Saturday, August 29, 2009

Statistics and Facts: Any Correlation?

All right, this is indeed a hilarious post from Greg Mankiw. The statistics show that children from higher income families are getting higher average SAT scores, and some people claim that there is a correlation between income and better result of tests. However, Mr. Mankiw theorizes that the correlation is not on the income rate, but on the fact that smart people are making more money and these people pass their genes to their children, thus smart children comes from smart parents not from rich parents.

Okay, I'm not a professional statistician, but when dealing with statistics, I always remember what David Hume, a Scottish philosopher, has taught us on making a conclusion from our experience: just because in your experience an act is always followed by the second act does not mean that there is a causality between the first act and second act.

In Nassim Nicholas Taleb's wisdom (taken from his book "Fooled by Randomness"): "no amounts of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion." If translated: even after going through 1,000 successfull experiments, you will never be able to claim that a hypothesis is correct with 100% degree of certainty, but it will only need one failed experiment to reject such hypothesis.

I agree with both of Hume and Taleb. Previously, I have made some hypotheses with certain logical reasoning in my blog. Will it always be correct? Of course not! Situation and condition may change or maybe I haven't considered all of the relevant issues and facts, or maybe there is a fallacy within my seemingly fine argument.

Mr. Mankiw is correct in saying that the ones who conclude that there is a relationship between family income and better test results might be wrong, but I also dare to say that his conclusion might not be correct either. Are there any relationship between smart people and their incomes, i.e. the smarter you are, the higher your income? I don't know, though I do know some rich stupid people and some poor to average smart people. Further, how many data should we collect before we can make such conclusion? Again, I don't know.

My advice is simple, be very careful when we are dealing with statistics as people can always make different conclusions and interpretations from such statistics. When you think that a correlation between facts exists based on a result of a statistic, you better think it through again.

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