Statistical Inference

At the heart of statistics lie the ideas of statistical inference. Methods of statistical inference enable the investigator to argue from the particular observations in a sample to the general case. In contrast to logical deductions made from the general case to the specific case, a statistical inference can sometimes be incorrect. Nevertheless, one of the great intellectual advances of the twentieth century is the realization that strong scientific evidence can be developed on the basis of many, highly variable, observations. The subject of statistical inference extends well beyond statistics’ historical purposes of describing and displaying data. It deals with collecting informative data, interpreting these data, and drawing conclusions. Statistical inference includes all processes of acquiring knowledge that involve fact finding through the collection and examination of data. These processes are as diverse as opinion polls, agricultural field trials, clinical trials of new medicines, and the studying of properties of exotic new materials. As a consequence, statistical inference has permeated all fields of human endeavor in which the evaluation of information must be grounded in data-based evidence. A few characteristics are common to all studies involving fact finding through the collection and interpretation of data. First, in order to acquire new knowledge, relevant data must be collected. Second, some variability is unavoidable even when observations are made under the same or very similar conditions. The third, which sets the stage for statistical inference, is that access to a complete set of data is either not feasible from a practical standpoint or is physically impossible to obtain. To more fully describe statistical inference, it is necessary to introduce several key terminologies and concepts. The first step in making a statistical inference is to model the population(s) by a probability distribution which has a numerical feature of interest called a parameter. The problem of statistical inference arises once we want to make generalizations about the population when only a sample is available. A statistic, based on a sample, must serve as the source of information about a parameter. Three salient points guide the development of procedures for statistical inference