A detailed explanation:

http://en.wikipedia.org/wiki/Accuracy_and_precision

A detailed explanation:

http://en.wikipedia.org/wiki/Accuracy_and_precision

Dear @Ierardi,

Thank you very much for your short illustrative and quick response. Also, about other part of my question "criteria for selecting the best model" I found the following paper:

Willmott, C. J. and K. Matsuura, 2005: Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 30 (1), 79.

It says that MAE is best for some model comparisons.

As far as my understanding goes I agree with you totally on the  differences existing between accuracy and precision.that you initially mentioned. Thank you. Tushar

Dear Professor Omid,

In models comparison these criteria (RMSE, MAE, AIC, R, etc.) are fitting criteria (goodness of fitting) not accuracy criteria. The accuracy of a mathematical model depends on how close the model solution is to its original governing equations. A mathematical model with fitting parameters can be solved inaccurately by unsuitable numerical methods but can produce good results in model calibration stage using a set of field data in terms of fitting criteria. This model is not necessarily a robust model for prediction of future events.

Ali R. Vatankhah

In the context of bi-class classification, the Precision is defined:

P = TruePositive / (FalsePositive + TruePositive) = TruePositive / AllPositive

and the Accuracy is defined:

A = (TruePositive + TrueNegative) / (TruePositive + TrueNegative + FalsePositive + FalseNegative) = TrueAll / All

The Precision focuses on the performance of the classifier on the positive class, while the Accuracy considers the performance on both classes.

Precision and accuracy pertain to instruments. An instrument can be calibrated to the correct value and be imprecise. While it is calibrated, it is not reliable; it is imprecise. An instrument that is precise obtains the same result within a small uncertainty. Nevertheless, if it is not calibrated it is not accurate. The same is true of models, but the definitions are dependent upon the input values.

Most instruments measure indirectly. They do not measure the actual, calibrated value. The instrument may measure voltage or current, but the value measured must use other effects that are translated to current or voltage. The investigator must ensure that the value intended for measurement is the value represented by the current or voltage.

Assume that an instrument will measure five different quantities and present the same voltage as an output. The investigator must have a means to eliminate the other four in order to claim a measurement of the fifth. The one in five can be claimed and quantified, if the calibration is correct with low uncertainty, the instrument is shown to be precise, and the value measured can be reliably associated with the quantity to be measured.

A further interpretation is necessary for each of the five. Precision and/or accuracy may be different with each. There is no simple claim for precision and accuracy of the instrument.

The same is true with models and calculation methods. A model can be claimed as accurate only by ground truthing. This requires that not only the model be calibrated to real results, it must be shown that the model correctly interprets each stage of the calculation and that the calculation is valid over a range of values. Accuracy is the ability to predict the correct value within given uncertainty limits. Precision is dependent upon the method of calculation. Some calculations will give the same answer for each model run if the the inputs are the same. A Monte Carlo type calculation will give a different answer for each model run. It is precise if the difference for each run is small. Models, like instruments, may be sensitive to the input and the quality of the input. Accuracy and precision must be defined based on the input. A sensitivity analysis is necessary to establish accuracy and precision for a given set of inputs.

Good question. I think that you're trying to compare terms from related, but still quite different, domains. It is my understanding that both precision and accuracy are applicable to measures and other *measurement* aspects. On the other hand, deciding on which criteria to use for model comparison and selection is a totally different perspective, as most of them refer to the *degree of fit* between model and data. In other words, goodness-of-fit indices are not characteristics of measurement, but of models (modeling). That is IMHO the key difference.

That is a very good question.  Scientifically, accuracy is the ability of a measurement to match the actual value of the quantity being measured.  It the degree of conformity and correctness of the observed values when compared to a true or absolute values.  Precision may considered as the ability of a measurement to be consistently reproduced and the number of significant digits to which a value has been reliably measured.  Precision refers to a state of strict exactness.

Please see the attached video defining precision and accuracy in some special cases.

https://www.youtube.com/watch?v=b38hFWvEjwI

Please allow me to illustrate precision & accuracy as we approach it in chemistry. Of course, other specializations (such as math & statistics) are expected to be better than us in this respect.

A chemist wants to determine the concentration of a chemical dissolved in a solution. The true or known concentration of the chemical in solution is 2.32 M (moles/liter). The chemist performed the experiment 3 times, and the concentration was found to be 1.64 M, 1.63 M, and 1.65 M. The average of these numbers is 1.64 M. This result is very precise, but it is not accurate.

