Null hypothesis statistical testing and p-values are used pervasively in research. In some fields of research, such as medicine and neuroscience, a p-value lower than 0.05 may simply be a good enough result to publish. But what does this p-value really mean? What does it rely on? Could we reach such a result by chance only? In this talk, I will present answers to these questions as well as their consequences in terms of the confidence we have in some published results. Finally, I will introduce some alternatives to null hypothesis statistical testing inspired from the Bayesian data analysis literature.