A pure significance test would check the agreement of a statistical model with the observed data even when no alternative model was available. The paper proposes the use of a modified p -value to make such a test. The model will be rejected if something surprising is observed (relative to what else might have been observed). It is shown that the relation between this measure of surprise (the s -value) and the surprise indices of Weaver and Good is similar (...) to the relationship between a p -value, a corresponding odds-ratio, and a logit or log-odds statistic. The s -value is always larger than the corresponding p -value, and is not uniformly distributed. Difficulties with the whole approach are discussed. (shrink)