Let us assume that another chemist performed 3 more experiments to determine the concentration of the same chemical in solution, and the following values were found: 2.87, 1.48 and 2.61 M. When averaged, these values accurately give 2.32 M, but the experiments were not precise. In fact, it may have been good luck that they averaged out perfectly.

Dear all,

Thank you very much for very good description of the differences between accuracy and precision. Accuracy describes the difference between the measurement and the part’s actual value, while precision describes the variation one might see when we measure the same part repeatedly with the same device.  It seems the two terms differ when we are assessing variation in a measurement system.

P.S.: Please note, this question is not about evaluating binary classification systems. As pointed out by @Reza in binary classification tasks precision and accuracy can be defined in terms of TP, FP, TN and FN precisely! However, for evaluating binary classification systems we must avoid the accuracy paradox. That is to say we should not use accuracy in an isolated way, but to use it with other less misleading measures such as Precision [TP/(TP + FP)], Recall [TP/(TP + FN)], or other metrics.  

 Dear Mahmoud Omid,

Look the link. May be useful. 

http://pmpaspeakingofprecision.com/2012/03/27/the-difference-between-accuracy-and-precision-measurement-in-your-machine-shop/

http://www.diffen.com/difference/Accuracy_vs_Precision

http://pmstudycircle.com/2012/04/precision-versus-accuracy-definitions-and-differences-between-them/

Regards, Shafagat

Definition

Accuracy: The degree of conformity and correctness of something when compared to a true or absolute value.

Precision: A state of strict exactness — how often something is strictly exact.

Measurements

Accuracy: Single factor or measurement

Precision: Multiple measurements or factors are needed

Relationship

Accuracy: Something can be accurate on occasion as a fluke. For something to be consistently and reliably accurate, it must also be precise.

Precision: Results can be precise without being accurate. Alternatively, results can be precise AND accurate.

Uses

Accuracy: Physics, chemistry, engineering, statistics, and so on.

Precision: Physics, chemistry, engineering, statistics, and so on.

http://www.diffen.com/difference/Accuracy_vs_Precision

All comments so far about these two terms are great.

Probably we can say accuracy and precision are, respectively, similar to the notion of reliability and validity issues in multivariate data analysis. Is it true to say the more time we spend on increasing the accuracy of a metric, the less chance we will have to make it precise? 

A dart board can help us visualize the difference between the two concepts. Suppose we throw seven darts at the center of a dart board. We try four times with the following results:

Although accuracy and precision are used interchangeably in non-technical settings (daily conversations) but in the context of engineering and statistics these two terms do not have the same meaning (as already explained by others in this thread).

From Wikipedia (please see the attached link)

"A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision. A measurement system is considered valid if it is both accurate and precise."

http://en.wikipedia.org/wiki/Accuracy_and_precision

I agree with the answers stating that a difference should exist - let's name it "accuracy" versus "precision" , but it could have been vice versa (i.e., what we understand now by "accuracy" be called "precision" ...). Also, I agree with most of the explanations related to this difference.

Meanwhile, in contrast to English or German, as far as I know, this difference is not (fully) assimilated in other languages, I mean in their scientific jargon.  Specifically, I have in mind Romance languages: in my mother tongue this is the situation, some Frenchmen or Italians may contradict me, but I see their scientific jargons are still facing the same ambiguity.

Thus, in the languages where the frequency of use of the word "precision" is very high, we have to be really careful to the whole context: the "precision" word (in those languages) has "precision" (En) meaning ? or "accuracy" (En) meaning ?

This brings me to mind another difference which is more frequently expressed in English than in other languages: efficiency and effectiveness. As it is known, efficiency refers to doing things right, but effectiveness means doing the right thing (to achieve the desired effect). In the Romance languages, (translated) "efficiency" is often used with both meanings. As it is the case with "precision".

I've just read again the question. When it comes to digital processing, the precision is related to the number of digits used for storing numbers in the computer.

Coming to the question, at each step of the data processing, we have to be aware how many digits are significant for the information expressed by the numbers; let's say, the (partial) results during the processing are accurate up to one decimal, but the numbers are stored in double-precision floating point format, which means the precision is 15-17 decimal digits; thus, in this case, most of them are meaningless and should not be used in the further steps of the processing or for current error estimations.

The definitions of accuracy and precision concern systematic error (accuracy) and random error (precision). The ISO defines each this way, but prefers trueness to accuracy.

