Charts & Graphs: The State of the Union
Earlier this month, when President Obama gave the "State of the Union" speech, the White House put out an "enhanced" version of the speech with graphics including some charts and graphs (see Source 1, below). NPR has done an excellent job of evaluating many of the graphs (see Source 2, below), a few of which demonstrate some of the common tricks of misleading charts. Check it out.
- "Enhanced State of the Union", The White House, 2/12/2013
- NPR Staff, "Chart Check: Did Obama's Graphics 'Enhance' His Big Speech?", NPR, 2/14/2013
Previous Charts & Graphs:
- Hey, Big Spender, 6/1/2012
- Charts and Graphs, 6/4/2012
- A "Gee-Whiz" Graph, 8/14/2012
- Charts & Graphs, 9/25/2012
- Charts & Graphs, 1/13/2013
Where's the harm?
Check out Phil Plait's recent "Bad Astronomy" post on the dangers of the anti-vaccination movement:
Fighting anti-vaxxers is critical. The misinformation they spread is incredibly dangerous. First, because itís simply wrong, almost to a letter. Second, because it spreads fear, and then parents donít vaccinate their kids or get booster shots themselves. And when that happens, herd immunity drops, and when herd immunity drops, kids start getting infected. Some die. This is no joke: It happens in Australia, it happens in the United Kingdom, it happens here in the United States.
If you have any doubts about the dangers of fallacious thinking, read the whole thing.
Source: Phil Plait, "Vaccinating Against McCarthyism", Slate, 2/4/2013
- Silly Celebrities, 4/22/2008
- Celebrities Vs. Science, 12/29/2008
- Silly Celebrities of the World, Unite!, 5/6/2009
- Conspiracies to the Left, Conspiracies to the Right, 12/22/2009
- New Books: The Doublespeak Dictionary & The Panic Virus, 2/17/2011
Note: 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.
PBS' Frontline showed a documentary a few years ago with examples of the fallacious thinking behind the fear of vaccination, as well as explaining the bad consequences of the failure to get vaccinated. For example:
Narrator: [Jennifer] Margulis…published a long article about the vaccine debate in Mothering magazine, a magazine promoting a natural lifestyle.
Margulis: … As a parent, I would rather see my child get a natural illness and contract that the way that illnesses have been contracted for at least 200,000 years that homo sapiens have been around. I'm not afraid of my children getting chicken pox. There are reasons that children get sick. Getting sick is not a bad thing.
This is argumentum ad naturam ad absurdum, that is, the appeal to nature taken to absurdity. So, illness is not a bad thing because it's natural? How about death? She's not afraid of her children getting chicken pox but what about small pox, which was eradicated by vaccine? If her child died of small pox would that be fine with her because it's a "natural illness", or perhaps because death is natural? If so, why all the fear of autism? Is autism not a "natural" illness, since it's supposedly caused by vaccination? Must we now divide all diseases up into those that are "natural", and therefore good, and those that are "unnatural", and thus bad? What about unvaccinated children who become autistic, would that be "natural" autism and therefore nothing to worry about?
The documentary does a good job of showing how the connection between vaccines and autism is due to post hoc reasoning, as well as explaining its limitations:
Narrator: [J.B.] Handley's son was diagnosed with autism following a series of shots in 2004. …
J.B. Handley, Founder, Generation Rescue: There were literally tens of thousands of parental reports of children regressing and changing after vaccine appointments."My child was fine before the vaccine." "The vaccine made Sam autistic." "He completely changed." "After the MMR, he wouldn't look at us." "Cole just stopped speaking." "He got the shot. We started losing him."…
Dr. Paul Offit: Parents reasonably thought, "My child was fine. They got an MMR vaccine, then they developed the first symptoms of autism. Could it have been the MMR vaccine that caused that autism?" That's a perfectly reasonable question.
Narrator: The fact that two events happen close together might mean they are causally related, but it could also be simple coincidence.
Dr. Eric Fombonne: This vaccination is given at an age where often the first symptoms of autism emerge. And typically, it occurs around 15 or 18 months of age, when these children start to walk, also when we expect them to develop language, which they usually fail to do.
Dr. Anthony Fauci: There are a certain set of diseases that become apparent when children reach a certain age. That's not cause and effect.
