Mean old regression. Phooey.
Anybody else watching "Top Shot" on the History Channel? It's a competition for marksmen(and women). It's kind of awesome.
Breaking News: Obama directs the DOJ to stop defending DOMA. It's about damn time.
Be advised: what follows is me pontificating about something interesting I'm reading. Proceed with caution and at your own risk.
So here's a question for thought: what do the sophomore slump, the Sports Illustrated curse, and parental devotion to time-outs have in common?
Answer: they're all illustrations of the statistical phenomenon known as regression to the mean. It explains so many things in the universe that have become superstitions or beliefs, but when you read it explained, it's so obvious. I'm reading a book now that explained it really clearly. So I'm passing it along.
Basically, regression to the mean can be summarized as "nowhere to go but up/down." Any measurement that's extreme is more likely to be followed by one that's less extreme. The Sports Illustrated curse is a great example. It's widely believed that being pictured on the cover leads to poorer performance. I don't have numbers on it, but it's most likely at least somewhat true. Not because SI is cursed, but because of regression effects. When is somebody or a group of somebodies on the cover of SI? When they've performed extraordinarily well. Just playing the odds, it is much more likely that after that, they'll go on to not perform quite as well, just because extraordinary performance is a statistical outlier. Their performance will regress towards their own average performance, and so will be seen to deteriorate. Consider also the sophomore slump that novelists are cursed with. Well, basically we only notice this or remark on it when someone's debut novel is somehow extraordinary, either in quality or in popularity. Odds are that the next one won't be quite as extraordinary, not as a fault of the author or the book-buying public, but because data points regress to the mean. So their next offering will more likely be seen as a disappointment. They had nowhere to go but down.
This has troubling implications for behavioral modification as well, as in parenting or teaching techniques. There are numerous studies that show that rewarding desired behavior is more effective than punishing undesired behavior, yet most people rely more heavily on punishment, believing it to be more effective. It is not. The fact that it seems more effective is a consequence of regression.
Consider little Sally. Let's assign little Sally's average behavior a letter grade of C. This is how Sally acts most of the time. Not a monster, not an angel. So one day, little Sally is especially good and exhibits A grade behavior. Sally's mom rewards her. Even if you discount the motivational effects of the reward, the most likely outcome in subsequent days, because Sally's A-grade behavior was an outlying data point, is that she will behave at the B or C level. Regression to the mean. Therefore Sally's mom will perceive her reward as being either ineffectual or counterproductive. Conversely if Sally behaves at F-level, she is punished. Even if the punishment has no effect on Sally, her behavior is likely to improve over the next few days because it had nowhere to go but up. So the punishment is seen as being effective.
This was demonstrated with a computerized simulation of a student arriving to class either early or late. The intended arrival time was 8:30. Observers were told what time the student arrived, and asked to punish or reward him accordingly. They rewarded him for being early but punished him for being late. The arrival times ranged from 8:20 to 8:40. After cycling through several dozen arrival times, the observers were asked to judge the efficacy of the punishment or reward. Over 70% said that the punishment was more effective.
Here's the kicker: the arrival times were randomized. The rewards or punishments had no effect on them. But due to regression effects, people more often saw the arrival times improve after being late, and worsen after being early. So they perceived the punishment as being effective.
The take-home lesson is simpy that statistically speaking, after somebody does Awesome, they're more likely to do Less Awesome than More Awesome. That's pretty intuitive. Nobody can do Super Awesome all the time, and our average performance is average for a reason. This leads to the perception that awesome performance is a curse that leads inevitably to failure, when in fact it's just a statistical reality. If you did, in fact, perform at the Super Awesome level all the time, then that would become your new average performance, and you'd still regress to THAT mean.
You can't escape statistics, man.
Breaking News: Obama directs the DOJ to stop defending DOMA. It's about damn time.
Be advised: what follows is me pontificating about something interesting I'm reading. Proceed with caution and at your own risk.
So here's a question for thought: what do the sophomore slump, the Sports Illustrated curse, and parental devotion to time-outs have in common?
Answer: they're all illustrations of the statistical phenomenon known as regression to the mean. It explains so many things in the universe that have become superstitions or beliefs, but when you read it explained, it's so obvious. I'm reading a book now that explained it really clearly. So I'm passing it along.
Basically, regression to the mean can be summarized as "nowhere to go but up/down." Any measurement that's extreme is more likely to be followed by one that's less extreme. The Sports Illustrated curse is a great example. It's widely believed that being pictured on the cover leads to poorer performance. I don't have numbers on it, but it's most likely at least somewhat true. Not because SI is cursed, but because of regression effects. When is somebody or a group of somebodies on the cover of SI? When they've performed extraordinarily well. Just playing the odds, it is much more likely that after that, they'll go on to not perform quite as well, just because extraordinary performance is a statistical outlier. Their performance will regress towards their own average performance, and so will be seen to deteriorate. Consider also the sophomore slump that novelists are cursed with. Well, basically we only notice this or remark on it when someone's debut novel is somehow extraordinary, either in quality or in popularity. Odds are that the next one won't be quite as extraordinary, not as a fault of the author or the book-buying public, but because data points regress to the mean. So their next offering will more likely be seen as a disappointment. They had nowhere to go but down.
This has troubling implications for behavioral modification as well, as in parenting or teaching techniques. There are numerous studies that show that rewarding desired behavior is more effective than punishing undesired behavior, yet most people rely more heavily on punishment, believing it to be more effective. It is not. The fact that it seems more effective is a consequence of regression.
Consider little Sally. Let's assign little Sally's average behavior a letter grade of C. This is how Sally acts most of the time. Not a monster, not an angel. So one day, little Sally is especially good and exhibits A grade behavior. Sally's mom rewards her. Even if you discount the motivational effects of the reward, the most likely outcome in subsequent days, because Sally's A-grade behavior was an outlying data point, is that she will behave at the B or C level. Regression to the mean. Therefore Sally's mom will perceive her reward as being either ineffectual or counterproductive. Conversely if Sally behaves at F-level, she is punished. Even if the punishment has no effect on Sally, her behavior is likely to improve over the next few days because it had nowhere to go but up. So the punishment is seen as being effective.
This was demonstrated with a computerized simulation of a student arriving to class either early or late. The intended arrival time was 8:30. Observers were told what time the student arrived, and asked to punish or reward him accordingly. They rewarded him for being early but punished him for being late. The arrival times ranged from 8:20 to 8:40. After cycling through several dozen arrival times, the observers were asked to judge the efficacy of the punishment or reward. Over 70% said that the punishment was more effective.
Here's the kicker: the arrival times were randomized. The rewards or punishments had no effect on them. But due to regression effects, people more often saw the arrival times improve after being late, and worsen after being early. So they perceived the punishment as being effective.
The take-home lesson is simpy that statistically speaking, after somebody does Awesome, they're more likely to do Less Awesome than More Awesome. That's pretty intuitive. Nobody can do Super Awesome all the time, and our average performance is average for a reason. This leads to the perception that awesome performance is a curse that leads inevitably to failure, when in fact it's just a statistical reality. If you did, in fact, perform at the Super Awesome level all the time, then that would become your new average performance, and you'd still regress to THAT mean.
You can't escape statistics, man.