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February 24th, 2015 (Permalink)

Sobriety Check

According to a brief news report―see Source 3, for the full article:

…[R]esearchers reported that in 2001 underage drinkers spent an estimated $22.5 billion, more than 17 percent of the total amount spent on alcohol [in the United States].

Were the researchers in question drunk or sober when they reported this? Is it plausible that underage drinkers would have spent so much on alcoholic beverages? Is it believable that those under the legal drinking age, which is 21 in the U.S., are responsible for 17% of sales of alcohol?

Don't assume that just because this news report was published in a reputable source―The New York Times!―that these statistics must be correct. We've seen in previous entries that false and misleading statistical claims sometimes make their way into the news―see the Resources, below, for a couple of recent examples. Reporters are not necessarily numerate, nor do they always think that it's their job to check the numbers they report for accuracy. In many cases, they pass along statistics generated by activist groups or advocacy researchers without getting a second opinion. Also, they often fail to inform their readers about the biases of their sources.

We've also seen, in the same Resources, how it's possible to use statistical benchmarks to check such claims for plausibility. A statistical benchmark is a statistic that is useful in many contexts for evaluating other statistical claims. One that may come in handy in evaluating the above claim is the fact that approximately four million babies are born in the United States each year.

Using just this information, can you check the sobriety of the claim that "in 2001 underage drinkers spent an estimated $22.5 billion" on alcoholic beverages? Is this a plausible amount given what you know about underage drinking and the cost of alcohol? When you think you have succeeded, click on the following link to see the results of one such check:

Sobriety Check



  1. A Mutant Statistic, 1/25/2015
  2. Sanity Check it Out, 11/23/2014

February 20th, 2015 (Permalink)

Blurb Watch: Citizenfour

Judging by a full-page ad in The New York Times a week ago, the new documentary Citizenfour has received considerable critical acclaim. However, as is often the case with movie ads, its critical acclaim is not quite all it's claimed to be.

The Times ad has a remarkable variant of a trick we've seen before in ads for movies: across the middle of the ad is a series of seven groupings of four stars from various publications, indicating that each publication gave the movie a four-star review.

What we're not shown is that five of these reviews are based on a five-star grading system. Of the seven reviews listed, the only one that I could verify was four-stars out of four possible was that from Godfrey Cheshire at the late Roger Ebert's site.

The Huffington Post is also listed in the ad, but it doesn't appear to have an official movie reviewer. Instead, there are multiple critics who post reviews on the site. I checked every review of the movie that I could find, but most didn't use a star rating system, and the only one that did use such a system gave it three-and-a-half out of four stars. Now, it may well be that there's another review on Huff 'n' Puff that I've missed that gives it four stars but, even if so, what justifies the blurber cherry-picking that one to use in the ad rather than the three-and-a-half star one?


February 10th, 2015 (Permalink)

Name that Fallacy!

It's time again to play America's favorite fallacy game. Can you name the fallacy committed in the following sentence?

Americans ate 43.3 pounds of chicken per person in 1976 compared to 15.5 pounds in 1910.―The Boston Globe, 7/19/1978, p. 65

When you think you know the answer, click on "Fallacy" below to see if you're right:


Source: Lucy Horwitz & Lou Ferleger, Statistics for Social Change (1980), p. 250

February 9th, 2015 (Permalink)

New Book:
Is Gwyneth Paltrow Wrong About Everything?

Why do we believe celebrity pseudoscience?

A recent headline at CBS News asks the burning question: "Why do we believe celebrity pseudoscience?" Well, I don't. But it's obvious that enough do to make it profitable for celebrities such as Gwyneth Paltrow and Jenny McCarthy to promote it.

Despite its headline, the article doesn't really explain why people are willing to give credence to uncredentialed celebrities. Instead, it seems to be primarily a puff piece for a new book by Tim Caulfield entitled Is Gwyneth Paltrow Wrong About Everything?: When Celebrity Culture and Science Clash. When they clash, I'm rooting for science.

I don't know why so much attention is given to Paltrow, since she's certainly not the only celebrity offender, nor the worst. Also, it's very unlikely that she's wrong about everything. Of course, I haven't read the book yet, so I don't know if it's any good, but it's an encouraging sign of some push back against those celebrities who are passing themselves off as experts on health or politics.


Fallacy: Appeal to Celebrity

February 4th, 2015 (Permalink)

We Need a Vaccination Against Contextomies

Did Barack Obama, when he was running for president in 2008, say that he was suspicious that there might be a connection between vaccines and the rising rate of autism? If you've heard this claim, you may have seen the following quote:

"We've seen just a skyrocketing autism rate. Some people are suspicious that it's connected to the vaccines. This person included. The science right now is inconclusive, but we have to research it."―Barack Obama, Pennsylvania Rally, 4/21/2008

This quote has been used both by political opponents of Obama who want to attack him for being "anti-science", as well as by some of those who are critical of vaccination and want to enlist him on their side. No doubt the quote sounds pretty damning if you assume that by "this person" Obama was referring to himself. However, if you watch the video of the campaign event at which Obama made the quoted remark, you should get a different impression―see the embedded video; the relevant remarks start at about the fortieth minute. This event seems to have been an outdoors question and answer session in which Obama is surrounded by a small group of voters. When he speaks the words "this person included", he points towards someone off camera.

