Result, error and uncertainty.

Abstract

Several recent documents, from international standardization bodies, present the philosophical and statistical background for understanding the components of a measured value and its uncertainty, as well as the relevant nomenclature for their description. The value is the output of a function relating values from reading, calibrator, corrections and influence quantities. The corrected value may be regarded as the sum of a true value, bias of measurement procedure, laboratory deviation, and random error; in some cases there are also biases from aberrant sample and undetected mistakes. The contributions of laboratory deviation and random error vary with the precision conditions that must be specified. The uncertainty measures are no longer a sum of systematic errors and the positive square root of quadratically added random errors. Now, the measured corrected value is the best estimate and the components of its uncertainty, one from each input, are all expressed as statistically or non-statistically derived variances that are combined according to the function relating the input values. The positive square root of the outcome is the combined standard uncertainty that is regarded as a standard deviation from which an expanded uncertainty may be obtained by multiplying with a coverage factor.