Offit: Just because one event followed another, it doesn't mean it was caused by the other. I mean, every morning, the rooster crows, the sun comes up. It doesn't mean the rooster's causing the sun to come up. The question is, was it caused by it?
Jenny McCarthy makes her obligatory appearance:
Narrator: Former Playboy playmate Jenny McCarthy knew little about autism until her son, Evan, received a series of vaccines, including the shot for mumps measles and rubella, the MMR triple shot. A few weeks later, Evan developed seizures and was diagnosed with autism. …
McCarthy: Today I am not a celebrity. Today I am a mom of a child who had autism.
Sorry, Charlie―I mean Jenny!―the only reason anyone pays attention to your ignorant opinions is because you're a celebrity.
Source: "Transcript: The Vaccine War", Frontline, 4/27/2010
Check it Out
Michael Shermer's latest "Skeptic" column for Scientific American takes a shot at Chris Mooney's book of several years ago, The Republican War on Science, by talking about a liberal war on science. I've never read Mooney's book, partly because I was put off by the title. Of course, it's possible that Mooney wasn't responsible for the title, which may have been supplied by his publisher. It's at least an exaggeration to suggest that Republicans or conservatives are at "war" with science, which is not to deny that there is a religious conservative wing of the party that tends towards anti-intellectualism. However, writing a book about the scientific sins of just one of the major political parties only contributes to the politicization of science.
In his column, Shermer points out some of the elements of the left that do much the same thing as the religious right, only about different issues. He points to the recent book Science Left Behind―see Resource 2, below, for a relevant article by one of it's co-authors. I also haven't read it, but I gather it's a sort of conservative version of Mooney's book. If so, it's just contributing further to the problem, though I suppose that one could treat the books as a set that taken together give an account of both sides' sins against science.
Shermer mentions that some liberal opposition to science or its products is based on the appeal to nature (see the Fallacy, below), that is, that "natural" means "good" and whatever is unnatural―such as vaccines―is therefore bad. However, the appeal to nature is not restricted to the left or environmentalism, but is also a theme of some religious conservative opposition to science and technology. For instance, conservative disapproval of homosexuality, as well as Catholic opposition to birth control and abortion, is often premissed on their supposed unnaturalness.
Who's worse, the left or the right? Who knows? Those who answer one way or the other say more about their own political views than about who's really worse, since it's so easy to ignore or downplay the sins of your own side. It's safer to just say that there's enough sinning against science to go around, and those who claim to care for science should point out such sins no matter from which side of the aisle they come.
Source: Michael Shermer, "The Liberals' War on Science", Scientific American, 1/21/2013
- Ronald Bailey, "Are Republicans or Democrats More Anti-Science?", Reason, 10/4/2011
- Alex Berezow, "Column: GOP might be anti-science, but so are Democrats", USA Today, 9/20/2011
Fallacy: Appeal to Nature
New Book: Mastermind
Speaking of Sherlock Holmes, as we were about a week ago (see Resource 2, below), I just got my hands on a new book called Mastermind: How to Think Like Sherlock Holmes, by Maria Konnikova. Though I'm fond of the Holmes stories, I was skeptical about the book when I first heard about it because Doyle is notorious among logicians for his misuse of the term "deduction" (see Resource 1, below). What he calls "deductions" are usually inductions, or more accurately what logicians call "abductions" or inferences to the best explanation. Moreover, a lot of the "deductions" that Holmes makes in the stories are based on shaky evidence. Of course, as a fictional character, Holmes' "deductions" always turn out to be correct, but a real person who tried to follow Holmes' methods would not be so lucky without Doyle to stack the deck. For these reasons, I'm doubtful that it's even a good idea to try to "think like Sherlock Holmes". However, the book has a positive blurb on the back from Steven Pinker, which carries some weight with me despite the fact that Konnikova refers to him as a friend and mentor in the "Acknowledgments".
Also, though I haven't read the book yet, I see that the Cottingley fairy photographs (see Resource 2, below, for details) are reproduced in it (pp. 227 & 230), and I can't wait to find out what Konnikova will have to say about them. Just imagine what short work Holmes would have made of the case!
By the way, allow me to mention a book that I'm quite fond of: Conned Again, Watson! (see Resource 3, below). It's a collection of Sherlock Holmes stories by Colin Bruce, a physicist and statistician who does know a thing or two about logic. If you like Holmes, give it a try.
