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Information leaflets

The Two One-Sided t-Test (TOST)

Content

TOST Pic v1This information leaflet is intended for laboratories performing significance testing for two (mean) values, or for a mean value and a reference value. Unlike the conventional t-test, which assesses whether two values are different, the Two One-Sided Test (TOST) procedure presented here evaluates whether the difference is acceptable - that ism within a specified acceptance range. Deviations in both directions are tested separately using a one-sided t-test at the chosen significance level.

The leaflet has been prepared by the Eurachem Measurement Uncertainty and Traceability Working Group to introduce the use of equivalence testing.

 

Availability

Translation

Translation into other languages is encouraged for members of Eurachem. Other offers of translation should be directed to the Eurachem Secretariat for permission. The Eurachem policy on maintenance and development of Eurachem guidance, available on the Policies page, gives further information on translation.

 

*Publication dates are dates of website publication. English version first published on this site on 2026-04-17.

Using repeated measurements to improve the standard uncertainty

Content

Analysts often take multiple observations, and sometimes average the result of several observations to reduce the uncertainty associated with random variation. However, it is often unclear how the standard uncertainty associated with averaged results should be calculated from an observed standard deviation. Sometimes one should divide by the square root of the number of observations; sometimes the standard deviation is used unchanged, and sometimes some alternative formula is appropriate. 

This information leaflet has been prepared by the Eurachem Measurement Uncertainty and Traceability Working Group (see here for details) to give further explanation of when the classical 'root n' formula can, and can not, be used. The leaflet amplifies principles described in the Eurachem Guide "Quantifying uncertainty in analytical measurement", which is available here.

 

Availability

*2015 edition

Translation

Translation into other languages is encouraged for members of Eurachem. Other offers of translation should be directed to the Eurachem Secretariat for permission. The Eurachem policy on maintenance and development of Eurachem guidance, available on the Policies page, gives further information on translation.

Amendment history

This leaflet was amended to improve clarity in April 2016. The previous English version, as issued in 2015, is available for comparison.

Setting Target Measurement Uncertainty

Contents

orange tree trn 180Measurement results are only fit for purpose if the reported uncertainty is correct and has a magnitude small enough for the intended use. The target measurement uncertainty (target MU) is the maximum admissible uncertainty defined for a specific measurement goal. This information leaflet provides a short and accessible introduction to the idea of target measurement uncertainty.

For detailed information on setting a target measurement uncertainty, see the Eurachem/CITAC guide "Setting and Using Target Uncertainty in Chemical Measurement"

Availability

Translations

Translation into other languages is encouraged for members of Eurachem. Other offers of translation should be directed to the Eurachem Secretariat for permission. The Eurachem policy on maintenance and development of Eurachem guidance, available on the Policies page, gives further information on translation.

Treatment of an observed bias

Content

bias img 240x194Bias is routinely determined during the validation of analytical methods. Usually, the observed bias is not exactly zero. It is then important to decide whether the observed bias can reasonably be treated as unimportant, or whether some further action needs to be taken. This can be particularly difficult to decide when applying the principles of the 'Guide to the Expression of Uncertainty in measurement', which assumes that a correction has been applied for any important bias. 

This information leaflet has been prepared by the Eurachem Measurement Uncertainty and Traceability Working Group (see here for details). The leaflet discusses whether or not an observed significant bias should be corrected and the impact this may have on the measurement uncertainty (MU). The leaflet does not describe how to apply a correction or how to increase the uncertainty to take account of an uncorrected bias, though it does provide relevant literature sources.

 

Availability

 * 2nd printing; editorial amendment only

Translation

Translation into other languages is encouraged for members of Eurachem. Other offers of translation should be directed to the Eurachem Secretariat for permission. The Eurachem policy on maintenance and development of Eurachem guidance, available on the Policies page, gives further information on translation.

Publication date

This leaflet was first published in English on 2017-05-27.

* The English copy on this page is a minor (editorial) amendment, published 2022-10-21; the recommendations are unchanged.

What is the uncertainty factor?

Content

Distribution of GMO results showing approximately lognormal distribution

Appropriate expression of the measurement uncertainty (MU) is crucial, and there are situations when the traditional, symmetric, expanded uncertainty interval is not sufficient. This leaflet aims to explain the concept of the uncertainty factor and how it can be used to provide a convenient and realistic uncertainty interval in particular circumstances..

This leaflet was produced by the Eurachem Sampling Uncertainty Working Group and the Royal Society of Chemistry Analytical Methods Committee (AMC) Sampling Uncertainty Working Groups.

Availability

Translation

Please consult the Eurachem Sampling Uncertainty Working Group Chair, directly or by using the UfSWG contact form, if you would like to prepare a translation in your own language.

 

*Publication dates are dates of website publication. English version first published on this site on 2020-07-29.