Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis μ1=μ2 could be less supported by the data than a more restrictive hypothesis such as μ1=μ2=0, where μ1 and μ2 are two population means. This article intends to discuss and explicit some important assumptions inherent to classical statistical models and null statistical hypotheses. Furthermore, the definition of the p-value and its limitations are analyzed. An alternative measure of evidence, the s-value, is discussed. This article presents the steps to compute s-values and, in order to illustrate the methods, some standard examples are analyzed and compared with p-values. The examples denunciate that p-values, as opposed to s-values, fail to hold some logical relations.