“Degrees of equivalence” for chemical measurement capabilities: primary pH

Abstract

The key comparison (KC) studies of the Consultative Committee for Amount of Substance-Metrology in Chemistry help ensure the reliability of chemical and biochemical measurements relevant to international trade and environmental-, health-, and safety-related decision making. The traditional final evaluation of each measurement result reported by a KC participant is a ''degree of equivalence'' (DEq) that quantitatively specifies how consistent each individual result is relative to a reference value. Recognizing the impossibility of conducting separate KCs for all important analytes in all important sample matrices at all important analyte levels, emphasis is now shifting to documenting broadly applicable critical or ''core'' measurement competencies elicited through a series of studies. To better accomplish the necessary synthesis of results, data analysis and display tools must be developed for objectively and quantitatively combining individual DEqs. The information detailed in the 11 KCs of primary method pH measurements publically available as of 2013 provides an excellent ''best case'' prototype for such analysis. We here propose tools that enable documenting the expected primary pH measurement performance of individual participants between pH 1 and pH 11 and from 15°C to 37°C. These tools may prove useful for other areas where the uncertainty of measurement is a predictable function of the measured quantity, such as the stable gases. That results for relatively simple measurement processes can be combined using relatively simple analysis and display methods does not ensure that similarly meaningful summaries can be devised for less well understood and controlled systems, but it provides the incentive to attempt to do so.

Consensus building for interlaboratory studies, key comparisons, and meta-analysis

“…This suggests an alternative definition for the unilateral DoE that could be applied generally: based on the difference µ = − * − D x j j j , where µ −j denotes an estimate of the consensus value derived from the measurement results produced by all the participants but leaving out the results from participant j, for = … j n 1, , . Viechtbauer and Cheung [148] have used this idea to identify outliers in meta-analysis, and [40] have promoted it specifically for the evaluation of degrees of equivalence in key comparisons. This alternative definition may then be carried forward and lead to an alternative definition of the bilateral DoEs based on…”

Thermodynamic Modeling of Aqueous Electrolyte Systems: Current Status

“…These problems with pH interpretation are closely associated with limitations in the treatment of liquid junction potential corrections, both experimentally and theoretically. Even recently there has been an emphatic declaration that pH as a measure of the single ion activity of H + is undefinable and of no practical benefit but we and others ,− do not share this opinion.…”

An evolutionary algorithm for consensus building in inter-laboratory comparisons

“…An analysing tool called Pomplot, plotting u (d i ) as a function of d i was also developed [16]. A different approach is to omit results from participants on-by-one to assess the influence of a particular value on the reference value [17].…”

“…As well as the two main techniques described above, a family of approaches called 'Linear Pool (LP)' was conceived by the Marquis de Laplace [18] and studied recently by many authors [17,[19][20][21][22][23][24]. It consists of pooling all the Monte-Carlo samples x (r) i in a unique vector v and estimating the parameters of the probability density function of this pooled data set.…”