The graph shown by Ieradi Enzo and the targets shown by Mahmoud Omid illustrate these definitions, but are misleading. Ieradi's graph shows the important concept of systematic error and precision of reproducing the value. Mahmoud's targets show the same, but reinforce the idea that the errors are independent. As defined, they are correct, but as ISO defines 'true value' they are combined. The total uncertainty is required for the true value so accuracy or trueness is total propagated uncertainty.

A standard or reference value is used for calibration. There is only one meter (metre) in existence. All other standards or references are copies of that one meter. The quality of the copy (or a copy of a copy of a copy ...) is the first source of error. (There are excellent copies of the meter based on wavelengths of light.) So, a standard or reference has error.

The standard may be known to, say, 1%. Nevertheless, that particular standard has a single value. Applying it introduces a systematic error.

The standard or reference must be applied to the measuring device. The application of the standard introduces error, random and systematic. The measuring device is adjusted to the standard value so, at the time of adjustment, there is no systematic error in the measuring device relative to the standard, except the ability to adjust exactly.

Application of the calibrated device introduces systematic and random error when the device is applied to the measurand. It is necessary to estimate these errors for total propagation.

A calibrated device in use for some time after calibration may drift from the calibration. Methods are employed to account for or adjust for drift. Drift may be both random and systematic. Indeed, the method for accounting and adusting has both random and systematic errors.

The final claim for accuracy or trueness includes the fully propagated error. While accuracy has been defined as systematic error. Reported accuracy must include all error.

Another source of confusion for the term accuracy is if the systematic error is known (difference from a reference value) then compensation makes the measurement accurate. The problem is knowing how to compensate without systematic and random error.

Modeling includes systematic and random errors. The same definitions of accuracy and precision can be applied. The concept of trueness as used by ISO should include all sources of error models. A simple model, a single equation, is true if it exactly predicts the output based on the input. Mathematically the equation may be exact, but physical reality requires correction. The equation may be near exact for physics under close to ideal conditions. Nevertheless, error in defining the conditions introduce systematic errors. Application to less than ideal conditions may require additional terms relying on measurement and estimation. The result for the corrected equation might be like Ierardi's graph. The reference value is the ideal calculation compared to the spread in corrected values. One hopes the measured values correspond closely to the calculated values. Should that be the case, we declare the model calibrated.

Models may require assumptions, approximations, and measured input. Often an equation accepted to follow a theoretical ideal is only a close approximation. The inputs should produce systematic errors because the calculation will return the same result with every application of the same inputs. Nevertheless, small changes in the inputs may not give similar changes in the output for non-linear equations. While systematic, the effects for several variables may appear random.

The same definition of trueness applies if all errors are propagated through the model. Correct propagation will give the total uncertainty. The total uncertainty requires that each assumption and approximation be evaluated for uncertainty. As with an instrument calibrated to reference, there is a fixed systematic uncertainty that cannot be quantified; therefore, no adjustment is possible.

I once presented the results of a measurement to an interagency team. The result was 36 +/- 3. I was immediately challenged by a modeler who said the correct answer was 32. My response was that I was within 2 sigma of his number. He claimed that he had performed the calculation to six significant figures or 32.1376, so 36 +/- 3 was unacceptable. His supervisor asked if his calculation contained any assumptions or approximations. The answer was, of course. Then come back tomorrow and tell us what the propagated uncertainty is of 32.1376. Answer, there was no uncertainty because I used exact values for my assumptions and approximations. Supervisor: Think about what you said. Come back tomorrow with the propagated uncertainty or consider where you will work in the future. Next day: 32.1376 +/- 250.

Moral of the story. Models are uncertain. Using exact values does not remove the uncertainty.

Thank you, dr. Alvarez, for making these things clearer to me.

Would it be best to be directionally accurate or precisely wrong?

Let's look at these terms 'Precision' and 'Accuracy' within business forecasting and their possible implications. When you’re building a product, it’s important to be cognizant of whether you’re striving for accuracy or precision within the context of your product  or company. If you find yourself carefully justifying feature decisions with overly tidy, buttoned-up, high confidence items, ask yourself whether you’re sacrificing accuracy for precision. 

