Introduction to Statistical Methods

Every real phenomenon has uncertain elements in it. We do not know how many patients will be admitted to a hospital on a given day, nor do we know how long a cancer patient will survive. The response of a new drug is not known and the success of a new business enterprise cannot be determined in advance. We do not know if the price of a stock will go up tomorrow or if the yield of a given variety of wheat will increase under a new fertilizer. The percentage of defectives produced by a machine and the number of auto accidents in a city cannot be determined with surety. Whether the U.S. unemployment rate will go down or whether the mortgage interests rates will go up depends on many uncertain factors.

Modern statistics provides various methods to answer these problems. Although statistics is usually regarded as being concerned with the collection, analysis, and interpretation of data, it can be described more broadly as the science of making decisions under uncertainty. The mathematical model of uncertainty is the theory of probability, and probability is an essential component in the study of statistics.

Descriptive statistics provides condensation of numerical information in the form of graphical displays, tables, and charts and is an essential aspect of data analysis. Modern computers have made these analyses easily accessible, and the use of statistics has grown as a result of this convenience.

The theory of probability provides a model of uncertainty. By a model we mean a mathematical description of a phenomenon. Just as the model of a building provides essentials of its dimensions and form but not all the details, a mathematical model describes the essentials of a phenomenon. Mathematical models involving concepts of probability are called stochastic; otherwise, we call them deterministic.

Statistical methods are being used in manufacturing and production to improve quality; in sales and marketing to develop strategies of product distribution, and in field experimentation and clinical trials to determine the efficacy of new varieties of treatments and drugs. They are used in surveys of populations, agricultural censuses, and in estimating unemployment rates and the gross national product in order to formulate national economic policies. There are hardly any areas of modern life where statistics is not applied. A collection of important examples of the application of statistics is in Statistics: A Guide to the Unknown edited by Tanur et al. (1972). Mathematical models in genetics are given by Elandt – Johnson (1971), in social sciences by Kemeny and Snell (1962), and in medicine by Rustagi (1971).