  We emphasize that the mention of the significance level when rejecting the
null hypothesis (H0) which assumes that what is observed is pure noise) can
mislead one to think that the H0 hypothesis is unlikely to occur with that
significance level. We show that the significance level has nothing to do with
the posterior probability of H0 given the observed data set, and that this
posterior probability is very much higher than what the significance level
naively provides. We use Bayes theorem for deriving the posterior probability
of H0 being true assuming an alternative hypothesis H1 that assumes that a mode
is present, taking some prior for the mode height, for the mode amplitude and
linewidth.We report the posterior probability of H0 for the p modes detected on
HD49933 by CoRoT. We conclude that the posterior probability of H0 provide a
much more conservative quantification of the mode detection than the
significance level. This framework can be applied to any stellar power spectra
similar to those obtained for asteroseismology.
