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The construction of a statistical test is investigated which is based only on “reliability” and “precision” as quality criteria. The reliability of a statistical test is quantifiedin a straightforward way by the probability that the decision of the test is correct. However, the quantification of the precision of a statistical test is not at all evident. Thereforethe paper presents and discusses several approaches. Moreover the distinction of “nullhypothesis” and “alternative hypothesis” is not necessary any longer.