October 06, 2005
Statistical exercise
Today's WSJ has an article which announces the findings of a group of researches at the Rand group doing an FDA funded study (subscription only, so no link). The researchers conclude that obesity rates in children are directly proportional with the price of fresh fruit and produce. They tracked weight gain in young children (K-3) in 59 metropolitan areas and discovered that as the price of fresh produce went up, the rate of obesity went up as well. In Mobile, AL, the area with the highest relative price for such goods, children were 50% more likely than the norm to be obese, whereas in a California community (the name of which escapes me at the moment) with very low prices, children were less likely to be obese.
So, our conclusions are that 1) obese children don't eat enough fresh fruit and vegetables, 2) not eating enough fresh fruit and vegetables is the result of not being to afford them, and 3) we need to adjust our public support for low-income families to enable better access to these goods. Right? Right?
Wrong. Those are things we may not conclude from the study. The reasons for this follow.
First, and most importantly, the study makes no correlation between the price of produce and the consumption of produce. Thus there is no statistical reason to believe that people who live in areas in which produce is more expensive than the norm consume any less than people who live in areas with lower prices. While such a correlation may exist, this study does not make it, and further research would be needed to forge such a connection. Furthermore, the study does not comment on whether areas with high produce prices are also areas of high income. You would need to compare their data with mean and median income levels to adjust for that. E.g. lower Manhattan has disgustingly high produce prices, but mean/median income is in the high-five/low-six figure range, so access to fresh produce is pretty unrestricted (heck, they even deliver, if that's your thing). Finally, the FDA officer who commented on the study advised that even in high-price areas, it is still possible to buy six or seven servings of fresh fruit and produce for around a dollar.
One thing the study did disprove is the theory that an excess of fast-food restaurants and a dearth of supermarkets in low income areas are responsible for an increase in obesity in low-income areas. The study found this not to be the case, as obesity patterns showed no relationship with proximity to fast-food and supermarkets.
I would suggest that areas with higher obesity have higher prices due to lower demand for the fruits and vegetables. Less demand means the expense of shipping and growing and marketing, etc., spread among fewer people.
Posted by: april at October 6, 2005 03:46 PM'Tis possible, but again, this study doesn't provide any data on consumption patterns. Thus, demand isn't a variable to which we can assign a value given the outputs of this study. For all we know people are eating more vegetables.
Posted by: ryan at October 6, 2005 03:56 PM"For all we know people are eating more vegetables."
Yeah, for all we know, badgers sneak fruits and vegetables into their homes at night, and force-feed them to the kiddies. Since data were not provided on this aspect, we really can't tell, can we?
Posted by: joe public at October 6, 2005 04:03 PMNo. No we can't. You can feel free to make that inference if you want, and I'll even probably agree with you. But this study doesn't say that, and you can't draw that inference from the available data. It can suggest a direction for future research. But without actually doing said research, the best you can do is to say "It seems likely that in areas with high produce prices that people would consume fewer fresh fruits in vegetables."
The point here is what kind of conclusions it is appropriate to draw from statistical data. Most people haven't a clue. Try to get one. In short, the only conclusions you can draw from a statistical analysis are those immediately required by the mathematics. If you think further conclusions likely, do more research, but you can't claim those conclusions unless you've done the research.
Posted by: ryan at October 6, 2005 04:30 PMI do have an inkling (though I slept through a lot of my college Introductory Statistics lectures) of what kinds of conclusions are appropriately drawn from statistical data. "Appropriately," of course, being defined as strictly mathematical, as you point out.
That said, I also have a clue (yep, went and got it) about things that are easily surmised without the use of statistical studies to begin with. We don't always have to lose our view of the forest by picking through the cells that make up the trees.
Posted by: joe public at October 6, 2005 04:43 PMOne of the stated weaknesses of the study is that they don't have any data on consumption. It would seem to follow from that that drawing conclusions related to consumption based on the information provided by the study is uncalled for.
Posted by: ryan at October 6, 2005 04:57 PMStatistics never has to do with causation, though, only correlation. So even with all the research in the world run through all the statistical models, you could never say "this" causes "this". You always have to make outside assumptions that have to do with causation.
Posted by: Mello at October 6, 2005 05:27 PMA Humeian to the end, I see. A nice observation with a conclusion I'll grant. But if we also grant that statistics are useful indicators of probability and can be useful tools in assigning causation - at least for the purposes of argument - it still wouldn't follow from these statistics that produce consumption is affected by price. You'd need more data.
Posted by: ryan at October 6, 2005 05:41 PMGranted and agreed.
I had to look up Humeian, and my googling doesn't give me a sufficient context in which to comprehend it. I suppose I fall on that side of the spectrum, though, but only because I'm trying to keep the world from any more CCC's (crappy causitive conclusions) like Baby Mozart videos and annual colorectal cancer screenings.