13 September 2008

Accuracy vs precision

I'm getting a modest but insistent shoal of queries about the distinction between "accuracy" and "precision" in the Collisions post. Several correspondents offer entries from dictionaries to support the contention that these words are interchangeable.

I also note the comment to that post that I ask too many questions. So, no questions this time: just explanation.

For a statistician, and for any scientist who takes a statistical view of data (which is to say, almost all present day scientists) the distinction is between central tendency and dispersion respectively. If you've not had contact with those terms, that won't have helped – so here's a visual illustration which I use for teaching. Imagine that four people each take turns firing six rifle shots at a target. All of them are aiming to place every shot at the dead centre of the target. When they've all finished, we compare their results and find the following (double click on any target for a larger view)...

Avril's shots are all placed right inside the central circle, very close to the true centre. We say that her shooting is very accurate.

Her shots are also clustered very close together, in a small bunch. We say that her shooting is also very precise.

Avril's shooting is both accurate and precise.

Brian's shots are also clustered close together. We say that his shooting is just as precise as Avril's.

However, this cluster is a long way off the centre of the target at which he was aiming – so we say that his shooting is much less accurate than Avril's.

Brian's shooting is precise but not accurate.

Carole hasn't managed to group the shots very closely together; they are scattered over a much wider area than either Avril's or Brian's. We say that her shooting is not precise.

On the other hand, the centre of her cluster is pretty much on the centre of the target – so, despite their spread, the accuracy is as good as Avril's.

Carole's shooting is accurate but not precise.

Finally ... Dave's shots are even more scattered (less precisely grouped) than Carole's.

And their centre is some way to the right of the target centre – so less accurate than Avril's or Carole's.

Dave's shooting is neither accurate nor precise.

Clear as mud? Good, good, good. I'm off to mow the carrots.


Poor Pothecary said...

Good stuff - although within the shooting analogy, Brian is bizarre: a clearly skilled marksman shooting at the wrong point. With real data in some kind of scientific situation, the equivalent would be of a precise measurement with some kind of unknown systematic bias.

Felix Grant said...

PP> ... Brian is bizarre: a
PP> clearly skilled marksman
PP> shooting at the wrong point.
PP> With real data ... a precise
PP> measurement with some kind of
PP> unknown systematic bias.

From my experience on the dodgier sort of fairground stall, I suspect that the systematic bias is down to someone bending the foresight slightly to the left with a pair of pliers, deepening the "V" in the rearsight with a file, then touching up the damage with a touch of paint! [grin]

Ed Eager said...

The alphabetic(al?) sequence of names, the choice of rifle shooting for illustration, and a suspiciously detailed knowledge of gun sights, cause me to suspect that the writer is a "thematic murderer" as described by Poor Pothecary in his first comment to "The Yiddish Policeman's Universe" on September 5th.

My name gives me cause for concern.

Poor Pothecary said...

bending the foresight slightly

Just so. The "bizarre" aspect was why Brian, sufficiently expert to shoot so precisely, didn't spot the bias and correct for it after the first couple of shots.

A thematic murderer

As in Christie's The A.B.C. Murders even (although that one didn't involve a fully fledged thematic series - the intention wasn't to get through the full set, but merely a distraction from the murder of C being the chief aim.

Felix Grant said...

PP> ...why Brian ... didn't
PP> spot the bias ...

Good point.

I shall take his severely to task and make it clear that unless he bucks up his ideas I shall not be using him in any further examples...


Poor Pothecary said...

he bucks up his ideas

Actually, that suggests a different plausible scenario for the observed patterns; that the four pictures show the result of single shots, with varying range and skill, from a shotgun with some kind of custom 6-pellet buckshot cartridge. Brian's still a bit lame, unless he was distracted by simultaneously fighting off Grammaton Clerics.

Felix Grant said...

Suggestion by a nine year old: Brian is blind, aiming at where the target usually is, but somebody has moved it...

Poor Pothecary said...

The targets were painted after the shots, and Avril paid the painter more than Brian did.

Poor Pothecary said...

The whole exercise is faked, since if you look closely at the images, the borders of the bullet-holes impossibly over-write each other.

Felix Grant said...

PP> ...Avril paid the painter more
PP> than Brian...


I like that one.

Going back to your earlier six-pellet shotgun cartridge: perhaps a more realistic alternative would be a six shot burst from an automatic weapon. There would then be no time for correction of aim between shots.

Felix Grant said...

PP> ...the borders of the
PP> bullet-holes...

Yes ...

When I first produced the demonstration images, I drew the bullet holes in as pure black circles with slightly ragged images for realism. I found, though, that although realistic the result looked unclear.

So, I tried different versions of the holes on students. They liked (and understood) cleaned up edges better, and white edges better still.

Since the object of the exercise was to explain a principle, and shooting was only a vehicle, I opted to sacrifice realism in the cause of educational clarity. Few students knew anything (and cared even less) about shooting.

On a wall-sized projected image, the white edges are laughably obvious, but everybody is happy!

There is, of course, always that one smart alec student at the back, making catcalls and remarking on the artistic integrity of my diagrams ... I always wondered who he was: now I've got you at last! [grin]

Tamsein Etheridge said...

Poor Pothecary said "The whole exercise is faked".

Isn't this obvious?

Felix Grant said...

Tamsein: yes, it is, but PP is being humorous in line with our (his and my) to and fro above. I've known PP for a long time ... perhaps the humour is less obvious to someone stumbling upon it for the first time! :-)