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Background: Event-related potentials (ERPs) are increasingly used in cognitive science. With their high temporal resolution, they offer a unique window into cognitive processes and their time course. In this paper, we focus on ERP experiments whose designs involve selecting participants and stimuli amongst many. Recently, Westfall et al. (2017) highlighted the drastic consequences of not considering stimuli as a random variable in fMRI studies with such designs. Most ERP studies in cognitive psychology suffer from the same drawback. New method: We advocate the use of the Quasi-F or Mixed-effects models instead of the classical ANOVA/by-participant F1 statistic to analyze ERP datasets in which the dependent variable is reduced to one measure per trial (e.g., mean amplitude). We combine Quasi-F statistic and cluster mass tests to analyze datasets with multiple measures per trial. Doing so allows us to treat stimulus as a random variable while correcting for multiple comparisons. Results: Simulations show that the use of Quasi-F statistics with cluster mass tests allows maintaining the family wise error rates close to the nominal alpha level of 0.05. Comparison with existing methods: Simulations reveal that the classical ANOVA/F1 approach has an alarming FWER, demonstrating the superiority of models that treat both participant and stimulus as random variables, like the Quasi-F approach. Conclusions: Our simulations question the validity of studies in which stimulus is not treated as a random variable. Failure to change the current standards feeds the replicability crisis.
The inner region of the Milky Way halo harbors a large amount of dark matter (DM). Given its proximity, it is one of the most promising targets to look for DM. We report on a search for the annihilations of DM particles using gamma-ray observations towards the inner 300 pc of the Milky Way, with the H.E.S.S. array of ground-based Cherenkov telescopes. The analysis is based on a 2D maximum likelihood method using Galactic Center (GC) data accumulated by H.E.S.S. over the last 10 years (2004-2014), and does not show any significant gamma-ray signal above background. Assuming Einasto and Navarro-Frenk-White DM density profiles at the GC, we derive upper limits on the annihilation cross section <sigma nu >. These constraints are the strongest obtained so far in the TeV DM mass range and improve upon previous limits by a factor 5. For the Einasto profile, the constraints reach <sigma nu > values of 6 x 10(-26) cm(3) s(-1) in the W+W- channel for a DM particle mass of 1.5 TeV, and 2 x 10(-26) cm(3) s(-1) in the tau(+)tau(-) channel for a 1 TeV mass. For the first time, ground-based gamma-ray observations have reached sufficient sensitivity to probe <sigma nu > values expected from the thermal relic density for TeV DM particles.