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We emphasize that the mention of the significance level when rejecting thenull hypothesis (H0) which assumes that what is observed is pure noise) canmislead one to think that the H0 hypothesis is unlikely to occur with thatsignificance level. We show that the significance level has nothing to do withthe posterior probability of H0 given the observed data set, and that thisposterior probability is very much higher than what the significance levelnaively provides. We use Bayes theorem for deriving the posterior probabilityof H0 being true assuming an alternative hypothesis H1 that assumes that a modeis present, taking some prior for the mode height, for the mode amplitude andlinewidth.We report the posterior probability of H0 for the p modes detected onHD49933 by CoRoT. We conclude that the posterior probability of H0 provide amuch more conservative quantification of the mode detection than thesignificance level. This framework can be applied to any stellar power spectrasimilar to those obtained for asteroseismology.

On posterior probability and significance level: application to the power spectrum of HD49933 observed by CoRoT