Accuracy, Precision and Sensitivity for measurement instruments

In summary: The dartboard analogy is an interesting one, but I don't think it really helps. In fact, it might be confusing. Suppose I have a dartboard with six circles and I'm trying to hit the bull's-eye. If I hit the center circle half the time, I'm accurate. If I hit the center circle all the time, I'm precise. But if I hit the center circle only 1 out of 6 times, I'm neither accurate nor precise.In summary, Accuracy is the closeness of a measurement to the real/actual value, precision is when a set of values are consistent with each other (i.e. close to each other) and sensitivity is the smallest possible reading of an instrument (i
  • #1
Acid92
43
0
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). I've searched the web and I am finding these definitions too.

However I've 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?
 
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  • #2
As is, the ruler is precise. It is accurate to the extent that it agrees with some standard ruler.
 
  • #3
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
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 separate 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
shpongle said:
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?
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
D H said:
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.

If the object of the game is to hit the center, then consistently hitting the outer ring is not accurate.
 
  • #7
mathman said:
If the object of the game is to hit the center, then consistently hitting the outer ring is not accurate.
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
D H said:
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 ...
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.
 

1. What is the difference between accuracy and precision?

Accuracy refers to how close a measured value is to the true or accepted value. Precision, on the other hand, refers to how close multiple measurements of the same value are to each other. In other words, accuracy is a measure of correctness while precision is a measure of consistency.

2. How can I determine the accuracy of a measurement instrument?

The accuracy of a measurement instrument can be determined by comparing its measurements to a known standard or accepted value. This can be done through calibration or by using a reference material with a known value. The smaller the difference between the measured value and the known value, the higher the accuracy of the instrument.

3. What is sensitivity in measurement instruments?

Sensitivity refers to the smallest change in the measured quantity that can be detected by the instrument. It is often expressed in terms of the instrument's resolution or smallest division on its scale. A more sensitive instrument can detect smaller changes in the measured quantity, making it more precise.

4. How can I improve the precision of a measurement instrument?

There are several ways to improve the precision of a measurement instrument. One way is to take multiple measurements and calculate the average. Another way is to use a more sensitive instrument with a smaller resolution. Additionally, regularly calibrating the instrument and ensuring proper handling and usage can also improve its precision.

5. Can an instrument be accurate but not precise, or vice versa?

Yes, it is possible for an instrument to be accurate but not precise, or vice versa. For example, a scale may consistently measure a weight as 10 pounds (precise) but the true weight is actually 12 pounds (inaccurate). On the other hand, a scale may consistently measure a weight as 12 pounds (accurate) but the measurements vary by 2 pounds each time (imprecise).

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