Non-Gaussian error distribution of 7Li abundance measurements

Crandall, Sara; Houston, Stephen D.

doi:10.1142/s0217732315501230

Cited by 20 publications

(16 citation statements)

References 46 publications

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“…The results of this study agree with earlier research that also observed Student-t tails, but only looked at a handful of subatomic or astrophysics quantities up to z ∼ 5 − 10 [16,19,[56][57][58]. Unsurprisingly, the tails reported here are mostly heavier than those reported for repeated measurements made with the same instrument (ν ∼ 3−9) [59][60][61], which should be closer to Normal since they are not independent and share most systematic effects.…”

Section: A Comparison With Earlier Studiessupporting

confidence: 90%

Not Normal: the uncertainties of scientific measurements

Bailey¹

2017

R. Soc. open sci.

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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.

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Section: A Comparison With Earlier Studiessupporting

confidence: 90%

Not Normal: the uncertainties of scientific measurements

Bailey¹

2017

R. Soc. open sci.

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“…More specifically, we examine the Gaussianity of these error distributions. 2 We begin by following and Crandall & Ratra (2015) and construct an error distribution, a histogram of measurements as a function of N σ , the number of standard deviations that a measurement deviates from a central estimate. This is similar to the z score analysis of de Grijs et al (2014), however, we use a central estimate from the data compilation itself whereas de Grijs et al (2014) use two published values that are assumed to well represent the measurements.…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

Crandall

Ratra

2015

ApJ

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We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs et al. (2014) that give an LMC distance modulus of (m − M) 0 = 18.49 ± 0.13 mag (median and 1σ symmetrized error). Central estimates found from weighted mean and median statistics are used to construct the error distributions. The weighted mean error distribution is non-Gaussian -flatter and broader than Gaussian -with more (less) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of unaccounted-for systematic uncertainties. The median statistics error distribution, which does not make use of the individual measurement errors, is also non-Gaussian -more peaked than Gaussianwith less (more) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of publication bias and/or the nonindependence of the measurements. We also construct the error distributions of 247 SMC distance moduli values from de Grijs & Bono (2015). We find a central estimate of (m − M) 0 = 18.94 ± 0.14 mag (median and 1σ symmetrized error), and similar probabilities for the error distributions.

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“…Similar to Ratra et al ( [4]), we calculated the estimates using two methods: median statistics and weighted mean estimates. The weighted mean (Θ M ) is given by [25]:…”

Section: A Error Distribution and Distribution Functionsmentioning

confidence: 99%

“…In the last decade, Ratra and collaborators have used a variety of astrophysical datasets to test the non-Gaussianity of the error distributions from these measurements. The datasets they explored for this purpose include measurements of H 0 [3], Lithium-7 measurements [4] (see also [5]), distance to LMC [6], distance to galactic center [7]. Evidence for non-Gaussian errors has also been found in HST Key project data [8].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian error distributions of galactic rotation speed measurements

Rajan

Desai

2018

Eur. Phys. J. Plus

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We construct the error distributions for the galactic rotation speed (Θ0) using 137 data points from measurements compiled in De Grijs et al. [1], with all observations normalized to the galactocentric distance of 8.3 kpc. We then checked (using the same procedures as in works by Ratra et al) if the errors constructed using the weighted mean and the median as the estimate, obey Gaussian statistics. We find using both these estimates that they have much wider tails than a Gaussian distribution. We also tried to fit the data to three other distributions: Cauchy, double-exponential, and Students-t. The best fit is obtained using the Students-t distribution for n = 2 using the median value as the central estimate, corresponding to a p-value of 0.1. We also calculate the median value of Θ0 using all the data as well as using the median of each set of measurements based on the tracer population used. Because of the non-gaussianity of the residuals, we point out that the subgroup median value, given by Θ med = 219.65 km/sec should be used as the central estimate for Θ0.

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Non-Gaussian error distribution of 7Li abundance measurements

Cited by 20 publications

References 46 publications

Not Normal: the uncertainties of scientific measurements

Not Normal: the uncertainties of scientific measurements

Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

Non-Gaussian error distributions of galactic rotation speed measurements

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