Sunday, 15 April 2007

Accuracy vs Precision

One of the most useful things I learnt in first year Engineering (I think it was in my Physics class) was the dual concept of Accuracy and Precision. The way that scientists and engineers think of these terms is a principle that is incredibly useful, and yet one that is not immediately obvious.

Since relatively few people learn this, and even those who do often don't extend the lessons to other areas of their thought, these concepts tend to languish generally unused. Let's see if I can help put an end to that unjustified neglect, shall we?


Let's use the simple scientific context to explain the terms:

  • Accuracy is how close a measurement is to the true value
  • Precision is how small the unit of measurement was (or, how many decimal places)

An example will help. Let's say there are two scales to measure weight: Scale A is accurate but imprecise, Scale B is precise but inaccurate.

Let's say we are trying to measure a lump of metal which has a true weight of 10.05 kg.

Now let's say that Scale A has a precision of 0.1 kgs (ie. it reads in kgs to one decimal place) and an accuracy of +/- 0.005kg (ie. it's measurement is guaranteed to be no less that 0.005kg less than the true weight and no more than 0.005kg more).

Scale A will therefore measure the weight as between 10.045 and 10.055kg, and will round this to either 10.0 or 10.1. We can see that the we can only really speak of the scale as having an accuracy of +/- 0.05, due to the limited precision.

Now let's say Scale B has a precision of 0.001 kgs, and an accuracy of 0.5kg.

The lump of metal will be measured as between 9.55 and 10.55kg, and Scale B will display any value between these. Basically, any of the decimal points are completely meaningless in Scale B, so a measurement of 9.557kg, despite seeming more authoritative than 10.0kg, is actually less accurate.

Thus, Scale B, with more decimal places on its readout, and which the uninitiated would have taken as being more useful to a scientist trying to measure weight, turns out to be much less useful than Scale A.

Application Outside Simple Measurement

This principle is easily applied outside simple measurement. For example, statistics are often quoted to an extraordinary precision (40.5% of so-and-so do such-and-such), and people tend to incorrectly apply them as if they spoke accurately to each instance of so-and-so, even when the standard deviation may be huge, which indicates that not even close to 40.5% of so-and-so's are such-and-such.

Radioactive dating techniques are an obvious area where high precision and low accuracy is prevalent -- radioactive dates often conflict with one another on the order of millions of years, so clearly, no matter how precise they are (and they're very precise) they are wildly inaccurate.

Another example is confusing a wealth of documentation or discussion on a topic (say, the inferiority of certain races, documentation pre-WWII) with the accuracy of the general opinion (ie. it's closeness to the truth). There are numerous examples of this: the documentation on biological evolution (voluminous and laboriously detailed, ie. precise) vs. its accuracy (hopelessly inaccurate, with massive problems like homoplasy -- independent evolution resulting in similar physical forms -- completely ignored); documentation on Freudian psychology (huge and detailed) vs. accuracy (now almost universally condemned as hopelessly incorrect), etc., etc.

Science is rich in fields with large amounts of enormously precise, hopelessly inaccurate documentation. This is not a condemnation of science, but merely a reflection of its fallible nature.

Other areas we see this is in medicine, where a doctor makes a precise, but often inaccurate diagnosis (of course, we almost force them into this situation, since we are rarely happy with vague diagnoses and would generally prefer a more precise, if less accurate, diagnosis and prescription).

Other examples are advertising claims, often very precise (lose 18kg in two weeks!) but hopelessly inaccurate.

Even ideologies or ideas can be precise and detailed, but terribly inaccurate. In fact, it is often a temptation for people to extend arguments beyond their expertise, and they end up making precise, but inaccurate statements in support of a precise but inaccurate position.

Take away lesson

So, what can we take away from this?

  1. Don't confuse precision with accuracy. Precision is essentially worthless without accuracy, while accuracy is always worthwhile, but is increasingly valuable as combined with increasing precision.
  2. An accurate but imprecise position (on almost anything) is more valuable than a precise but inaccurate one.
  3. Don't ask for more precision than something or someone can accurately deliver -- you'll just be burdening yourself with misleading detail.
  4. Focus on accuracy first, precision second, and things will generally work out better.

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