The rationale of customary "null hypothesis testing" procedures of statistical inference is examined. This approach is not incorrect, but it is prone to misuse and misinterpretation, including neglect of "power" and inappropriate conclusions based on conventional significance levels. The estimation approach, which often seems preferable, is briefly described. The kind of reasoning involved in statistical inference is required whenever we wish to assess the evidence relevant for or against any general proposition, whether we make any formal computations or not, and whether or not we have observed all possible real instances of relevant evidence. Statistical inference is logically unproblematic if we interpret it as a way of assessing the evidence more clearly. But statistical results cannot be directly converted into probabilities of the truth of hypotheses. This requires additional assumptions about appropriate probabilities of the hypotheses prior to consideration of the research evidence.