Source: Maria Konnikova, Mastermind: How to Think Like Sherlock Holmes (2013)
- Logical Literacy: Induction and Deduction, 1/28/2008
- Fairy Tale, 2/6/2013
- Colin Bruce, Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability (2001)
Untie the Nots, Part 5
Here's a sentence from a newspaper article about an appeals court ruling:
The grounds of appeal announced on Monday state Justice Sifris erred in not finding Mr Goldberg was wrong in failing to set aside the summonses.
There's only one explicit negation in this sentence―"not"―but there are perhaps as many as four additional concepts that can be defined negatively. As a result, it's difficult to understand. Can you untie the "nots" by rewriting the sentence to remove as many of the negatives as possible while retaining its meaning?
Previous "Untie the Nots":
- Untie the Nots, 1/22/2005
- Untie the Nots, Part 2, 2/1/2005
- Untie the Nots, Part 3, 2/1/2010
- Untie the Nots, Part 4, 3/2/2010
Speaking of smart people who believe weird things (see the Resource, below), I was just reminded of my favorite example: Sir Arthur Conan Doyle, author of the Sherlock Holmes stories. Doyle in his later years became a devout believer in ghosts and mediums and devoted himself to proselytizing for spiritualism. Here's a passage from Michael Coren's biography (see the Sources, below) describing Doyle's performance during a debate on spiritualism:
[Doyle] then performed a dramatic gesture that he had been preparing for ever since the debate had been announced. He took from his jacket pocket a small, black leather-covered notebook. In this book, he said, I have the names of 160 people―politicians, diplomats, authors, scientists, generals, admirals, businessmen and artists―who believed without any doubt or question in the truth of spiritualism. Were these men fools and dunderheads? When these grand sailors led ships into deadly battle against Germany's navy were they idiotic and impractical? When these cabinet ministers decided on affairs of state that could affect the world were they uneducated or callow? … There was a spontaneous round of applause and some in the audience even stood up to show their approval.
This is an interesting example of an appeal to authority, since Doyle was an intelligent man who was silly on the subject of spiritualism appealing to the authority of other intelligent men who were silly on the same subject. Doyle's wording of his rhetorical questions is revealing:
- "Were these men fools and dunderheads?" Not generally speaking, of course, which is what gives this question whatever power to persuade it has. One is hesitant to say that Doyle, or any other of these unnamed gentlemen, is a fool and dunderhead. But the lesson of examples such as Doyle is that people who are generally not fools and dunderheads can be foolish and dunderheaded about specific subjects, especially if it involves religion.
- "When these grand sailors led ships into deadly battle against Germany's navy were they idiotic and impractical? When these cabinet ministers decided on affairs of state that could affect the world were they uneducated or callow?" Probably not, but who knows? This relates to a point about the ways in which appeals to expert opinion can go wrong, namely, when an expert opines outside of his or her area of expertise. When the grand sailors were leading ships into deadly battle and the cabinet ministers were deciding affairs of state, they may have been smart, practical, educated, and experienced; but when they formed their opinions on spiritualism, they may have been idiotic, impractical, uneducated, and callow. Expertise and intelligence in one area do not necessarily transfer to another, unrelated area.
This is why Doyle's argument in this passage is fallacious: the fact that intelligent people who were experts in various subjects endorsed spiritualism carries little if any logical weight, since their expertise was in fields unrelated to spiritualism and they may have failed to bring their intelligence to bear upon it. In a later passage, Coren writes:
As he aged Conan Doyle became even more convinced of the truth of his beliefs. …[W]e cannot dismiss his religious and philosophical ideas as absurd if we wish to retain any intellectual consistency in the study and appreciation of Conan Doyle. A man who was sufficiently gifted and brilliant to invent and develop Sherlock Holmes and Professor Challenger, qualify as a doctor and suggest military reforms far ahead of their time surely did not have one gargantuan weak spot when it came to his personal belief in life after death and the supernatural.