We are confronted daily with making tradeoffs between:

1) Precision: Building features we have strong conviction in based off of past success and internal data (eg, we can precisely estimate impact), and

2) Accuracy: Taking bigger risks on opportunities that are more difficult to quantify, but that we believe will drive step function changes in the business (eg, accurately nail big opportunities).

http://blog.kentonkivestu.com/accuracy-vs-precision-what-it-means-for-your-product-decisions

Accuracy is to hit the target in one shot while precision is to assign optimal value for each contributing component in achieving and hitting the target. Period I like the figure of impulse relationship that Ierardi Enzo posted. 

To Cambridge Dic., "accuracy-how correct or exact smth is", "precision-when smth is very exact and accurate" To MW Dic.of Synonyms, "Accurate implies more positively fidelity to fact or truth attained by the exercise of care. Precise stresses of definition or delimitation, or scrupulous, exactness".In other words, we take into consideration Semantics and collocation."Accurately hitting the target means you are close to the center of the target, even if all of the marks are on different sides of the center.Precisely hitting a target means all the hits are closely spaced, even if they are very far from the center of the target".Precision as a highly desirable thing: to language, arts, sciences- meticulous precision, with the mathematical precision, aesthetic precision. Besides, in literature ("Woe from Wit"by Griboyedov) there is a character of Molchalin, who symbolizes an official-"moderation and accuracy"(in other words, a person who respects a virtue, but doesn't deny a vice.Or in relation to instruments."Surgery which requires great precision"http://chemistry.about.com/od/unitsconversions/fl/What-Is-the-Difference-Between-Accuracy-and-Precision.htm

I think Accuracy is the difference between the measured value and the true value of a tested material, Precision is the repeatability of successive measurements under the same conditions ( Accuracy is how close a measured value is to the actual (true) value. Precision is how close the measured values are to each other). That is to say the accuracy of a measurement system is the degree of closeness of measurements of aquantity to its actual (true) value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. 

The detail information can also be seen at   http://en.wikipedia.org/wiki/Accuracy_and_precision,   thank you.

Accuracy refers to the closeness of a measured value to a standard or known value whereas precision refers to the closeness of two or more measurements to each other. In other words, accuracy describes the difference between the measurement and the part’s actual value; while precision describes the variation you see when you measure the same part repeatedly with the same device.

Precision and accuracy are terms of measure theory and probabilistic theory. In measure theory precision of instrumentation and their calibration is required to able measured or extracted data fit with right models. Accuracy is more related to modeling  theory, data should be accurate with less uncertainty error within the chosen or the appropriate model and equations, and more close to optimality.

there is no duality between "accuracy" and "precision" : we have not to ask "Which criteria is more appropriate to use?" because "complementarity" is the relation between the two criteria.

The "accuracy" is the quality of the "precision": So when we obtain a measurement result, it's always with a certain precision. We can stop here ... but scientifically, it's more credible to obtain the quality of this precision : the "accuracy" which is the percentage of "getting a similar result every time you try".

The "Truth" is equal to one's initial observations plus the corrections discovered through added experience or knowledge. - R. B. Buckner

Accuracy is telling the truth . . . Precision is telling the same story over and over again -Yiding Wang

Dear @Yogesh. Thank you. A very clever answer, indeed. I found a more accurate set of definitions for these terms:

Accuracy : The nearness of a value to the "real" value

Precision : The probability of repeated measurement yielding the same result

Source: Wikipedia

https://en.wikipedia.org/wiki/Accuracy_and_precision

These terminology are best described and explained as above by RG members.

In the absence of systematic errors, precision defines accuracy of the method.

The reliability/quality of measurement results of water samples depends on strict adherence to each step of sampling, preservation of samples,time-interval between sampling and analysis for filtered but un-acidified water samples, and

on the methodology adopted, and not simply analyzed by any person or lab or any technique.

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Great discussion! I have lot of material to review. Thanks to all contributors!

Accuracy being, how often and how close to the "correct answer". While precision being, how often and how close to the "incorrect answer". Is this too far off? :-)

Precision is the accuracy of an unbiased estimator, for example it is measured for its variance. Accuracy is the mean square error of a estimator with respect to the parametric function to estimate.

Both of them are defined in Statistical books of inference.

Accuracy is the closeness of conformity between a measured value and a true or accepted value of the quantity being measured. Precision is a measure of how well a result can be determined. It is the degree of consistency and agreement among independent measurements of the same quantity

dear

In other words, accuracy describes the difference between the measurement and the part's actual value, while precision describes the variation you see when you measure the same part repeatedly with the same device

from this bellow link

blog.minitab.com/blog/real-world-quality.../accuracy-vs-precision-whats-the-difference

regards

Well said @ Ali Hadi