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Non-standard errors
(2021)
In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in sample estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: non-standard errors. To study them, we let 164 teams test six hypotheses on the same sample. We find that non-standard errors are sizeable, on par with standard errors. Their size (i) co-varies only weakly with team merits, reproducibility, or peer rating, (ii) declines significantly after peer-feedback, and (iii) is underestimated by participants.
In this letter we report the first multi-differential measurement of correlated pion-proton pairs from 2 billion Au+Au collisions at sNN=2.42 GeV collected with HADES. In this energy regime the population of Δ(1232) resonances plays an important role in the way energy is distributed between intrinsic excitation energy and kinetic energy of the hadrons in the fireball. The triple differential d3N/dMπ±pdpTdy distributions of correlated π±p pairs have been determined by subtracting the πp combinatorial background using an iterative method. The invariant-mass distributions in the Δ(1232) mass region show strong deviations from a Breit-Wigner function with vacuum width and mass. The yield of correlated pion-proton pairs exhibits a complex isospin, rapidity and transverse-momentum dependence. In the invariant mass range 1.1<Minv(GeV/c2)<1.4, the yield is found to be similar for π+p and π−p pairs, and to follow a power law 〈Apart〉α, where 〈Apart〉 is the mean number of participating nucleons. The exponent α depends strongly on the pair transverse momentum (pT) while its pT-integrated and charge-averaged value is α=1.5±0.08st±0.2sy.