Monday, October 20, 2014

Moar Accuracies

You've probably heard the saying, "It's better to be mostly accurate than precisely wrong." But what does that mean exactly? Aren't accuracy and precision basically the same thing?

Accuracy relates to the likelihood that outcomes fall within a prediction band or measurement tolerance. A prediction/measurement that comprehends, say, 90% of actual outcomes is more accurate than a prediction/measurement that comprehends only 30%. For example, let's say you repeatedly estimate the number of marbles in several Mason jars mostly full of marbles. An estimate of "more than 75 marbles and less than 300 marbles" is probably going to be correct more often than "more than 100 marbles but less than 120 marbles." You might say that's cheating. After all, you can always make your ranges wide enough to comprehend any range of possibilities, and that is true. But the goal of accuracy is just to be more frequently right than not (within reasonable ranges), and wider ranges accomplish that goal. As I'll show you in just a bit, accuracy is very powerful by itself.

Precision relates to the width of the prediction/measurement band relative to the mean of the prediction/measurement. A precision band that varies around a mean by +/- 50% is less precise than one that varies by +/- 10%. When people think about a precise prediction/measurement, they usually think about one that is both accurate and precise. A target pattern usually helps make a distinction between the two concepts.
The canonical target pattern explanation of accuracy and precision.

The problem is that people jump past accuracy before that attempt to be precise, thinking that the two are synonymous. Unfortunately, unrecognized biases can make precise predictions extremely inaccurate, hence the proverbial saying. Jumping ahead of the all too important step of calibrating accuracy is where the "precisely wrong" comes in.

Good accuracy trucks many more miles in most cases than precision, especially when high quality, formal data is sparse. This is because the marginal cost of improving accuracy is usually much less than the marginal costs of improved precision, but the payoff for improved accuracy is usually much greater. To understand this point, take a look again at the target diagram above. The Accurate/Not Precise score is higher than the Not Accurate/Precise score. In practice, a lot of effort is required to create a measurement situation that effectively controls for the sources of noise and contingent factors that swamp efforts to be reasonably more precise. Higher precision usually comes at the cost of tighter control, heightened attention on fine detail, or advanced competence. There are some finer nuances even here in the technical usages of the terms, but these descriptions work well enough for now.

Be careful, though - being more accurate is not just a matter of going with your gut instinct and letting that be good enough. Our gut instinct is frequently the source of the biases that make our predictions look as if we were squiffy when we made them. We usually achieve improved accuracy through the deliberative process of accounting for the causes and sources of the variation (or range of outcome) we might observe in the events we're trying to measure or predict. The ability to do this reflects the depth of expert knowledge we possess about the system we're addressing, the degree of nuances we can bring to bear to explain the causes of variation, and a recognition of the sources of bias that may affect our predictions. In fact, achieving good accuracy usually begins by assessing that we may be biased at all (and we usually are) and why.

Once we've achieved reasonable accuracy about some measurement of concern, it might then make sense to improve our precision of the measurement if the payoff is worth the cost of intensified attention and control. In other words, we only need to improve our precision when it really matters.
[Image from by Salvatore Vuono.]

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