Why in the world not? Coren here is making the same fallacious argument that Doyle did in the debate. If you have any doubts about Doyle's "gargantuan weak spot", consider the case of the Cottingley fairies. Here's Coren's own description:
…Conan Doyle wrote to the spiritualist Sir Oliver Lodge in Britain and told him about a series of photographs that he had been sent of so-called fairies. He wanted Lodge's opinion of the things. … The photographs had been taken by two Bradford girls, fifteen-year-old Elsie Wright and her cousin, ten-year-old Frances Griffiths, who in 1917 had seen what they described as a goblin and a similar creature. …[A] specialist photographer…had stated that the pictures had not been touched up or altered in any way and were almost certainly genuine. When Conan Doyle saw the photographs, of dancing goblins and elves in a ring, he suggested that some sort of official inquiry take place. He was told that as the girls had grown up they were reluctant to make too much of what had happened and that their families did not want any publicity at all. Sir Oliver Lodge said that this was all for the best because whatever any photographer might say these photographs were obviously fakes―they looked preposterous. Conan Doyle was shocked. How on earth could two innocent, honest north of England schoolgirls achieve such a thing, and why would they want to in the first place?
Lodge was right: the photos were obvious fakes (see the one shown, to the right and above if you have any doubt). Doyle made a big deal about the fact that the photos were not double exposures or touched-up in some way, and that teenaged girls wouldn't know how to do such things anyway. But they were much simpler hoaxes than that: the girls simply traced pictures of fairies out of children's books, cut them out, propped up the tracings in the weeds, and photographed themselves with them. And that's exactly what they look like. Coren continues:
In early 1922 he published an account of the story in The Coming of the Fairies. This case had probably done more damage to Conan Doyle's reputation and credibility than any other, perhaps deservedly so. If we look at the photographs today it is difficult to imagine how anybody could have been convinced by them at any time. … The case rested on a heavy dose of wishful thinking, spiced with the trusting assumption that the two young girls were above board. In fact it took many years for photographers to develop the equipment and technology to prove that the photographs were fake, and many years for the girls, when grown women, to admit that it was all meant to be a bit of harmless fun.
That "perhaps" is one doozy of an understatement!
Source: Michael Coren, Conan Doyle (1996), pp. 169-170, 174-175, 178, 182
- Why do smart people believe weird things?, 1/28/2013
- James Randi, Flim-Flam!: Psychics, ESP, Unicorns and Other Delusions (1982), Chapter 2: "Fairies at the Foot of the Garden"
I'm probably the only person who regularly reads Slate's weekly "Corrections" column, which collects together all the corrections issued by Slate for the preceding week. Thankfully, Slate also corrects the articles that made mistakes and adds a notice at the bottom, so that the reader who pays no attention to the corrections page―like most people―won't be misled. The following correction was part of the most recent column (see the Sources, below):
In the Jan. 29 "The Kids," Melinda Wenner Moyer inaccurately stated that male baby sitters are three times more likely to commit sex crimes than female baby sitters. But while 77 percent of sex crimes by baby sitters are committed by males [sic] baby sitters, because most baby sitters are women, the relative likelihood that a man commits a sex crime compared to a woman while baby sitting is likely higher than three to one.
The correction itself needs a small correction, since the "s" should be removed from the end of "males". Here's the relevant passage from the uncorrected article (see the Sources, below):
According to a U.S. Department of Justice report from 2001 (unfortunately the most recent statistics on baby sitter crimes), male baby sitters are three times more likely than female baby sitters to sexually abuse the children they care for.
And here's the corrected sentence:
According to a U.S. Department of Justice report from 2001 (unfortunately the most recent statistics on baby-sitter crimes), 77 percent of sex crimes by baby sitters are committed by males.
So, apparently the author saw that 77% of these crimes were committed by men and concluded that a man was three times more likely than a woman to commit such a crime. However, this neglected to take into consideration the fact that there are far fewer male than female babysitters, a point emphasized in the article itself. Therefore, a small minority of babysitters appear to be responsible for three-quarters of all these crimes, so that the proportion of sex crimes committed by male babysitters to those committed by female ones will be greater than three to one, as the correction notes.
Exercise for the Reader: The correction says that probably a male babysitter is more than three times likelier to commit a sex crime than a female, but it doesn't say how much more. However, there's enough information included in the article to estimate this greater likelihood. Do so.
- "Corrections", Slate, 2/1/2013.
- Melinda Wenner Moyer, "In Defense of the Manny", Slate, 1/29/2013. Google's cache of the uncorrected article.
- Melinda Wenner Moyer, "In Defense of the Manny", Slate, 1/29/2013. The corrected article.
