Sunday, November 07, 2004

Questioning Potential Suitors;
The Difference Between Accuracy and Precision

In the summer of 1974, as I rode with my family in a new Ford Galaxy 500 station wagon, the air conditioning was on.  It was on because we were in New Mexico, and it was Very Hot.  We came over the Organ mountains, approaching Las Cruces.  My sister cried out: "wow, they have a lot of sky here!"

Organ MountainsIndeed, they do have a lot of sky.  My parents got us a membership at the NMSU swimming pool, because, although there is a lot of sky, there is not much for teenagers to do.  When I was not at the pool, I was at the local library.  In fact, I read all the books in the library's psychology section that year.  I learned about the principle of psychic determinism.  That is the notion that everything that is going on in your brain, at any given moment, is a product of what was going on in your brain the moment before, plus whatever sensory input is occurring at the time. 

According to the principle of psychic determinism, there are no non sequiturs.  Sometimes people say things that do not seem to fit with the topic at hand.  But, in the mind of the speaker, there always is a connection between what was said a moment ago, and what is being said now.  Apparent non sequiturs can be annoying.  Usually, though, one merely has to wait a few moments in order for the connection to become clear.

One day, at the pool, I met a young lady.  We became friends.  One other day, I think she was trying to impress me, because she made me lunch.  I was at her house, she opened the refrigerator, and asked me if I wanted a steak.  I, like almost any 15-year old boy, when asked if he wants a steak, did in fact want a steak.  Honoring my mother's direction to be honest at all times, I said "yes."

She cooked the steak.  I ate it.  It was very good.  I didn't think about it again for several weeks.  Later, I went to the young lady's house again.  Her father was there.  He looked up at me and asked, rather gruffly, "Are you the guy who ate my steak?"

"Uhhh, yes, I am."

White Sands Missile Range MuseumHe looked down at the table for a moment, as though to soften the impact of what might have been perceived as a rude way to introduce yourself to someone you just met.  He then asked, "What is the difference between accuracy and precision?"  I did not know it at the time, but he was a civilian engineer at the White Sands missile range.  He was involved in the design and testing of missiles.  (The military is interested in the accuracy of its missiles.)

The alert reader will have deduced that I was a bit of a bookworm, at the time, so I happened to know the answer.  I also knew about the principle of psychic determinism, so I knew that if I were patient, the rationale for the apparent non sequitur would become apparent.  I replied something like this: "Accuracy is how close a measurement is to the real value, whereas precision is how close repeated measurements are to each other."

He threw his hands in the air, and said, "I can't believe it!  I've been trying to get the US military to understand the difference, and they can't get it straight.  But here's some teenage kid who knows!"  He was nice after that.

What was the connection? I had eaten his steak, and dated his daughter.  Apparently, those two things were OK, since I knew the difference between accuracy and precision.  It does not matter if you get two strikes, if the third swing results in a home run.

Ever since then, I have understood the importance of the ability to make a distinction between two related concepts. 

There was more discussion of accuracy and precision.  "Accuracy means truth.  Precision means repeatability."  If missiles are perfectly accurate, then all missiles launched at Target A will hit Target A.  If missiles have perfect precision, then all missiles launched at Target A will hit the same spot, which may or may not be the target.  Thus, it is possible to have perfect precision, but no accuracy; whereas perfect accuracy always is accompanied by perfect precision.  People get mixed up about this all the time. 

It is tempting, of course, to think that if you measure something several times, and come up with the same value every time, that the measurements indicate some kind of fundamental truth.  But is someone hands you a ruler that is not really a foot long, all the measurements you make with that ruler will be wrong.  The errors you make will be systematic errors.

Likewise, if you listen to someone talk, and he or she always says the same thing, it is tempting to think that what they are saying reflects the truth about what is going on inside their head.  It follows from the principle of psychic determinism, that what they are saying is related to what is going on in their head.  The thing is, the relationship between what is going on in their head, and what they are saying, may be systematically distorted.  Thus, the fact that the person always gives the same answer does not mean that the answer is correct. 
Phrenological Map
When you listen to a person talk, you are trying to get a measurement of what is going on inside their head.  Of course, this is a bit like trying to size up your daughter's suitor.  If the person is honest, what he says is a good reflection of what he is thinking.  But if he is systematically dishonest, you cannot believe anything he says, never mind that he always gives the same answer to the same question.  In fact, the precision with which he speaks may be a part of his effort to deceive.  Like the person who handed you the fake ruler, the pathological liar knows that if he always gives the same answer, you will be tempted to mistake precision for accuracy.

Taking the measure of a potential suitor is sort of like taking the measure of a potential president.  It is reassuring if he or she always says the same thing, but that does not mean that that the truth is being spoken.