Use and misuse of statistics seems to be the signum temporis of past decades. But nowadays this practice seems slowly to be wearing away, and common sense and responsibility recapturing their position. It is our contention that little by little statistics should return to its starting point, i.e., to formalizing and analyzing empirical phenomena. This requires the reevalu­ ation of many traditions and the rejection of many myths. We hope that our book would go some way towards this aim. We show the sharp conflict between what is needed and what is feasible. Moreover, we show how slender are the links between theory and practice in statistical inference, links which are sometimes no more than mutual inspiration. In Part One we present the consecutive stages of formalization of statistical problems, i.e., the description of the experiment, the presentation of the aim of the investigation, and of the constraints put upon the decision rules. We stress the fact that at each of these stages there is room for arbitrariness. We prove that the links between the real problem and its formal counterpart are often so weak that the solution of the formal problem may have no rational interpretation at the practical level. We give a considerable amount of thought to the reduction of statistical problems.

One. Formalization of statistical problems.- 1 Statistical description of empirical phenomena.- 2. A scheme of statistical problems.- Two. Selected theoretical topics.- 3. Discriminant analysis.- 4. Screening problems.- 5. Evaluation of stochastic dependence.- Three. Selected practical problems.- 6. Statistical problems of population genetics.- 7. Paternity proving.- 8. Studies on sister cells.- 9. Survival analysis for censored data.- 10. Latent variables in experimental psychology.- 11. Queueing models of computer systems.- Closing remarks.- Appendix. Algorithms for evaluating monotone dependence function and screening threshold.- A.1. Introduction.- A.2. Algorithm for evaluating monotone dependence function for a bivariate discrete distribution /J. ?wik, A. Kowalski.- A.3. Algorithm for evaluating monotone dependence function for an empiricaldistribution based on a raw sample /J. ?wik, A. Kowalski.- A.4. Algorithm for evaluating screening threshold /J. ?wik.- References.