It is widely held that the classical decision version of the Neynman- Pearson test theory is inappropriate in the scientific context. The Fisherian p-value mode of statistical testing is preferable and it is more widely used. The weight of a test result in the form of a p-value should be judged on the background of the test power. The concept of power is however usually neglected for p-values. The distribution of the p-value under the alternative hypothesis is a natural concept of power, for which the Neyman-Pearson lemma works.
The need for efficient accumulation of test evidence is pointed out. It is argued that a score statistic summarizing the relevant power properties of the test should be published along with the p-value, to make locally optimal combination of test evidence from independent sources possible. The score function gives the terms of trade with other hypothetical or realized test results for the same hypothesis, and makes the power considerations explicit when judging the weight of the test result.