About not Correcting for Systematic Effects

Abstract

In practice, measurement results are sometimes described by an estimate, which is not the best one as defined in the GUM. Such alternative estimates arise when the result of a measurement is not corrected for all systematic effects. No recommendation exists in the GUM for associating an uncertainty with an uncorrected estimate. A common choice in guidelines and in the literature is the uncertainty u\left( {y'} \right) = \sqrt {{u^2}\left( y \right) + {{\left( {y - y'} \right)}^2}} for an alternative estimate y′. It arises from the expected quadratic loss, on which, also in the GUM, the standard uncertainty u(y), and the best estimate y are based. However, such an uncertainty is not a standard uncertainty and we establish, it may not be used for uncertainty propagation. One consequence is, for example, that pairs (y′, u(y′)) are not to be used in calibration certificates.

Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and ranking probability matrix. I. Theory

“…Remark. Establishing the power of the test (1 − β), where β is the probability of type II errors (false negative, or the non-rejection of a false null hypothesis) 50 requires the definition an alternative hypothesis 51 . In the present case, there is a infinity of ways to realize the s 1 = s 2 alternative, so the power estimation is practically intractable.…”

“…A false positive (type I error) is obtained when a true null hypothesis is rejected by a test 50,51 .…”

Impact of non-normal error distributions on the benchmarking and ranking of Quantum Machine Learning models

“…Reliable use of statistical tests of normality require typically at least N = 100 points [8,9]. For a given sample size, the Shapiro-Wilk W statistics has been shown to have good properties [8], and it is used in this study.…”

“…The values of W range between 0 and 1, and values of W 1 are in favor of the normality of the sample. If W lies below a critical value W c depending on the sample size and the chosen level of type I errors α (typically 0.05), the normality hypothesis cannot be assumed to hold [9].…”