Suppose you wanted to put together a test of athletic ability, maybe to aid in the scouting of players for some team. Here’s one way you could do it. Give the subject a series of tests, like how much can he bench press, how fast can he run the 100, the quarter mile, the mile, how high can he jump, etc? Be sure to include some eye-hand coordination tasks, some height, weight, and bulk measurements, in fact, put in everything you can think of.
Now just add up all the scores, and viola! You’ve got your “A. Q.” measurement.
Well, that isn’t very good, is it? At the very least, you’re probably double counting some abilities, at least partly. After all, the speed tests probably correlate to some degree, as do a lot of strength tests. So let’s put all our scores through a mathematical procedure called “principle component analysis” (PCA). That will “orthogonalize” our test scores, and give you a series of “principle components” or “principle factors” that do not correlate with each other. You might wind up with uncorrelated factors that largely correspond to “strength”, “flexibility” and “reaction time.” Alternately, you might wind up with factors that look like “weightlifter”, “swimmer”, or “racketball player.” In truth, what you’re going to wind up with is a series of mathematical constructs, whose sole reason for existence is that each one is largely uncorrelated to the others. Also, owing to the nature of PCA, you’re only going to wind up with two or three components before measurement variance turns the remaining factors into gibberish or noise.
You could, of course, then call the largest component “general athletic ability,” and call the second component “crystallized athletic ability.” That’s how it’s done with I.Q. after all.
With athletic tests, of course, it’s pretty easy to see the problem. We know that upper body strength is different from eye-hand coordination, and that neither of them have much to do with how fast you can run 100 meters from a standing start. To be sure, there might well be some correlation; someone who is old, sick, sedentary, or drunk isn’t likely to be very good at any of them and that is correlative. But it’s still obvious that they are different abilities.
Moreover, our hypothetical scout doesn’t give a damn about “overall athletic ability.” If he’s a baseball scout, he wants to know how well the player can play baseball. There’s a cluster of skill associated with baseball, and that cluster is different from other sports. There’s no other sport where being left-handed is rewarded to the extent that it is in baseball, for example.
Similarly, height is useful to a basketball player, in almost exactly the way that it isn’t helpful to a jockey. Nor will you see many people who are triple threats in weightlifting, pistol shooting, and figure skating.
So while our scout might very well give a battery of tests to a potential player, those tests will be different, or at least weighted very differently, from one given by a scout for a different sport. And in any case, the eventual test of the matter will be in how well the player plays the sport.
While this may be obvious when it is applied to physical characteristics, for some reason, people don’t find it obvious when applied to mental characteristics. Maybe it’s because mental characteristics are abstract that people want a number to go with them, but I don’t find that argument persuasive. After all, there are all those baseball statisticians.
For my own part, I’ve gone from once putting a lot of value on I.Q. testing and scores to putting almost no value on it at all. I’ll stipulate that testing has been very good to me, giving me access to an education and a profession that I’d not have had, given the other aspects of my origins. But I’ve known too many smart people who tested poorly, and too many people who test well whose judgment I would not trust on anything.
Moreover, I’ve become very aware over the years of all the different mental skills that people possess, and how often one very different trait can substitute for another. And I’ve also seen how many times test scores of one sort or another have been used to beat up on the disadvantaged, to cut them out of the opportunity to even play the game.