# Accuracy, Precision and Sensitivity for measurement instruments

1. Mar 9, 2012

### Acid92

My book defines accuracy as the closeness of a measurement to the real/actual value, precision as when a set of values are consistent with each other (i.e. close to each other) and sensitivity as the smallest possible reading of an instrument (i.e. to how many decimal places it can measure). Ive searched the web and Im finding these definitions too.

However Ive read "precision" in the context of an instrument (rather than actual measurement values) being applied to what my book defines as sensitivity and have even heard accuracy too. Are these just non technical words used in the lay world or am I missing something here?

Would it be,for example, incorrect to say my ruler is precise to the nearest mm or accurate to the nearest mm?

2. Mar 9, 2012

### mathman

As is, the ruler is precise. It is accurate to the extent that it agrees with some standard ruler.

3. Mar 9, 2012

### shpongle

This is what I was told in my maths lecture a few days ago:

Imagine you have some darts and a dartboard. If majority(I don't know if I should say maximum in this context) of darts hit the center circle then your aims are accurate.

If majority(or maximum) number of darts hit the same ring then your aim is precise.

Did it help?

4. Mar 9, 2012

### Acid92

Ive been looking around and it seems that sensitivity is generally not used at all. The term "precision" is used for it as well so here it seems to have two seperate definitions, the precision of a set of measurement values is their relative closeness to each other but the precision of an instrument is how small of a unit it can measure to (e.g. to the nearest cm).

5. Mar 9, 2012

### Staff: Mentor

I disagree with both of those assessments. Suppose two throwers consistently misses the center, one always hits the outermost ring with the darts nicely distributed about this outer ring, and the other thrower has a very tight cluster of darts several inches from the center circle. The first thrower is accurate but is not precise. The second is precise but not accurate.

Accuracy is a statement about the mean, while precision looks at the variance.

6. Mar 10, 2012

### mathman

If the object of the game is to hit the center, then consistently hitting the outer ring is not accurate.

7. Mar 10, 2012

### Staff: Mentor

In the lay meaning of the term "accurate", you're right. This thread is not about the lay meaning. In a lay sense, accuracy and precision are more or less synonyms.

When one is talking about scientific instruments, for example, accuracy and precision have very distinct meanings. With the technical meaning of "accurate", consistently hitting the outer ring is accurate if the mean is right on target. This kind of throwing is not very precise (technical meaning).

Two statisticians went duck hunting ...

8. Mar 11, 2012

### mathman

I am well aware of the distinction between accuracy and precision. My point is that if all the darts hit the outer ring, the average turning out to be the center would be dumb luck.