The error statistical approach of Mayo and others comprises a general philosophy of science as well as a particular viewpoint on the philosophy statistics. We briefly focus on the latter, through a discussion of the notion of a severe test (cf. Mayo and Spanos 2006). The claim is that we gain knowledge of experimental effects on the basis of severely testing hypotheses, which can be characterized by the significance and power. In Mayo's definition, a hypothesis passes a severe test on two conditions: the data must agree with the hypothesis, and the probability must be very low that the data agree with the alternative hypothesis.  Ignoring potential controversy over the precise interpretation of “agree” and “low probability”, we can recognize the criteria of Neyman and Pearson in these requirements. The test is severe if the significance is low, since the data must agree with the hypothesis, and the power is high, since those data must not agree, or else have a low probability of agreeing, with the alternative. 