Answer to the Exercise: According to the article, 5.5% of American child care workers are men. This, of course, isn't exactly the same thing as the percentage of babysitters who are male, but it's probably not too far off, and all that we're aiming for is an estimate. Also according to the article, 77% of sex crimes by babysitters are committed by men. So, 77% of sex crimes are committed by only 5.5% of babysitters.
To make things simpler, let's assume that there are only 200 such crimes―the exact number doesn't matter because we're looking for an estimate of proportions, not absolute numbers. So, 77% of those crimes are committed by male babysitters, which totals 154 crimes, and the remaining 23%, or 46, by female ones.
Since only 5.5% of the sitters are male, for a total of 11 sitters, that means an average of 14 crimes are committed by each male babysitter―of course, this is just an average, and it's possible that all 154 are committed by just one bad guy. Similarly, since 94.5% of the sitters are female, a total of 189 sitters committed 46 crimes, for an average of about .24 crimes per female sitter.
Therefore, the proportion of male to female crimes is 14 to .24, or a little over 58 times as many crimes committed by male babysitters as by female ones. In other words, assuming that these statistics are correct, a male babysitter is many more times likely to commit a sex crime than a female one, probably at least an order of magnitude more likely.
Of course, one should be cautious about drawing any sweeping conclusions about the risk of sex crimes by male babysitters from these statistics, as there could be many explanations for the seeming disparity between men and women. Perhaps men are regarded with greater suspicion than women, and are therefore more likely to be caught committing such crimes. Also, as the article mentions, the rate of sex crimes committed by babysitters is quite small, so that even if the difference between male and female sitters is as great as is suggested by these statistics, the likelihood of any given male sitter committing such a crime is still very small.
Solution to Untie the Nots, Part 5: To start, let's identify the four additional concepts that can be defined negatively:
- "Erred": To err is to act incorrectly, that is, not correctly.
- "Wrong": Similarly to "err", to be wrong is to not be right.
- "Failing": To fail to do something is to not do it.
- "Set aside": This one is a bit more difficult, but to set aside is to not leave in place.
Now, let's reformulate the sentence by making all of the negations explicit:
The grounds of appeal announced on Monday state Justice Sifris did not act correctly in not finding Mr Goldberg was not right in not not leaving in place the summonses.
This is still hard to understand, and more awkwardly written, but at least the negations are all explicit. Before we proceed, keep in mind that negations cancel each other out in pairs, so that if there are an odd number of negations―as in this case―then the best that we can expect to do is remove all but one of them. If we should be left with an even number of negations―zero is even―then we'll know that we made a mistake somewhere. So, let's now simplify the sentence step-by-step.
The last two negations clearly cancel each other out:
The grounds of appeal announced on Monday state Justice Sifris did not act correctly in not finding Mr Goldberg was not right in leaving in place the summonses.
To say that someone acted incorrectly in not doing something is to say that he should have done it, so we can rewrite the sentence as follows:
The grounds of appeal announced on Monday state Justice Sifris should have found that Mr Goldberg was not right in leaving in place the summonses.
This leaves just one negation, which is the fewest possible without changing the meaning of the sentence, though the original wording of that negation is smoother:
The grounds of appeal announced on Monday state Justice Sifris should have found that Mr Goldberg was wrong in leaving in place the summonses.
That this has the same meaning as the original sentence can be tested by placing it in its larger context (see the Source, below):
Two Fairfax Media journalists have launched an appeal to prevent them being forced to reveal their sources. Paul Holdenson…on Monday announced the fight now would continue in Victoria's highest court. Mr Holdenson told magistrate Phillip Goldberg an application to seek leave to appeal had been lodged on Friday with the Court of Appeal. Mr Goldberg had earlier ruled subpoenas compelling the journalists to give evidence in a bribery case had a legitimate forensic purpose. The journalists then sought a review of that decision to Justice Michael Sifris in the Supreme Court who ruled the magistrate had "acted properly…". The grounds of appeal announced on Monday state Justice Sifris should have found that Mr Goldberg was wrong in leaving in place the summonses. … Lawyers for the journalists had submitted there was no forensic purpose in revealing the sources…".
Source: Steve Butcher & Maris Beck, "Journalists appeal in bid to protect sources", The Age, 2/5/2013
- Eugene Volokh, "Quintuple Negative", The Volokh Conspiracy, 2/9/2013
- Mark Liberman, "Semantic gymnastics", Language Log, 2/5/2013