Social Statistics

This text is written primarily for those students of sociology, both advanced undergraduates and graduate students, who actually intend to engage in social research. Since the vast majority of students in the social sciences lack a background in college mathematics, this text has been written so as to avoid mathematical derivations in so far as possible. A quick review of certain algebraic principles listed in Appendix 1 should therefore be sufficient preparation for the average student. But although it is not necessary in a first course in statistics to stress mathematical derivations, the author is convinced that certain basic and fundamental ideas underlying the principles of statistical inference must be thoroughly understood if one is to obtain more than a mere “‘cookbook”’ knowledge of statistics. For this reason, you will find a relatively heavy emphasis on the underlying logic of statistical inference, including a chapter on probability, with relatively less attention being given to some of the more or less routine topics ordinarily discussed in elementary texts. One of the most difficult problems encountered in the teaching of applied statistics is that of motivating students, both in enabling them to overcome their fears of mathematics and in learning to apply statistics to their own field of interest. It is for the latter reason that the author has not attempted to cover a wide range of applications but has selected examples of primary interest to sociologists. ‘To some extent, examples have also been chosen from disciplines which border on sociology: fields such as social psychology, social work, and political behavior. In most instances each new topic has been illustrated by a single example, under the assumption that most students will lose track of the basic line of thought if too many examples are used to illustrate the same point. Additional examples are therefore given in the form of exercises at the end of each chapter. In general, the author has tried to strike a reasonable compromise between the desirability of stating basic principles as clearly and concisely as possible and the necessity of repeating some of the more difficult ideas each time a new topic is discussed. In so far as possible, new ideas have been introduced gradually and, equally important, an effort has been made to relate each new topic to those which have preceded it. In so doing, the major goal has been to give an appreciation of the basic similarities underlying many of the most commonly used tests and measures. Since this text is not primarily intended for the average undergraduate who does not actually expect to use statistics in his own research, the author has not covered descriptive statistics in exhaustive detail but has placed a much greater emphasis on inductive statistics. It is also assumed that most students using this text will already have been exposed to at least one course in research methods. Therefore, no attempt has been made to discuss such topics as the construction of interview schedules, reliability and validity, experimental design, coding and tabulating, or various types of scaling techniques or index construction. Most of these topics are far too complex to be discussed at all adequately in a general text on statistics. Nor is the present text intended as a general reference work treating all of the statistical techniques currently in use in the social sciences. Instead, an effort has been made to cover certain of the most important and basic statistical techniques with sufficient thoroughness that, once these have been understood, the student will be able to consult more specialized sources with some degree of confidence and understanding. The book is divided into three parts. Part I is intended as an introduction which will enable the student to place statistics in a larger perspective and which may serve to point out a few of the major problems encountered in relating theory, measurement, and statistics. Some of the descriptive measures and computing routines which will be needed in later work are taken up in Part II. The normal curve is also discussed in this section. Part III deals with some of the basic concepts of inductive statistics: the nature of statistical inference, probability, significance tests, confidence intervals, types I and II errors, and power functions. The problem of controlling for relevant variables is discussed first in Chap. 15 and again in Chaps. 16, 19, and 20. The importance of measures of association, as contrasted with significance tests, is stressed in Chap. 15 as well as later chapters, and attention is given to the basic problem of making causal inferences from correlational data (Chap. 19). A number of nonparametric procedures are treated in Chap. 14 and subsequent chapters, and in Chaps. 19 to 21 are discussed various multivariate techniques. A major emphasis running throughout the text is upon the limitations and possible misuses of statistics as well as its various applications.