Process, Population, and Sample: The Researcher’s Interest

A case is made that researchers are interested in studying processes. Often the inferences they are interested in making is about the process and its associated population. On other occasions, a researcher may be interested in making an inference about the collection of individuals the process has generated. We will call the statistical methods employed by the researcher to make such inferences about the process/population “estimation methods.” The statistical methods used in making an inference about the collection of individuals generated we call “prediction methods.” Since researchers are studying repetative processes, then according to Savage (The Foundations of Statistics. Wiley (1954)) the classical method of assigning probability should be used. Methods for obtaining interval estimates of a parameter and prediction intervals for a statistic are given. The analytical and enumerative methods discussed in Deming (Journal of the American Statistical Association 48, 244–255, 1953) are simply estimation and prediction methods, respectively.