hundred woodpeckers in the forest. 85 of these birds will be red-headed and 15 will be white-headed. Since the birder is correct 80% of the time, he will have identified 68 of the red-headed birds correctly, and 12 of the white-headed ones right, for a total of 80 correct identifications. Because the birdwatcher is wrong 20% of the time, he will misidentify 17 of the red-headed birds as white-headed ones, and 3 of the white-headed ones as red-headed woodpeckers. So, the total number of birds that he identifies as white-headed is 29 of which 17 are actually red-headed, and 12 correctly identified. So, given that he identifies a particular bird as white-headed, the chance is 12 in 29 that he is correct, or approximately 41%. In other words, given that there are so few white-headed birds in the forest, and so many red-headed ones, it is actually more likely that it is a misidentified red-headed bird than a white-headed one.
If you thought that the answer was 80%, you are not alone. You were probably failing to take the so-called "base rate" into consideration, that is, the fact that the vast majority of woodpeckers in the forest have red heads, and white-headed ones are a small minority. Instead, you were assuming that the only thing that you needed to consider was the experienced birdwatcher's success rate in identification. This is a common mistake, known as "neglecting base rates" or the "base rate fallacy".
Technical Appendix: A more mathematical way to get the answer is to use Bayes' Theorem from probability theory, one version of which is as follows:
P(h | e) = P(h)P(e | h)/[P(h)P(e | h) + P(not-h)P(e | not-h)]
"P(h | e)" is called the "posterior probability", which is what we want to know, namely, the probability of the hypothesis, h, on the evidence, e. In the puzzle, h is the hypothesis that the bird has a white head, and e is the fact that the birder identified the bird's head as white. "P(h)" is the "prior probability" or "base rate" that the bird's head is white, which we know to be .15, since only 15% of the birds have white heads, and "P(not-h)" is the prior probability that the hypothesis is false, namely, .85. "P(e | h)" is the probability that the birder would identify the bird's head as white given that it is white, which we know from the puzzle is 80%, or .8. "P(e | not-h)" is the probability that the birder will identify the bird's head as white if it is not white, which is .2, because he is wrong 20% of the time. Simply plug these numbers into Bayes' formula and the posterior probability is .41, that is, the probability that the birder's identification is correct is only 41%.
Source: Amos Tversky & Daniel Kahneman, "Evidential Impact of Base Rates", in Judgment Under Uncertainty: Heuristics and Biases (1985), pp. 153-160. The puzzle is a variant of the taxicab example discussed on pp. 156-158.
Reader Response (8/31/2006):
Ellen Paul, Executive Director of the Ornithological Council, writes:
Your Ivory-billed Woodpecker quiz has stirred up quite a controversy on other blogs.
It's interesting that you mention the ivory-billed woodpecker, which was not part of the puzzle. Instead, I had an "ivory"-headed woodpecker. However, I was indeed inspired by the ivory-billed woodpecker to create this variant of the original problem.
As I noted at the bottom of the entry, the woodpecker puzzle is a variation on a problem which uses cabs instead of birds. In the original puzzle, there are two cab companies in a city: one company's cabs are green and the other's are blue. A cab is involved in a hit-and-run accident at night, and a witness identifies its color. The problem is to figure out the probability that the witness is correct. All I did was to change the cabs to birds, and the colors from green and blue to red and white. Back to Ellen:
I am writing to say that I am worried about your omission of two very critical words: "on average". You wrote:The easiest way to see that this is correct is to suppose that the birdwatcher, while on a bird counting expedition, counts one-hundred woodpeckers in the forest. 85 of these birds will be red-headed and 15 will be white-headed.
Not so. That's a faulty assumption. Though 15% of the birds are white-headed, that doesn't mean that 15 of the 100 birds you see will be white-headed. Let's go back to the 7th grade, when you first learned about probabilities. A coin has 2 sides. What is the probability that you can flip it 100 times and come up heads every time? Not very high―but it can happen. On the other hand, you aren't likely to get 50 heads and 50 tails, either. Same thing with the birds. On any single visit, you may see no white-headed woodpeckers, you may see 1 or 2. Or you may see all white and no red.
After multiple trips, it is likely that on average, you will have seen 85% red and 15% white. Were you writing just for mathematicians and statisticians, they would know what you meant, but would probably think you'd just been careless in your writing.
However, you are writing for the general public, most of whom don't "believe" in evolution, much less understand even the simplest elements of probability theory. Therefore, it is really important to be clear and accurate. You don't want people thinking that if there are 85 red and 15 white, they will see 85% red and 15% white.
I grant you that I shouldn't have used the word "will", but should have said "suppose that the birdwatcher sees 85 red heads and 15 white heads". You are certainly right in your point about probabilities, but it isn't really relevant to the example. The passage that you quote is intended to explain why the surprising answer of 41% is correct. For this reason, the example uses exactly 100 birds, exactly 85 of which have red heads and exactly 15 of which have white heads, in order to match the percentages given in the puzzle. It is a miniature version of the puzzle which, being smaller, is easier to mentally grasp. Since I'm writing for the general public, I attempted to give an example that could be understood by people who would be intimidated by Bayes' Theorem. Because it is simply an example, the numbers are givens. Here's Ellen again:
And then there is another major flaw―a biological flaw. You are a huge variable in this puzzle. You move around the forest. Unless the birds have the exact same habitat preference and behavioral preferences, you are going to be moving in and out of best viewing sites for one or the other. Say that the red-headed just don't like to cross open areas, and are thus simply harder to see. You will likely see fewer red-headed birds, even though they are far more numerous. Even if you stood in one spot the entire time, you won't necessarily see 85 red and 15 white.
As I said above, the numbers of woodpeckers of different types seen by the birder are givens. It's not a fair criticism of a mathematical problem to challenge the assumptions on which the problem is based, unless those givens are impossible. However, the scenario used in the example is perfectly possible.
The point made by both versions of the puzzle is that most people will greatly overestimate the likelihood that the observer is correct, because they neglect to take into consideration the base rates. The example is intended to make it easier to see why the correct answer is so counterintuitively low. However, the example is just a pedagogical tool, and the real work is done by Bayes' Theorem.
Resource: Richards J. Heuer, Jr., "Biases in Estimating Probabilities", Psychology of Intelligence Analysis, Chapter 12, see under "Base Rate Fallacy". This chapter contains a nontechnical explanation of the fallacy illustrated by another version of the same puzzle, with Vietnamese and Cambodian fighter planes instead of taxis!