measurement result

Also contains definitions of: bias, expectation value, expected value, limiting mean
The outcome of an analytical measurement (application of the @[email protected]), or value attributed to a @[email protected] This may be the result of direct observation, but more commonly it is given as a statistical estimate derived from a set of observations. The distribution of such estimates (estimator distribution) characterizes the chemical measurement process, in contrast to a particular estimate, which constitutes an experimental result. Additional characteristics become evident if we represent \(\hat{x}\) as follows: \[\begin{array}{c} &&& e & \\ &&& ⎴ ⎴ ⎴ & \\ \hat{x}=\tau +e = &\tau& + &\Delta& + &\delta&= \mu +\delta \\ & ⎵ ⎵ ⎵ &&& \\ & \mu &&& \end{array}\] The @[email protected], \(\tau \), is the value \(x\) that would result if the chemical measurement process were error-free. The @[email protected], \(e\), is the difference between an observed (estimated) value and the true value; i.e. \(e=\hat{x}- \tau \) (signed quantity). The total error generally has two components, bias (\(\mathit{\Delta}\)) and @[email protected] (\(\delta \)), as indicated above. The limiting mean, \(\mu\), is the asymptotic value or population mean of the distribution that characterizes the measured quantity; the value that is approached as the number of observations approaches infinity. Modern statistical terminology labels this quantity the expectation value or expected value, \(E(\hat{x})\). The bias, \(\mathit{\Delta}\), is the difference between the limiting mean and the true value; i.e. \(\mathit{\Delta} = \mu - \tau \) (signed quantity). The @[email protected], \(\delta \), is the difference between an observed value and the limiting mean; i.e. \(\delta = \hat{x} - \mu \) (signed quantity).
PAC, 1995, 67, 1699. (Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995)) on page 1705 [Terms] [Paper]