The Precise Meaning of Precision

Use the word "uncertainty" it will be more "precise".

I do not dare give more explanations since you pinpoint at redfred I let him have the pleasure to give the whole explanation you - I presume - will fill better if it comes from him!

Only one basic idea have you ever measured (that means quantified with an instrument) "precision"?

By the way did you find what is special when the pipes are vertical?

I'm still not certain about the horizontal vs vertical pipe question. I'm thinking; I'm just really slow.

When I taught error analysis, the class learned that the antonym for "precise" is "approximate" and the antonym for "accurate" is "wrong".

I agree with Baffled. "Precision" and "resolution" are exactly the same thing. This might be why ISO prefers to use one instrument-specific term (resolution) instead of the more general term (precision).

Repeatability has to do with the instrument's accuracy, not with precision. If the item being measured is unchanged, it is up to the instrument to be consistent in its readings. If not, some readings are inaccurate.

Reproducibility means that other instruments produce the same result as this one - in other words, it indicates whether the instrument is properly calibrated or not. Again this is about accuracy, rather than precision or resolution.

Suppose an object were 1.14 meters in length. A measurement of length is made and the result is 0.94357281 meters.

This sounds like our wonderful (!) media and government bodies. Input data good to 2 significant figures, but results given to 5 significant figures.

It gets used to describe the resolution of an instrument, the repeatability, and the reproducibility. Gorblimey! Little wonder folks like me get confused.

I think you are on the right track. I have seen it used synonomously with resolution. Then again, you can say "this is a precision instrument". Precision is an ambiguous term.

To set the resolution of an instrument, the repeatability/reproducibility of test values compared with established standard values is used.

I prefer to use these two terms to define an instrument's performance: accuracy and reproducability; the resolution is something stated in the instrument's specifications, and is derived from evaluation of these two parameters.

With ISO, you must have a reliable method of evaluation of your product's performance, that your written procedures will ensure meeting your stated product specifications, and then consistently following said written procedures.

Maybe that's as clear as mud! Anyway, that's how I understand it.

Wow, talk about a command performance. I'm flattered and a little terrified now to come up with a good answer.

A major part of the problem is that the English language wants to be a flexible language so a precise instrument in one discipline at one time will be sloppy instrument another time or in another discipline. I believe that this ambiguity alone is the major reason why ISO discourages the use of the word.

Now I do believe that "precision" does have a specific meaning that reflects exactly your definition of the resolution of an instrument, the repeatability, and the reproducibility. A precision instrument is one that possesses all three of these attributes simultaneously. But quantum mechanics has taught science that one cannot obtain all three of these to an absolute precision. An instrument with sufficiently high resolution will always produce non-repeatable values as true random noise effects become apparent. But if the random variation recorded agrees sufficiently with the expected random distribution then I say that this instrument is more precise than the process being measured.

Look at it this way. Imagine you are firing a machine gun at a target. If you miss the target completely by a very wide distance away from it but all your shots lie within a very small radius, you are precise but inaccurate. Likewise, if your shots are widely scattered but the target lies in the exact center of all your shots, then you are accurate but imprecise. Finally, if you blow the target to smithereens because all your shots hit it, then you are both accurate and precise.

Referring back to the old metrology notes yields this:

All with a given test set up

Precision: no. of times you hit the correct value.

Accuracy: the degree of confidence with which you can claim your obtained value approaches a correct value

Resolution: ability to distinguish clearly and individually 2 or more close lying indications

Yep, this is precisely what I expected. Sorry for that little joke, I just could not resist.

The concepts of precision and accuracy comes from a repeated manufacturing process. Placing arrows or bullets onto a target and getting a close grouping or repeatably able to make many objects the same size is considered a precise process. Accuracy is how closely the average of the group of these projectiles or manufactured objects coincide with the desired value. But these attributes are completely different from resolution. Staying with the concept of an archer precisely hitting a target. This archer may be able to precisely group his/her shots and know that they're close to the center of the target. But from across the field he may not have enough resolution to be able to score his results. The archer has to walk down field to the target to now observe with sufficiently high resolution where the arrows have landed to score the results.

But unfortunately as the variety of differing replies have shown, the use of the word "precision" can easily lead a person astray. So while people do still try to use "precision" to mean a tight grouping of results, many will use it to mean a different thing. This is why it is becoming a "waste basket" term and the ISO standards try not to use this term.

In my documents that must clearly define these concepts, I've been using the statistical terms of mean (accuracy) and variance (precision) when required. Now these terms really only track the original meanings of accuracy and precision if the random process that is causing these differences has a low skew to the PDF like a Gaussian distribution. But when you think about it carefully, these terms are assuming precisely that.

Maybe they discourage it because it has four meanings and they want you to use the exact description of what you are talking about.

• Precision (arithmetic), the number of digits from which a value is expressed
• Precision (information retrieval), the percentage of documents returned that are relevant
• Precision (computer science), a measure of the detail in which a quantity is expressed
• Precision (statistics), a model parameter or a quantification of precision

I have always striven to correctly use the terms precise and accurate. The way I learned to think of them was to think of an archer.

Now, when the archer consistently places all of his arrows at any given time in a tightly grouped cluster, he is being precise. He may be aiming at the bullseye on the target and his cluster may be anywhere on the target, at 12 o'clock or at at the 7, but he is precise in repeating each step of his shot in the same manner, his draw, his breathing, his release and follow-thru... However precise he might be, with each arrow trying to enter the same hole as the previous shot, he is NOT hitting what he is aiming at, and thus NOT accurate.

An accurate shooter, may place his arrows all over the target, top, bottom, both sides, but the AVERAGE location, the sum of his horizontal and vertical errors cancel out over many shots, the average may place him dead center in the middle of the bullseye where he was aiming without a single arrow hitting in that small circle.

