Statistical Theory: Some Recent Developments

Abstract

THE FIRST part of this chapter is devoted to a review of some recent developments in statistical theory. The review covers only the periodical literature which appeared from January 1943 to the present time. It has been divided into four somewhat overlapping subsections which, in order of presentation, treat questions of prediction, estimation and description, statistical inference in the nonparametric case, and other miscellaneous problems of statistical inference. An effort was made in the case of the first three subsections to provide sufficient detail to give the reader a general notion of certain recent developments without his having to refer to original sources. The relatively large number of articles covered in the last subsection made such a treatment impossible. The last subsection, therefore, reduces to little more than annotated bibliography. Considerable difficulty was experienced in the selection of material which it was thought might be useful to educational research workers. Some of the theory reviewed has not yet been applied to problems of educational research and perhaps never can be. On the other hand, some of the theory not reviewed may in time prove to be of the greatest importance. Finally, it should be noted that many phases of statistical theory are rapidly becoming highly abstract. Toward such phases of the theory the attitude of the practical statistician should be one of tolerance, for it is never known when the theory may provide new tools which are not only more widely applicable but also simpler to use.