March 3rd, 2015 (Permalink)

Sobriety Check, Part 2

In part one, we saw that the statistical claim that underage drinkers spent $22.5 billion on alcoholic beverages in the United States in 2001 was implausible―see the Resource, below. In order for this to be true, underage drinkers would have had to spend an average of over $600 apiece. However, though this is an implausibly high amount, it isn't impossible.

To perform this statistical check, all that we needed was the information included in a short New York Times article that reported the claim―see Source 2, below―as well as the statistical benchmark that approximately four million babies are born each year in the U.S. Unfortunately, the information contained in the Times report, together with statistical benchmarks, does not appear to be sufficient to show that the original paper that reported this statistic must be in error. In this sequel, we will turn to the paper itself―see Source 1, below―and use a different technique to check it.

As a general matter, not every dubious statistic that you come across in the news media can be detected by the use of statistical benchmarks. Sometimes the needed benchmarks won't be available, or a questionable number may survive a benchmark test. Luckily, there's an alternative test that sometimes works when the benchmark test fails.

Turning now to the paper itself, here's how the researchers arrived at the estimate of the amount spent by underage drinkers on alcoholic beverages:

  1. They used census data from 2000 to estimate the number of people between the ages of 12 and 20. Nowhere do they actually provide this figure, as far as I can tell, but based on the information they do give I estimate it as a conservative 40 million. See the Technical Appendix, below, if you want to know exactly how I arrived at this estimate.
  2. Using survey data, they estimated the proportion of those in this age group who are drinkers, and thus underage drinkers. Again, the precise number is not given, but based on the data I estimate it as approximately 19 million. Again, see the Technical Appendix, below, for the details of this estimate.
  3. Again using survey data, they estimated the mean number of drinks by underage drinkers in a month: 35.2.
  4. From the two previous numbers, they calculated the total number of drinks taken by underage drinkers in 2001, which they give as just over 20 billion.
  5. From this last number, together with data about the average price of alcoholic beverages, they estimated the amount of money spent on underage drinking.

Now, as I suggested above, it's unlikely that you can use benchmarks to check these statistics, but there's another way you can do it. You can check these numbers using only the information above. Moreover, you won't need any sophisticated math, though the use of a calculator would make the calculations less tedious. When you've done so, click on "Sobriety Check", below, to see the results of one such check.

Sobriety Check


  1. Susan E. Foster, Roger D. Vaughan, William H. Foster, Joseph A. Califano Jr, "Estimate of the Commercial Value of Underage Drinking and Adult Abusive and Dependent Drinking to the Alcohol Industry", Archives of Pediatrics & Adolescent Medicine, 5/2006
  2. Eric Nagourney, "Addiction: Sales Estimates Paint Portraits of Alcohol Abusers", The New York Times, 5/2/2006

Resource: Sobriety Check, 2/24/2015

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

Why do we believe celebrity pseudoscience?
February 9th, 2015 (Permalink)

New Book: Is Gwyneth Paltrow Wrong About Everything?

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 4, 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:

Weíve seen just a skyrocketing autism rate. Nobody knows exactly why. There are some people who are suspicious that itís 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 Obamaís 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

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