The goal of being very precise is the elimination of the error between individual shots. In other words, each individual shot PRECISELY duplicates any other, from the first to the last, thus placing them all of the arrows in a very small cluster, grouped very tightly together along with every other arrow. The problem with precision alone is that every shot is potentially WRONG: Precisely Wrong.

In our technical world, the use of accurate and precise have been confused by the lazy use of one or the other to represent some combination of one or both meanings.

I have had electronic flow meter and pressure sensor salesmen boast the precison (or accuracy) of thier equipment, however when I try to pin them down on the accuracy (or precision) of the same product they suddenly go deaf, or lose thier data sheets, or suddenly are in conversation with somebody else and don't hear me, they try to shift the conversation away from the fact that their equipment MIGHT BE precisely wrong.

You can be precisely wrong to the exact same amount or percent of scale or some other factor and this is the weakness in the design or operational methodology that they do not want you to realize as it may be the critical factor in your particular case.

This is why calibration is so critical. In calibration, you determine both, how big the precision cluster is, where it's center is (or how 'precisely' wrong a device is) and then shift the center of the nice grouping over to the bullseye to add the required accuracy. Accuracy and precision must always be judged jointly to understand the larger picture.

be very careful of the terminology and use of either of these words when used alone or together.

You can be highly accurate without any precision and NEVER hit the bullseye, (but you WILL have it surrounded!) Or you can be so precise that nobody ever questions you, you ability or maybe the tool used and yet NEVER hit or even be near the bullseye. Just think of a man making very very high decimal measurements with a calpher that does not know one finger of the tool was bent by a previous user. As result, his careful measurments are precise, and every one of them is wrong by the same amount, that being how far the tool was "bent away from true zero when closed.

PRECISION of an instrument (or archer) is an effective means to evaluate how consistent and tight the cluster is given a specific set of parameters to be measured. where the ACCURACY of an instrument is a measure of the deviation of the average reading (or arrow shot at the target) is relative to the known Bullseye.

This excellent picture conveys nucely some of the verbal descriptions that have been given. Thanks!

I agree that's a good graphic and very concise definition that makes sense.

The other aspect of precision, that is the resolution of the instrument, could be illustrated in a similar bullseye diagram, where the limit of resolution can be defined as one of the rings in the target. The lower the precision of the instrument, the farther from center is the ring.

Good description, particularly notice that this bullseye pattern provides only a one dimensional piece of information, but the dart location can vary in two dimensions. So if one only has the target result values, it becomes difficult if not impossible to discriminate between accuracy and precision.

I'd like to thank everyone who answered. Your many points of view really helped me focus in on what I wanted. I'm working with folks who make measurements, but who don't have any output, i.e., no process. So, I think my starting point is to just say that precision is the smallest division on my instruments, and then admit that to be an over-simplification. But, at least I can get out two machinist's scales and easily demonstrate the point.

By the way, I already did a test run on this and it was my misfortune to have an architectural draftsman in the group. She whipped out a scale that (I think) had 3/32" divisions and I turned bright red and sputtered.

"precision is the smallest division on my instruments"

NO this is RESOLUTION!

Sorry TVP45, but Nick Name is exactly right. The smallest division is resolution not precision. Lets go back to the target diagrams that kvsridhar found.

Resolution is how well you can measure something, its the one item in this discussion that can be determined by making absolutely no actual measurements. In this diagram our resolution is finer than the resolution of the target. Also as I mentioned earlier our resolution contains two dimensional information while the target ring values are actually only the one dimensional quantity of distance away from center. In contrast accuracy and precision can be found only with multiple measurements. In this diagram there's an implied piece of information most have overlooked, where was the marksman aiming with each shot?

I have the feeling that some practical theory has to be made since if not meanings are misused.

Let us consider a series of measurements Xi. The number of measurements is "N".

This group is characterized by a mean value Xm=ΣXi(from 1 toN)/N and a standard deviation σ = ( Σ(Xi-Xm)^2/(N-1))^0.5. The target was Xt. With the 2 mentioned values one can characterize how the result is with respect to the target:

- the difference between Xm and Xt indicates the offset

- the σ value indicates the dispersion of the process.

An instrument can have for instance a resolution of 10µV but when it is calibrated (this means its results are compared with the results of an other reference instrument) it comes out that the off-set is 50µV and that the σ value is 42 µV (can be also a value not multiple of 10µV since it is the result of a computation). What can you now say about its "precision"? In fact nothing because the off-set can be compensated so that it is a systematic error and we can forget it but the dispersion says that "even if the display is 30µV the REAL value is in a larger interval and not the displayed 30µV". The width of the "grey zone" around the displayed value depends on the number of measurements (N). If the number is > 30 AND the distribution is NORMAL (i.e. near to the Gaussian distribution) then the probability for the true value is within 3*σ almost 100%. So that your device has a RESOLUTION of 10µV but the true value is 50 ± 126µV. What is the "precision" of your instrument ? This is the reason I mentioned FROM THE BEGINNING that you should NOT use PRECISION but UNCERTAINTY which is modern way to interpret results since ALL measurements are PROBABILISTIC.

I am sorry if I disturb by such comments but as I wrote many times engineering is a PRECISE (sic) profession and words have meanings and I thing independently of our experience we should always progress and keep abreast with evolution of techniques.

Please. . .

If you read my original post, I do understand that precision is a sometimes ambiguous term. It is a term that I do not use when possible; yet I find myself having to talk with others who do use it.

I do know what resolution, reproducibility, and repeatability are, even when not in all caps.

I was trying to find a way to be able to talk about this term. I apologize if I asked too dumb a question, but I was trying hard to not begin with preconceptions.

Again, thanks to all who answered.