He-Man was a Statistician


As ruler of Eternia, He-Man had to make many decisions. Often, he would resort to the use of statistical tests to support his decisionmaking.

He-Man knew that even statistical tests could be wrong on occasion. If a test said there was a difference between two quantities when there actually was not, he called that a "false positive" or a "Type I error." If a test said there was no difference between two quantities when there actually was one, he called that a "false negative" or a "Type II error." The rate at which a statistical test makes a Type I error he called "alpha" and the rate at which a statistical test makes a Type II error he called "beta." Being royalty, He-Man had confidence in himself and his decisions. So he called the quantity {1 - alpha}.the confidence of a statistical test.

He-Man's advisors were always wringing their hands and whining to him about having 95% confidence. He-Man knew confidence was important because it is a measure of how sure he would be that a significant statistical test result was real. (And next to confidence, significance was one of those things that his advisors just wouldn't give a rest.) However, being a wise ruler, He-Man knew there is much more to decisionmaking than just controlling the Type I error. He knew his test must also have the power to detect meaningful differences. So He-Man called the quantity {1 - beta} the POWER of his statistical test.

In a statistical test, power, confidence, the number of samples, and the size of a "meaningful difference" are all related parameters. Given the variance of a sample population, He-Man would decree what three of the four parameters were and calculate the last. Usually, he would mandate that the confidence be 95% (to keep his damn advisors quiet) and collect as many samples as his royal accountant would allow. Then, he would calculate how big a difference he could detect and still have POWER. Usually, he would try for at least 80% power. And it must have worked, otherwise he wouldn't have gotten his own television show (not to mention the stage play, all those ice shows, and the profits from the action figures).

So now you know what He-Man really meant when he said ...



I have the Power