Wednesday, June 2, 2010

Perils of Cross-sectional Studies

I am reading Jean Chatzky's book "The Difference"; in in she attempts to look at what traits are associated with good economic outcomes. Some of her examples are very good and a lot of it is thought provoking. But there were a few cases where she seems to run into trouble.

For example, risk taking behavior is u-shaped (highest for the wealthy and the permanently indebted). I can't tell if this relationship in her data is statistically significant (as the variance is not presented) but that doesn't get at the main point, anyway.

The main point is that you would expect people who take risks to break into the highly successful and the impoverished. Looking at the final outcome and saying "what is the expected value of taking risks" is more informative than noting risk takers have more money. If somebody offered to double your wealth if you could roll a 1 or a 2 on a 6 sided die, would this be a good idea? Yet, if we offered this choice to a room of people and then ranked them by net worth, it's likely that the wealthiest people would have rolled the die. So would the least wealthy, as well.

What if you doubled your income on a 1 to 4; the expected value of the roll is positive but losing everything you own might be worse than doubling what you currently have. It's a very complicated inference and it probably requires a posterior distribution to properly express what the choices look like.

Now, I suspect that prospective data would support intelligent risk taking and the book has a lot of good data in it (so don;t take this as a slam of the book as a whole; actually gathering and interpreting data adds a lot to the conversation even if the interpretation isn't always trivial). But it does highlight the complexity of drawing any inferences from cross-sectional retrospective studies. It's not just an issue with Epidemiology data but can occur anywhere else.

[note: some typos were corrected after the initial posting]

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