# Precision

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Precision refers to the closeness of two or more measurements to each other.
For example, if you weigh a given substance five times, and get $3.2$ kg each time, then your measurement is very precise. Precision is independent of accuracy. You can be very precise but inaccurate, as described above. You can also be accurate but imprecise.
For example, if on average, your measurements for a given substance are close to the known value, but the measurements are far from each other, then you have accuracy without precision.
The term precision is used in describing the agreement of a set of results among themselves. Precision is usually expressed in terms of the deviation of a set of results from the arithmetic mean of the set.
The student of analytical chemistry is taught - correctly - that good precision does not mean good accuracy.
However, It sounds reasonable to assume otherwise.
Why doesn't good precision mean we have good accuracy? We know from our discussion of error that there are systematic and random errors. We also know that the total error is the sum of the systematic error and random error. Since truly random error is just as likely to be negative as positive, we can reason that a measurement that has only random error is accurate to within the precision of measurement and the more precise the measurement, the better idea we have of the true value, i.e., there is no bias in the data. In the case of random error only, good precision indicates good accuracy.
Now lets add the possibility of systematic error. We know that systematic error will produce a bias in the data from the true value. This bias will be negative or positive depending upon the type and there may be several systematic errors at work. Many systematic errors can be repeated to a high degree of precision. Therefore, it follows that systematic errors prevent us from making the conclusion that good precision means good accuracy. When we go about the task of determining the accuracy of a method, we are focusing upon the identification and elimination of systematic errors. Don't be misled by the statement that 'good precision is an indication of good accuracy.' Too many systematic errors can be repeated to a high degree of precision for this statement to be true.
The VIM uses the terms 'repeatability' and 'reproducibility' instead of the more general term 'precision.' The following definitions and notes are taken directly from the VIM:
• Repeatability (of results of measurements) - the closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement.
Additional Notes:
• These conditions are called repeatability conditions.
• Repeatability conditions include the same measurement procedure, the same observer, the same measuring instrument, used under the same conditions, the same location, and repetition over a short period of time.
• Reproducibility (of results of measurement) - the closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement.
Additional Notes:
• A valid statement of reproducibility requires specification of the conditions changed.
• The changed conditions may include principle of measurement, method of measurement, observer, measuring instrument, reference standard, location, conditions of use, and time. When discussing the precision of measurement data, it is helpful for the analyst to define how the data are collected and to use the term 'repeatability' when applicable. It is equally important to specify the conditions used for the collection of 'reproducibility' data.

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