I’m voting for this concept, one that is so central to the scientific process, so much a given, that hardly any scientist ever actually speaks those words.
Scientists present their work—say, “We manipulated Variable X, and observed that this caused Z to happen,” or “We measured this and found that it takes Z amount of time to happen.” And when they do, most of the time what they’re actually saying is, “We manipulated Variable X, and observed that, on the average, this caused Z to happen.” “We measured this and found that, on the average, it takes Z amount of time to happen.” Everyone knows this.
Of course. Everyone in a population doesn’t have the exact same levels of something or other in their bloodstream. A causes B to happen most of the time, but not every single time. There’s variability.
When scientists present their data, they typically display the average—the mean, the X on a graph, the bar of a particular height in the figure. And it always comes with an “error term—a measure of how much variability there was around that average, a measure of how much confidence there is in saying “on the average.” Measure something or other in three people, observe values of 99, 100, and 101, producing an average of 100; measure that something in three people and observe values of 50, 100, and 150, producing an average of 100. This are two very different circumstance; “the average was 100,” tells you a lot more about how some sliver of the universe works in the first case than the second.
This is how scientists in most disciplines go about their business, with the recognition that you’re always seeing how things work on the average. So why is it important that this be more widely known? I can think of at least three reasons, of increasing importance.
First, this should constitute a big shout-out to scientists and the scientific process. Perhaps counter to the general perception, scientists don’t pronounce upon some fact that they have discovered; they pronounce upon the temporary way station of statistical confidence that they have discovered. “On the average” means that there’s stuff you can’t explain yet, and there’s even the possibility that you’re entirely wrong. It’s a badge of the humility that defines science, when things are working right. And it sure couldn’t hurt if that sort of humility became more commonplace in lots of other settings.
The second reason is that the variability around an average is usually much more interesting than the average itself. “More interesting” in the scientific sense; if variability means that there’s stuff you can’t explain yet, it’s also the guide to where to look to understand things more, to identifying previously unappreciated factors that give rise to the variability.
For example, “On the average, having a particular variant of a gene produces a particular behavior in people….unless, as it then turned out with additional research, someone had a particular type of childhood.” Pursuing the question of why there were exceptions revealed all sorts of things about environmental regulation of gene transcription, child development, gene/environment interactions, and so on.
Moreover, variability is often more interesting in the human sense as well. All things considered, it’s not that exciting that humans average a score of 100 on this thing called an IQ test. It’s the variation that interests us. Or that, on the average, adult humans males can run 100 meters in, say, 25 seconds. It’s Usain Bolt that gets our attention. Or that there’s an average life expectancy—it’s what you and your loved ones are destined for that matters. Crowds of protestors don’t gather in some nation’s capital because of the average income in that country; it’s because of the magnitude of the variance, the extent of inequality.
The third reason is the most important and subtle, and ultimately has little to do with science. Take a population of people. Figure out their average height. Their average weight. Average IQ, shoe size, number of friends, hip/waist ratio, radiant brightness of smile, symmetry of face, athletic skill, sex drive, scores on psych instruments that measure perkiness or optimism or gumption. Define your average human across these parameters. And then good luck trying to find such a person. Because they don’t exist. Even if someone seems to be, say, the average weight, they won’t really be if you look closely enough, measuring things out to the level of grams, or milligrams, or micrograms, or…. Nothing and no one is precisely average, because “averageness” is an emergent property of populations, an artificial construct. It’s like a strange attractor in chaotic systems, which oscillates around a singular point, a hypothetical average that, no matter how closely you look, is never actually achieved. Oh, it does “on the average,” but never in reality.
This matters because, psychologically, we tend to morph “average” into “the norm” and then into “normal” or “ideal.” And what that means is that we all always come up short in achieving what we have labeled as normal and ideal; we’re all a little too heavy, or too tall, with a nose that’s a little too much this, a personality that’s a bit too little that. We all deviate from the norm, from something that is an artificial, statistical construct that does not really exist. We all are “abnormal,” in a sense that’s more pejorative than statistical. And thus feel badly about who we are. What “on the average” truly means in populations is liberating.