Some remarks on the error analysis in the case of poor statistics

Abstract

A prescription for the error analysis of experimental data in the case of stochastic background is formulated. Several relations are given which allow to establish the significance of mother-daughter relationships obtained from delayed coincidences. Both, the probability that a cascade is produced randomly and the probability that the parameters of an observed event chain are incompatible with known properties of a given species are formulated. The expressions given are applicable also in cases of poor statistics down even to single events.

Eleven new heaviest isotopes of elementsZ=105toZ=117identified among the products ofOganessian1, Abdullin2, Bailey3 et al. 2011Phys. Rev. C1255350View full textAdd to dashboardCite

“…The measured half-lives for Db isotopes gradually become larger with increase in neutron number on approach to the neutron shell N = −0.6 pb at E*=35 MeV and E*=39 MeV, respectively (see Table III). Error bars correspond to statistical [42] Table III experimental cross sections of the 3n and 4n reaction channels within experimental uncertainties do not contradict the calculated values of [23][24][25].…”

“…By using the approach offered in [42] and the calculation method [43] for all five events, the probabilities of chance correlations imitating each of the observed decay chains were determined. The total number of ER-like events with E ER =7.5-17.5 MeV that were followed by α-like events in the focal-plane detector with E α1 =11.03± 0.25 MeV occurring in the same strip, within a position window corresponding to ±FWHM ER-α position resolutions (98% c.l.…”

Hot fusion-evaporation cross sections ofSc45-induced reactions with lanthanide targets

“…To determine which data were above background, a simple statistical test similar to that described in Ref. [33] was used.…”

“…The associated errors are statistical only; due to uncertainties primarily from the transmission efficiency of MARS, absolute uncertainties are estimated to be ±50%. All reported errors are calculated at the 1σ level, with symmetric error bars reported for channels with sufficient statistics (≥ 15 counts after background subtraction), and asymmetric error bars reported for channels with low statistics [33].…”

γ-ray spectroscopy of the odd-oddN=Z+2deformed proton emitter112Cs

“…The energy of the peak is 710(20) keV, and it has around 10% of the intensity of the main 112 Cs decay peak. The half life of the decay has been estimated using the maximum-likelihood method [29,30] to be 170 +50 −30 µs. This observation would represent fine structure in the proton decay of 112 Cs.…”