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December 16, 2007 | 1 Comment

12 million kids are being held hostage by a psychiatric disorder

Ad campaign pic for 12 million warped kidssource: New York Times

My God! 12 million! Something must be done!

This bulletin board appears at various places in New York City (as reported in the New York Times). It is sponsored by the New York University Child Study Center. It’s purpose is to—wait for itraise awareness! (Of autism and other maladies that afflict the young.)

But the only thing that I was made aware of, is that this number almost certainly cannot be true. And that this ad is yet another example of a group nobly, but wildly, exaggerating a claim in order to make a point. The inherent dishonesty in this practice is ignored or explained away because the topic is so awful. This isn’t the place to talk about it, but if the lesson of Chicken Little or the Little Boy Who Cried Wolf have taught us anything, it is that exaggeration ultimately undermines its very purpose. When people discover the original claim is false, they tend to discount whatever else the claimant might say.

Anyway, how do I know that there can’t be 12 million kids with psychiatric disorders? Let’s figure it out together.

How many people live in the United States? According to the Census Bureau, a little over 300 million. And how many of these people are “kids”? Well, what’s a “kid”? Somebody under 12? Under 18? We can’t be sure what the advertisement actually implies, but let’s suppose, say, 14 (which I chose because that’s a break-point in the Census Bureau tables; but it makes little difference to my conclusion).

About 21% of all people, then, are kids. Which is about 63 million. And if 12 million kids are being “held hostage”, that means 1 out of every 5 kids must have some sort of ransom (in the form of prescriptions?) paid for them.

To put that number into perspective, if we were to walk into a typical school classroom with 30 kids, then there is a 50% chance that we would see 6 or more of these kids currently being “held hostage”!

I need hardly tell you that that number is not consonant with our experience. That is to say, that the original “12 million” estimate, is almost certainly false. And probably by an order of magnitude, too: which is a fancy way of saying we should divide the 12 million by 10 or so. That makes a 50% chance that we see one kid held hostage per room. And that number is more realistic.

So this ad gets a 5 on the Briggs Statistical Deception Scale. Of course, the original 12 million number could be right if we are allowed to, as unfortunately is increasingly the case, define “normal” behavior narrower and narrower, with even slight deviations from the accepted norm being declared due to newly discovered (or expanded in scope) “disorders” and “syndromes.”

December 13, 2007 | No comments

Another attempt to show abstinence is bad: “Losing virginity early or late tied to health risks”

That headline is from an MSNBC story of the same name. Taken at face value, it argues that, for maximum healthiness, we should all aim to lose our virginity at the same age.

No, just kidding. What the article actually says is that “People who start having sex at a younger or older than average age appear to be at greater risk of developing sexual health problems later in life”.

Which actually does sound like they think we should all start having sex simultaneously. But, still no. Actually, their intent is to “cast some doubts on the benefits of abstinence-only sexual education that has been introduced in U.S. public schools.”


How can you get from saying the people who start having sex at a younger age or those who start at an older age are “at higher risk” to “abstinence is bad”?

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December 11, 2007 | 11 Comments

Beer: alcohol, calories, and carbs

Boxplots of calories by beer style

Which beer style has the most calories? In general: porters. The least: lager, the style of beer with which you are probably most familiar. Budweiser, Miller, Coors, the majority of all mass-market beers are all brewed in the lager style.

These box-plots use data from the web site The editors of that site keep a running list of brewers, beers and the alcohol, calories, and carbohydrate content of, at this writing, 229 different beers from 72 different breweries. There are, naturally, many more beers and breweries than this around the world; this data reflects the beers of most interest to readers and users of The classification into styles of beer is my attempt, and any mistakes in classification are my own. You should visit to learn more about beer styles. The data set is most complete with alcohol values, but there is far less information about calories and carbs, owing to the greater difficulty of obtaining or measuring those values.

Here’s a quick lesson on how to read box plots: the dark, center line is the median, the point at which 50% of the values are above, 50% below. The next two horizontal lines are the quartiles: the top one is the 3rd quartile, which means 25% of the values are above it; the next is the 1st quartile, which means 25% of the values are below it. The top and bottom lines are the 5% and 95%-tiles, with the obvious interpretation. Points beyond these are more extreme values. Box-plots are intended to give you an idea of the spread, variability, and distribution of data.

But the main lesson is: if you are counting calories (and don’t insist on taste), lager beers are your choice. Lager and ales also have the widest ranges of calories, but this may reflect the fact that most of the data are from these two main groups. 44% of the beers listed are ales, 38% lagers, 4% porters, 8% stouts, and 6% wheats. There was also one barley wine, a style noted for its high alcohol content, which I classified into an ale since it is difficult to do statistics with just one data point.

How about alcohol content?

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December 10, 2007 | 3 Comments

Never use bar charts! Case study #1

Social secuity disability applications

This graphic comes from the New York Times article “Social Security Disability Cases Last Longer as Backlog Rises.” It obviously intends to show how applications have increased since 1998.

This is a terrible plot.

The reason is not that you should never, with only rare exceptions, use a bar chart. They are simple to construct, but there are nearly always better alternatives.

But the evil of bar charts is well known. The reason this plot is bad has to do with the number 0. Notice that the chart starts at 0, even though it isn’t until 2 million or so that we meet our first number. The only reason that the chart starts with 0 is that it is true that you can’t have less than 0 applications. This is not a good reason. They should have started with a higher number.

Don’t think it makes a difference? Then take a look at this re-drawing:

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