The power of self-fulfilling prophesies:
According to Vietnamese astrology, your year of birth shapes your chances in life. Some years are good luck, others are bad luck, and your prospects for health and professional success are dim if you happen to be born in the wrong year. A new study sponsored by The World Bank seems to offer empirical support for this belief: it finds that Vietnamese chilren born in auspicious years enjoy better health and higher education levels than those born in unlucky years. (This finding holds true even within families - children born in lucky years are healthier and better educated than their "unlucky" siblings.) However, the authors attribute this effect not to the influence of the zodiac, but to family planning. In a horoscope-conscious society, they argue, children born in auspicious years are more likely to have been planned for, and are more likely to reap the benefits of "favorable financial, pscyhological, or emotional conditions" than their unplanned for peers.
That's from The Atlantic. What I find fascinating about this research is how experience conspires against reaching the correct conclusion. After all, children born in "unlucky" years really are unlucky. The most obvious causal link - at least if you subscribe to astrology - is actually wrong, even though it appears true. In reality, the stars don't give a shit about us.
This reminds me of a classic Daniel Kahneman story. In the late 1960's, Kahneman was giving a lecture to flight instructors in the Israeli Air Force. The moral of his lecture that day was straightforward: praise is more effective than punishment for promoting skill-learning. This fact had been confirmed by countless psychology experiments across a wide range of species.
When Kahneman finished speaking, the most seasoned flight instructor in the audience raised his hand and made his own short speech. He said that Kahneman was completely wrong: the only way to produce good flight cadets was through relentless criticism. Positive reinforcement was for wimps. According to the flight instructor, whenever he complimented pilots for the clean execution of some maneuver, they usually did worse on their next attempt. On the other hand, when he screamed at cadets for bad execution, they generally improved on their subsequent flight. In other words, polite praise produced mediocrity, while criticism led to progress.
After listening to the flight instructor, Kahneman realized that any single performance by a pilot--good or bad--was likely to be followed by a flight that moved closer, or regressed, to that pilot's long term average. The pilots who were criticized for a subpar flight were more likely to do better the next time no matter what their instructors said. Likewise, those pilots who received compliments were more likely to do worse on their next run. Of course, the flight instructors weren't aware of this statistical law, and they believed that their reactions caused the resulting changes in performance.
This is analgous to Vietnamese believing in the luckiness of years. From the perspective of the flight instructors, bad flights tended to follow praise, and improved flights tended to come after criticism. Unless a flight instructor was well-versed in the laws of statistics, the only "rational" conclusion was the wrong one.
So what's the moral? We should make introductory statistics a mandatory high school class. I haven't used the quadratic formula for years, but I'm constantly wishing that I had a better understanding of correlation.
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So if over the long run, the average is to have 50% good luck and 50% bad luck, then each year regresses towards the average. Good years are followed by bad and vice versa. Does this only work, however, if there are 1) an equal number of "good" and "bad" years, and 2) if they follow sequentially: good-bad-good-bad-good...?
What if, according to the Vietnamese calendar, out of 100 years, 60 are good and 40 are bad? Or what if the sequence is something like good-good-bad-bad-bad-good-good-good...and so on?
Either way, the stars couldn't possibly care any less about our existence and yes, intro stats should be taught as a course (or at least woven more carefuly into existing courses) early in our education. I believe that Peter Donnelly, over at Ted Talks (ted.com), had a similar message.
H.G. Wells: In the future, an understanding of statistics will be as important as the ability to read and write.
Kahneman's realization actually seems to be based on a basic misapprehension of randomness, compounded by the mistaken belief that the performance of military pilots early on the learning curve is best modeled as a random variable.
I think a much more realistic explanation for the observed data would be that pilots that are still on the learning curve and have just been praised for their performance are more likely to "think they have it" when they really don't, and so incorrectly rely on their instincts the next time, resulting in relatively poor performance. The opposite effect is left as an exercise to the reader.
I won't speculate on the effectiveness of training methods here, except to say that it seems to me that the most effective trainers will use both methods as appropriate, depending on the student, their personality, and their current mood.
Gary England, a well-known and loved Oklahoma TV Meteorologist (who holds no degree in Meteorology), asserted in his weather column in the pages of the (nationally known) Daily Oklahoman that if tornados are scarce for several years in a row, they are more likely to appear in the next year. "We are due for a lot of tornados this year", in other words, and advanced as meteorology by a "meteorologist." A reader wrote in to complain, and Mr. England ridiculed him in the column. I wish I could find the clipping. It was pretty absurd to see him clinging to such obvious error. A lot of people don't understand just how random random truly is.
This realization also seems even more confusing after reading the Wikipedia article on Kahneman (this was admittedly my first exposure to him).