Statistical Inference

Abstract

Statistical methods nowadays are basically decision oriented. In parameter estimation a specific value or possibly a range of values are to be selected as probable or plausible values of an unknown parameter. In hypothesis testing, a decision whether to accept or reject a null hypothesis has to be made. Thus, statistical theory is basically about choices and their qualities and risks. In contrast to this point of view, an approach to reasoning about hypotheses rather than to deciding on hypotheses will be put forward here. It is argued that the true job of a statistician is not to make decisions. It is rather to provide sound methods for decision support, to look for arguments in favour and against a hypothesis and to judge its credibility and plausibility. The statistician must also face the fact that statistical data are rarely the only information available about a given question. Hence, decisions based on statistical data only may be biased. Therefore, methods for judging hypotheses based on statistical data are more appropriate than methods for deciding them because these judgments may be complemented with further information which is not of purely statistical nature.