## Monday, January 17, 2011

### Obesity epidemic cured!

I have good news to report -- the obesity epidemic is over.  And the solution turns out to be the best kind: simple and completely painless.  The solution is self-reporting.  Instead of weighing people, all we have to do is ask them what they weigh.  Problem solved!

I got data from the Behavioral Risk Factor Surveillance System (BRFSS), run by the National Center for Chronic Disease Prevention and Health Promotion.  In 2008, they surveyed 414,509 respondents and asked about their demographics, health and health risks.  In particular, they asked respondents for their weight now and their weight one year ago.

By taking the difference, we can characterize weight change in the population.  And the news is good.  According to these reports, the average weight change was -0.64 kilos; that is, the average respondent lost 1.4 pounds.

Of course, this result is unrelated to reality.  In fact, most adults gain about a pound a year.  The most likely explanation is some combination of inaccurate recall, self-delusion, and attempts by respondents to impress surveyors.

But before making harsh judgments, let’s look more closely at the data.  Before computing the mean change, I discarded a few outliers -- anyone who reported a change of more than 40 kg.  Even so, the mean can be misleading, so we should look at the distribution.  This figure shows the cumulative distribution (CDF) of reported weight changes:

About 25% of respondents reported a weight loss, 52% reported no change, and 23% reported a gain.  The distribution is roughly symmetric, but we can get a better look by plotting CDFs for gains and losses:

The curves have the same shape, but the distribution of losses is shifted to the right.  This result suggests that we can’t blame a small number of wildly inaccurate respondents; delusion seems to be widespread.

These data demonstrate the dangers of self-reporting.  Even when surveys are administered carefully, people tend to remember wrongly, kid themselves, and portray themselves in a positive light.

But if you want the obesity epidemic to go away, just ask!

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If you are interested in topics like this, you might like my book, Think Stats: Probability and Statistics for Programmers.