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A short entry on the NY Times website provides the Facts and Figures of pizza consumption in the United States. I have a casual interest in how statistics are used (or abused) to provide information to general audiences, and a couple questions have arisen based on the statistics presented:

  • If 1 out of 8 Americans will eat pizza today, does that mean that the average American will eat pizza once every 8 days? There's an assumption here that every american eats pizza, which is not the case; however, that raises the question of how to make a valid assumption of how many Americans eat pizza.
  • It is reported that 25% of a child's caloric intake is pizza. I'll define a child as a 9 year old who is moderately active and therefore needs a 2000 calorie daily intake. If we trust Google's estimate that the number of calories in a pizza slice is 285, then does that suggest that a child consumes 12 slices of pizza per week on average? (2000 * 7 * 0.25 / 285)

I suspect my interpretation of the statistics is flawed; it does not seem to me that a child could be part of the 1-out-of-8 Americans eating pizza today while also eating approximately 1.7 slices per day to achieve the 25% caloric intake number.

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Regarding your first bullet point, bear in mind that people are heterogeneous. There is a small proportion of people who eat pizza constantly, a lot of people who eat it occasionally, & some people who never eat pizza. Also, there is no average American. –  gung Feb 12 at 3:53
    
@gung Exactly! I find that the point you make is not obvious to the general public, yet these statistics are made for general public consumption. I am very interested in how one effectively presents this type of information in a way that is useful and concise but not misleading. –  bobthechemist Feb 12 at 4:10
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up vote 17 down vote accepted

To understand the limitation of these data one must understand the structure of NHANES. In the 2007-2010 cycle NHANES included two 24-hour dietary recalls as part of the interview process. Children's intakes might be co-reported by a proxy/caretaker. The dietary recalls served to just show on a typical day how Americans eat, it's not meant to be a long-term food preference survey.

If 1 out of 8 Americans will eat pizza today, does that mean that the average American will eat pizza once every 8 days? There's an assumption here that every American eats pizza, which is not the case

I don't see this assumption being necessary. It can easity be dispelled if you swap in something that is less modifiable. For instance: 1 out of 2 Americans is male. Apparently we don't need to shapeshift between male and female every other day.

however, that raises the question of how to make a valid assumption of how many Americans eat pizza.

I agree, as I have described above NHANES is not meant to report preference. At best we can just assume that today, our best guess is that 1 out of 8 Americans would be consuming pizza.

It is reported that 25% of a child's caloric intake is pizza. I'll define a child as a 9 year old who is moderately active and therefore needs a 2000 calorie daily intake. If we trust Google's estimate that the number of calories in a pizza slice is 285, then does that suggest that a child consumes 12 slices of pizza per week on average? (2000 * 7 * 0.25 / 285)

I don't think if I understand your concern, but please read the original release here. On page 3, it says that the 25% energy contribution only applies to children who had had pizza on the sampled day. For general US children population, the total energy contribution of pizza drops to 4%.

So, if some children have pizza on a given day and if their total daily calories end up being 2000 kcal, then the pizza would likely contribute around 25% of it. According to your pizza calorie number (285 kcal/slice), the children usually consume about two slices.

Also notice that the 2000 kcal I quoted here is the observed total calories, not "required calories" as you pointed out. From the report, I don't think they use any dietary guidelines (aka ideal amounts of nutrients and energy) as their denominator.

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Thanks for clarifying NHANES and their sampling process. Also, you hit the nail on the head wrt the 25% energy contribution; I missed the who had had pizza part of that number. +1 –  bobthechemist Feb 11 at 18:12
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NHANES - National Health and Nutrition Examination Survey cdc.gov/nchs/nhanes.htm –  Sam Feb 11 at 22:13
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Regarding your first bullet point, bear in mind that people are heterogeneous. There is a small proportion of people who eat pizza constantly (say, some college freshmen), a lot of people who eat it occasionally, and some people who never eat pizza. It is worth always remembering that there is no "average American". The confusion that you are recognizing is an instance of what economists call the ecological fallacy. In essence, this is assuming that what is true of an aggregate (e.g., all Americans) must be true of the components (e.g., each individual American).

It is hard for me to think how a newspaper might try to briefly state the statistics at issue and preempt this possible confusion without being pedantic or trying to give a statistics lesson. As critical as I am on occasion of the news media, this is a genuinely difficult task and they have competing demands. I suppose they could say, "because some people eat pizza so frequently, on a typical day one in eight Americans is eating pizza (albeit from day to day many of these are the same people)".

As to your question about how we can validly conclude the proportion of Americans who eat pizza, without more information, all we can say is that the proportion must be within the interval from 12.5% to 100%. Based only on loose familiarity with analogous phenomena, I would guess the distribution follows a power law.

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I was surprised as well that the newspaper would simply cut and paste (with citation, at least) the facts and figures with no commentary added. It reads more like an advertisement for the cited blog entry. –  bobthechemist Feb 12 at 14:04
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