This is a good example of a type of ambiguity that comes from the use of demonstrative words, such as "this", "that", "these", "those", etc. What such a demonstrative refers to is determined partly by context, including such clues as body language―Obama's pointing, in this case. Thus, when removed from context, such words are ambiguous, and you have to be careful not to misinterpret them.

Some of those who have recognized that Obama wasn't referring to himself in the quote have still criticized him for his subsequent statement: "The science right now is inconclusive, but we have to research it." That may sound as though he is giving aid and comfort to those who think that vaccination may be involved in autism. However, once again, looking at the larger context of Obama's remarks gives a different picture―I've highlighted the parts included in the original contextomy so that you can easily see what was excluded:

We’ve seen just a skyrocketing autism rate. Nobody knows exactly why. There are some people who are suspicious that it’s connected to vaccines and triggers, but―this person included. The science right now is inconclusive, but we have to research it. Part of the reason I think it's very important to research it is those vaccines are also preventing huge numbers of deaths among children and preventing debilitating illnesses like polio. And so we can't afford to junk our vaccine system. We've got to figure out why is it that this is happening so that we are starting to see a more normal, what was a normal, rate of autism. Because if we keep on seeing increases at the rate we're seeing we're never going to have enough money to provide all the special needs, special education funding that's going to be necessary.

Notice that the second sentence, "nobody knows exactly why", refers back to the "skyrocketing autism rate". This sentence―which was omitted from the original quote without even the courtesy of ellipses―when restored and considered together with the subsequent statements about special education funding, make it clear that "the science right now is inconclusive" refers to the rising autism rate rather than the supposed link with vaccines.

It would still be fair to take Obama to task for not having more definitively disavowed the link between vaccination and autism. I hereby do so.


  1. Michael Dobbs, "Dr. Obama and Dr. McCain", The Washington Post, 1/22/2015
  2. Louis Jacobson, "What Barack Obama said about autism and vaccines in 2008", PolitiFact, 2/3/2015
  3. Alex Knapp, "Obama Cites Link Between Vaccines and Autism", Outside the Beltway, 4/22/2015
  4. Robert Mackey, "Video Shows Obama’s 2008 Comments on Vaccines Were Misreported", The New York Times, 2/3/2015

Via: Paul Fidalgo, "One Ring to Fool Them All", The Morning Heresy, 2/4/2015

Update (3/15/2015): I've previously mentioned the book Science Left Behind―see the Resources, below―and expressed skepticism about it: concentrating on the scientific sins of one political wing only contributes to the politicization of science.

I don't need any convincing that there are anti-scientific elements on the political left; after all, it was the left that came up with the notions of "proletarian" science and "bourgeois" science. If we don't watch out, we're going to end up with Democrat science―evolution, global warming, and organic food―and Republican science―vaccination, nuclear power, and genetically modified food. I suppose one might defend the book as an answer to Chris Mooney's earlier book The Republican War on Science, but two wrongs don't make a right.

I recently acquired a copy of Science Left Behind and have just started reading it. In chapter 2, on the Obama administration's science record, what should I find but an appearance of the above contextomy―see the Source, below. It occurs in the context of a section entitled "Barack Obama vs. Vaccines", which gives the impression that Obama is referring to himself by "this person", and that he was claiming that the scientific evidence of a causal connection between vaccines and autism was inconclusive. As shown above, the former is clearly a false impression and the latter is at least doubtful.

That the authors would use this quote is discouraging as it suggests that their research and fact-checking for the book was shallow. Either that, or their desire to find damning quotes from progressives made it "too good to check".



Sobriety Check: It's virtually impossible to tell directly whether $22.5 billion is a plausible amount spent on alcohol by underage drinkers in a single year, since such a large number is outside of our experience. Furthermore, it's illegal to sell alcoholic beverages to underage buyers, so there are no official statistics to consult. At best, this is an estimate.

One way to evaluate such a large amount for plausibility is to divide it among the relevant population in order to get a per capita amount. The relevant population would be underage drinkers but, unfortunately, you're unlikely to have much of a notion of the size of that group. However, using the benchmark statistic that four million infants are born each year in the United States, together with the fact that the legal drinking age is 21, we can estimate the size of the underage population. There are twenty years worth of Americans who are underage, and for each of those years there are approximately four million people. Thus, there are about 80 million Americans less than 21 years of age.

If we divide $22.5 billion by 80 million, the result is $281―plus a quarter―per underage person. In other words, in order for the dollar amount reported in the news article to be correct, underage Americans would have had to spend an average of nearly $300 on alcohol in 2001. Does this sound like a plausible amount?

Keep in mind that not all of those who are underage could reasonably be categorized as drinkers. There are presumably very few drinkers among those less than ten years of age, and even many between the ages of ten and twenty are probably not "drinkers" in any serious sense. Thus, the average amount spent by underage drinkers in 2001 would have to be larger than $300, probably considerably larger, and perhaps two or three times as much. Is it plausible that underage drinkers spent an average of $600 or more on alcohol in a year? Wouldn't that mean, at the very least, that all underage drinkers are alcoholics?

Now, I don't know as a fact that the researchers who produced this estimate were drunk at the time, but the amount seems wildly inflated. Also, I don't know for sure that the amount is wrong, despite its implausibility. It's still barely possible that underage drinkers do spend such a large amount on drinking but, if so, then the problem of underage drinking is a much greater one than I have ever imagined. However, in a sequel to this entry next month, I intend to show that this amount is not merely improbable, but is certainly in error. Stay tuned.

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