(Unbiased) Variance estimation and uncertainty format

Compound Gauss–Markoff method for unbiased variance estimation is dissected to analyse separate contributions to the problem of quantifying uncertainty bearing on repeated experiment outcome. On one hand: Gauss’ original treatment of observed quantity values according to least squares principle; on the other hand: Markoff’s reformulation using independent identically distributed (IID) random variables (RVs). In this paper, critical to the construct of IID RVs (and tenability of consequent results) is claimed a clear-cut distinction between identical distribution and identity of RVs. The far-reaching theoretical and practical import is considered, stemming from diversity between a measurand (modelled in RV term) and its (the RV’s variate) measured values. It is shown how the situation can be fit into the vocabulary of metrology, which allows a correct handling of concepts and application of established formulas. Estimation criteria alternative to unbiasedness are explored, and implications on interval estimation and related expression of uncertainty are discussed.