- #1
ohwilleke
Gold Member
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There is solid empirical evidence that error in particle physics measurements is not actually distributed in a Guassian manner. Why don't particle physicists routinely use student t error distributions with fat tails that fit the reality of errors in experimental measurement more accurately?
(One of the cases studied was the effort to measure the mass of the electron.)
David C. Bailey. "Not Normal: the uncertainties of scientific measurements." Royal Society Open 4(1) Science 160600 (2017).
(One of the cases studied was the effort to measure the mass of the electron.)
Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties were studied by analysing 41 000 measurements of 3200 quantities from medicine, nuclear and particle physics, and interlaboratory comparisons ranging from chemistry to toxicology. Outliers are common, with 5σ disagreements up to five orders of magnitude more frequent than naively expected. Uncertainty-normalized differences between multiple measurements of the same quantity are consistent with heavy-tailed Student’s t-distributions that are often almost Cauchy, far from a Gaussian Normal bell curve. Medical research uncertainties are generally as well evaluated as those in physics, but physics uncertainty improves more rapidly, making feasible simple significance criteria such as the 5σ discovery convention in particle physics. Contributions to measurement uncertainty from mistakes and unknown problems are not completely unpredictable. Such errors appear to have power-law distributions consistent with how designed complex systems fail, and how unknown systematic errors are constrained by researchers. This better understanding may help improve analysis and meta-analysis of data, and help scientists and the public have more realistic expectations of what scientific results imply.
David C. Bailey. "Not Normal: the uncertainties of scientific measurements." Royal Society Open 4(1) Science 160600 (2017).