The Problem of Mathematical Statistics
A statistical inquiry is usually made up of three parts, first the collection of the data, second, the analysis of the data and third, its interpretation for the particular purpose in view. The first and third stages depend almost entirely upon the field of investigation. Biological data should be collected and interpreted by a biologist. The collection of economic data should be planned by economists and interpreted by one well acquainted with the field of inquiry. The second stage on the other hand, is in general common to all fields. Whatever may be the subject matter the mathematical analysis has in a great degree the same essential features. Lack of appreciation of this three-fold problem of statistics has led to some extremely doubtful results in statistical analysis. No amount of mathematical training and ability can take the place of the judgment and common sense that comes from a thorough knowledge of the field in which the problem lies. On the other hand much time and energy may be wasted in the analysis of data by lack of understanding of the fundamentals of the mathematical processes used in the investigation. This is usually exhibited in the blind use of formulas without realization of the assumptions and limitations used in their derivation.