• Table of Content
• Foreword
• Scope
• Uncertainty
• Analytical Measurement
• The Process
• Step 1: Specification
• Step 2: Identification
• Step 3: Quantification
• Step 4: Calculation
• Reporting Uncertainty
• Appendix A: Examples
  • Example 1: Calibration Standard
  • Example 2: Standardising NaOH
  • Example 3: An Acid/Base Titration
  • Example 4: In-house Validation Studies
  • Example 5: Determ. Cadmium Release
  • Example 6: Crude Fibre in Animal Feed
  • Example 7: Lead in Water - double IDMS
• Appendix B: Definitions
• Appendix C: Analytical Proc.
• Appendix D: Analyse U Sources
• Appendix E: Statistics
• Appendix F: MU at the Limit
• Appendix G: Common Sources
• Appendix H: Bibliography

Uncertainty

2.1. Definition of Uncertainty

2.1.1. The definition of the term uncertainty (of measurement) used in this protocol and taken from the current version adopted for the International Vocabulary of Basic and General Terms in Metrology [h.4] is:

"A parameter associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand"

2.1.2. In many cases in chemical analysis, the measurand [b.6] will be the concentration of an analyte. However chemical analysis is used to measure other quantities, e.g. colour, pH, etc., and therefore the general term "measurand" will be used.

2.1.3. The definition of uncertainty given above focuses on the range of values that the analyst believes could reasonably be attributed to the measurand.

2.1.4. In general use, the word uncertainty relates to the general concept of doubt. In this guide, the word uncertainty, without adjectives, refers either to a parameter associated with the definition above, or to the limited knowledge about a particular value. Uncertainty of measurement does not imply doubt about the validity of a measurement; on the contrary, knowledge of the uncertainty implies increased confidence in the validity of a measurement result.

2.2. Uncertainty Sources

2.2.1. In practice the uncertainty on the result may arise from many possible sources, including examples such as incomplete definition, sampling, matrix effects and interferences, environmental conditions, uncertainties of weights and volumetric equipment, reference values, approximations and assumptions incorporated in the measurement method and procedure, and random variation (a fuller description of uncertainty sources is given in section 6.7.)

2.3. Uncertainty Components

2.3.1. In estimating the overall uncertainty, it may be necessary to take each source of uncertainty and treat it separately to obtain the contribution from that source. Each of the separate contributions to uncertainty is referred to as an uncertainty component. When expressed as a standard deviation, an uncertainty component is known as a standard uncertainty [b.14]. If there is correlation between any components then this has to be taken into account by determining the covariance. However, it is often possible to evaluate the combined effect of several components. This may reduce the overall effort involved and, where components whose contribution is evaluated together are correlated, there may be no additional need to take account of the correlation.

2.3.2. For a measurement result y, the total uncertainty, termed combined standard uncertainty [b.15] and denoted by u_c(y), is an estimated standard deviation equal to the positive square root of the total variance obtained by combining all the uncertainty components, however evaluated, using the law of propagation of uncertainty (see section 8).

2.3.3. For most purposes in analytical chemistry, an expanded uncertainty [b.16] U, should be used. The expanded uncertainty provides an interval within which the value of the measurand is believed to lie with a higher level of confidence. U is obtained by multiplying u_c(y), the combined standard uncertainty, by a coverage factor [b.17] k. The choice of the factor k is based on the level of confidence desired. For an approximate level of confidence of 95%, k is 2.

NOTE: The coverage factor k should always be stated so that the combined standard uncertainty of the measured quantity can be recovered for use in calculating the combined standard uncertainty of other measurement results that may depend on that quantity.

2.4. Error and Uncertainty

2.4.1. It is important to distinguish between error and uncertainty. Error [b.20] is defined as the difference between an individual result and the true value [b.3] of the measurand. As such, error is a single value. In principle, the value of a known error can be applied as a correction to the result.

NOTE: Error is an idealised concept and errors cannot be known exactly.

2.4.2. Uncertainty, on the other hand, takes the form of a range, and, if estimated for an analytical procedure and defined sample type, may apply to all determinations so described. In general, the value of the uncertainty cannot be used to correct a measurement result.

2.4.3. To illustrate further the difference, the result of an analysis after correction may by chance be very close to the value of the measurand, and hence have a negligible error. However, the uncertainty may still be very large, simply because the analyst is very unsure of how close that result is to the value.

2.4.4. The uncertainty of the result of a measurement should never be interpreted as representing the error itself, nor the error remaining after correction.

2.4.5. An error is regarded as having two components, namely, a random component and a systematic component.

2.4.6. Random error [b.21] typically arises from unpredictable variations of influence quantities. These random effects give rise to variations in repeated observations of the measurand. The random error of an analytical result cannot be compensated by correction but it can usually be reduced by increasing the number of observations.

NOTE: The experimental standard deviation of the arithmetic mean [b.23] or average of a series of observations is not the random error of the mean, although it is so referred to in some publications on uncertainty. It is instead a measure of the uncertainty of the mean due to some random effects. The exact value of the random error in the mean arising from these effects cannot be known.

2.4.7. Systematic error [b.22] is defined as a component of error which, in the course of a number of analyses of the same measurand, remains constant or varies in a predictable way. It is independent of the number of measurements made and cannot therefore be reduced by increasing the number of analyses under constant measurement conditions.

2.4.8. Constant systematic errors, such as failing to make an allowance for a reagent blank in an assay, or inaccuracies in a multi-point instrument calibration, are constant for a given level of the measurement value but may vary with the level of the measurement value.

2.4.9. Effects which change systematically in magnitude during a series of analyses, caused, for example by inadequate control of experimental conditions, give rise to systematic errors that are not constant.

2.4.10. The result of a measurement should be corrected for all recognised significant systematic effects.

NOTE: Measuring instruments and systems are often adjusted or calibrated using measurement standards and reference materials to correct for systematic effects. The uncertainties associated with these standards and materials and the uncertainty in the correction must still be taken into account.

2.4.11. A further type of error is a spurious error or blunder. Errors of this type invalidate a measurement and typically arise through human failure or instrument malfunction. Transposing digits in a number while recording data, an air bubble lodged in a spectrophotometer flow-through cell, or accidental cross-contamination of test items are common examples of this type of error.

2.4.12. Measurements for which errors such as these have been detected should be rejected and no attempt should be made to incorporate the errors into any statistical analysis. However, errors such as digit transposition can be corrected (exactly), particularly if they occur in the leading digits.

2.4.13. Spurious errors are not always obvious and, where a sufficient number of replicate measurements is available, it is usually appropriate to apply an outlier test to check for the presence of suspect members in the data set. Any positive result obtained from such a test should be considered with care and, where possible, referred back to the originator for confirmation. It is generally not wise to reject a value on purely statistical grounds.

2.4.14. Uncertainties estimated using this guide are not intended to allow for the possibility of spurious errors/blunders.