The concept of precision is widely understood. International definitions recognise that there are different conditions for measuring precision (repeatability, intermediate precision and reproducibility conditions). However, this concept appears to attract informal terminology, especially ‘internal’ precision and ‘external’ precision, which is not recognised across the measurement sciences, and is creating unnecessary terminology that adds confusion.
Examples of good and bad practice
Quantification of internal errors on …
Replicate analyses of multiple digestions of this material yield a reproducibility …
The typical daily 2 standard deviation (2 SD) reproducibility of the …
Typically, internal precision during measurement is better than external reproducibility [using the ICP-MS instrument in our lab.]
The external error determined from the 5 laboratories involved in the analysis …
Quantification of the measurement repeatability on …
Replicate analyses of multiple digestions of this material yielded an intermediate precision for the measurement results of … [where the time period over which the measurements were made is specified]
The typical repeatability precision (on a day-to-day basis), expressed as 2s, of the …
Typically, repeatability precision during measurement was better than the intermediate precision [using the ICP-MS instrument in our laboratory.]
The measurement reproducibility determined from the five laboratories involved in the analysis …
Precision is a measure of the closeness of agreement between replicate measurements made under specified conditions. However, there are significant differences in the way in which replicate measurements can be made, and this is recognised by defining three different conditions: repeatability conditions, intermediate precision conditions and reproducibility conditions. The differences between these three conditions depend on how much changes. It is easiest to examine the end member conditions first.
Repeatability conditions involve measurements made in the same laboratory by the same operators using the same technique on the same or similar materials over a short period of time. Because so little changes, repeatability will offer the most optimistic measure of precision and its interpretation should be undertaken with care as its optimistic magnitude could be misleading.
At the other end of the scale, reproducibility conditions involve measurements made by different operators in different laboratories using different techniques, over an extended period of time, although the test materials may be the same or similar. The magnitude of reproducibility precision will be larger than that of repeatability – hence, reproducibility is commonly regarded as being much more realistic in terms of the precision capabilities of an area of measurement. Depending on the design of the experiment, not all the conditions listed above may change, so reproducibility needs to be accompanied by a brief description of how the replicate measurements were made.
Conditions for the measurement of intermediate precision usually involve the same operator, the same location, the same technique, but with measurements made over a period of time, with the possibility of other conditions changing. Again, for clarity, the conditions under which measurements were made should be described.
Thus, an XRF laboratory making replicate measurements on a test material over an afternoon can provide from an analysis of the results a measure of repeatability.
If the same replicate results were made over a period of six months, an analysis of data would provide a measure of the intermediate precision.
If that material were circulated to 10 other XRF laboratories, an analysis of replicate measurements would provide a measure of the reproducibility of the technique.
It has become common practice in some laboratories to use the term ‘internal precision’ in place of ‘repeatability’ and ‘external precision’ in place of either ‘intermediate precision’ or ‘reproducibility’, depending on measurement conditions. Use of this alternative terminology is unhelpful and redundant in view of the existing internationally-approved definitions.
Measurement precision (precision)
Closeness of agreement between indications or measured quantity values obtained by replicate measurements on the same or similar objects under specified conditions.
NOTE 1 Measurement precision is usually expressed numerically by measures of imprecision, such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement.
NOTE 2 The ‘specified conditions’ can be, for example, repeatability conditions of measurement, intermediate precision conditions of measurement, or reproducibility conditions of measurement (see ISO 5725-1:1994).
NOTE 3 Measurement precision is used to define measurement repeatability, intermediate measurement precision, and measurement reproducibility. NOTE 4 Sometimes “measurement precision” is erroneously used to mean measurement accuracy. (VIM 3: 2.15)
Repeatability condition of measurement (repeatability condition)
Condition of measurement, out of a set of conditions that includes the same measurement procedure, same operators, same measuring system, same operating conditions and same location, and replicate measurements on the same or similar objects over a short period of time.
NOTE 1 A condition of measurement is a repeatability condition only with respect to a specified set of repeatability conditions.
NOTE 2 In chemistry, the term “intra-serial precision condition of measurement” is sometimes used to designate this concept. (VIM 3: 2.20)
Measurement repeatability (repeatability)
Measurement precision under a set of repeatability conditions of measurement. (VIM 3: 2.21)
Intermediate precision condition of measurement (intermediate precision condition)
Condition of measurement, out of a set of conditions that includes the same measurement procedure, same location, and replicate measurements on the same or similar objects over an extended period of time, but may include other conditions involving changes.
NOTE 1 The changes can include new calibrations, calibrators, operators, and measuring systems.
NOTE 2 A specification for the conditions should contain the conditions changed and unchanged, to the extent practical.
NOTE 3 In chemistry, the term “inter-serial precision condition of measurement” is sometimes used to designate this concept. (VIM 3: 2.22)
Intermediate measurement precision (intermediate precision)
Measurement precision under a set of intermediate precision conditions of measurement.
NOTE Relevant statistical terms are given in ISO 5725-3:1994. (VIM 3: 2.23)
Reproducibility condition of measurement (reproducibility condition)
Condition of measurement, out of a set of conditions that includes different locations, operators, measuring systems, and replicate measurements on the same or similar objects.
NOTE 1 The different measuring systems may use different measurement procedures.
NOTE 2 A specification should give the conditions changed and unchanged, to the extent practical. (VIM 3: 2.24)
Measurement reproducibility (reproducibility)
Measurement precision under reproducibility conditions of measurement NOTE Relevant statistical terms are given in ISO 5725-1:1994 and ISO 5725-2:1994. (VIM 3: 2.25)
Index to terms
|Concept||Metrological terms considered||Metrological terms covered|
|Say no to ppm||The ambiguities associated with the use of ‘ppm’|
|Sigma is out, standard deviation is the way to go!||What symbols are used to represent the properties of population- and sample-distributions|
|Standard ≠ reference material||Avoiding the use of the term standards when referring to (certified) reference materials or calibrators||Reference material, certified reference material, standard reference material, calibrator, calibration, validation, measurement standard (étalon), verification|
|Please, no more errors from your laboratory||Explaining the difference between uncertainty and error||Measurement uncertainty, measurement error, systematic measurement error, measurement bias, random measurement error, confidence level|
|Precision||Distinguishing between repeatability, intermediate precision and reproducibility and discouraging the use of ‘internal precision’||Measurement precision, repeatability condition of measurement, intermediate precision of measurement, reproducibility condition of measurement, repeatability, intermediate precision, reproducibility|
|Small bias yes, high accuracy no||Explaining the difference between accuracy, bias and trueness||Measurement accuracy, measurement trueness, measurement bias|