Some Statistical Concepts

Abstract

This book is concerned with making inferences about parameters of probability distribution functions. An inference is a generalization made from some specific observations. The specific observations are the data; the generalization is about the values of the parameters. The data are presumed to be a (relatively) small subset of values obtained, measured, or observed in some way from a larger population (sample space). Generally, the parameters are unknown. What we have instead are sample statistics, which are functions of the data. These statistics are themselves random variables, in that every new subset of values from the population yields potentially at least a new value for the statistic. As a result, the sample statistic also has a sample space associated with it, and a probability distribution function as well. The probability distribution function for a sample statistic is often referred to as a sampling distribution function (Meyer 1970). The form of the sampling distribution usually depends on the formula for the statistic, and the distribution function of the random variable for which the data constitute a subset of values or observations.