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Some Obesity Math

When I was in graduate school, we had an old book laying around titled something like How to Lie with Statistics.  I don't remember ever actually reading the book but the title says it all: one can tell two entirely different stories depending on how one chooses to report the numbers.

I fear that much of the rhetoric surrounding obesity has fallen into this trap.  According to CDC data, the average weight of men aged 40-49 has increased roughly 15 lbs in the past 10 to 15 years (compare data in this publication to this one showing the average weight going from about 187 lbs in 1988-1994 to about 202 lbs in 2003-2006; I should also note that more recent data shows these weight gains leveling off).  

Fifteen pounds doesn't seem like a huge number to me (I've personally lost and gained much more than this amount in my adult life).  So, how is it that this small to medium sized increase in average weight gets translated into a message that there is an epidemic?  Part of the answer is that when scientists translate averages into prevalence rates, the numbers look a lot scarier.   

Stick with me while I illustrate with an example.  

Let’s take a hypothetical population of men whose average weight is 180 lbs.  Suppose, men’s weights vary in the population according to a normal distribution with a standard deviation of 30 lbs.  This means roughly 68% of the men will have weights between 150 lbs and 210 lbs.  Suppose also, for convenience sake, that all the men are the same height: 5 ft 10 inches. 

Obesity is defined as BMI greater than 30 (BMI is weight in kg divided by height in meters squared).  In our hypothetical example, where everyone is the same height, a man will be obese if he weighs more than 209 lbs.  Moreover, given our assumptions about the normal distribution, we can readily project that 16.6% of men in this population will be obese (1 minus the cdf of a normal distribution with mean 180 and standard deviation of 30 evaluated at the point 209 is 0.166).

What if all men gain a paltry 5 lbs?  The average weight goes from 180 up to 185 lbs.  Yet, (again given the assumption of the normal distribution), obesity prevalence will go up from 16.6% to 21.1%.

Thus, we have what most of us would consider a rather trivial gain in weight (an increase in 5 lbs or a 2.8% increase in weight); however, we have what appears to be a rather dramatic increase in obesity prevalence (prevalence goes up 4.48% or a 27% increase in prevalence of obesity!).

If we run through the same example again assuming men gain an average of 10 lbs, we can find that obesity prevalence goes up almost 58% even though weight only increased 5.5%!

Both statistics are "true" but they tell very different stories.  

How Important is Food Freedom?

Last night 60 Minutes aired an interview between Anderson Cooper and a gentleman named  Shin Dong-hyuk. Shin was born in captivity in North Korea and had never experienced life outside the prison compound much less North Korea.  Shin eventually came into contact with a prisoner who had lived on the outside and it opened his eyes to new possibilities.  I found this exchange between Cooper and Shin remarkable:

Shin: The most important thought was that a prisoner like me could eat chicken and pork if I were able to escape the barbed wires. 
Cooper: I've heard people define freedom in many ways. I've never heard anyone define it as broiled chicken. 
Shin: I still think of freedom in that way.
Cooper: Really?! That's what freedom means to you?
Shin: People can eat what they want. It could be the greatest gift from God. 
Cooper.: You were ready to die just to get a good meal?
Shin: Yes.

One might have thought it was the regular beatings or the forced witness to murder that would have motivated Shin to escape.  But the biggest driver seemed to be his desire to freely eat.  

My TEDx talk is up

If you care to watch my TEDx talk from a couple weeks back, it is now up.  I'm not sure why the organizers gave it the title they did, but the talk is really about food innovation, food prices, and the poor.

Oklahoma State University Professor Jayson Lusk researches many aspects of the economics of food health, safety and quality. Lusk points out in his TEDxOStateU talk that an ideology that blanket-rejects "unnatural" food is one that will ultimately doom us to poverty.

The News and Our Misperceptions of Risk

As news reports continue to circulate on the safety of pork and now on animal welfare and fracking, it is useful to step back and consider how we humans perceive and respond to risk.    

I happened to have recently picked back up Kahneman's book Thinking Fast and Slow, and he summarizes some interesting research on these topics.  First on page 138 after showing results from Slovic's research that people were really bad a judging the relative risks of dying from different cases, Kahneman concludes:

The lesson is clear: estimates of causes of death are warped by media coverage.  The coverage is itself biased toward novelty and poignancy.  The media do not just shape what the public is interested in but are also shaped by it . . . Unusual events (such as botulism) attract disproportionate attention and are consequently perceived as less unusual than they really are.  The world in our heads is not a precise replica of reality; our expectations about the frequency of events are distorted by the prevalence and emotional intensity of the messages to which we are exposed.

That last sentence is revealing: the key to creating a public panic is to 1) make the issue emotional and 2) repeat the message so that it is readily available in people's memory.   A few pages later (p. 142), he develops this idea further when discussing Sunstein's research:  

An availability cascade is a self-sustaining chain of events, which may start from media reports of a relatively minor event and lead up to public panic and large-scale government action.  On some occasions, a media story about a risk catches the attention of a segment of the public,k which becomes aroused and worried.  This emotional reaction becomes a story in itself, prompting additional coverage . . . The cycle is sometimes sped along deliberately by 'availability entrepreneurs,' individuals or organizations who work to ensure a continuous flow of worrying news.  The danger is increasingly exaggerated as the media compete for attention-grabbing headlines.  Scientists and others who try to dampen the increasing fear and revulsion attract little attention, most of it hostile: anyone who claims that the danger is overstated is suspected of association with a 'heinous cover-up.'  The issue becomes politically important because it is on everyone's mind, and the response of the political system is guided by the intensity of public sentiment.  The availability cascade has now reset priorities.  Other risks, and other ways that resources could be applied for the public good, all have faded into the background.

Beware of the availability entrepreneur.