This chapter discusses nonparametric multivariate techniques. Time series analysis, which appears to follow the pattern of other least squares procedures, in fact presents special problems. Demographers attempting to project population shifts have long exploited time-series methods originally developed by economists for the analysis of long-term trend and periodic (cyclic and seasonal) fluctuations in economic indicators. Increasingly, social scientists interested in such questions as changes in voting patterns or religious affiliation, or other attitudinal shifts over time are making use of these techniques. To use this linear model and to apply the least-squares machinery, it is necessary to make three assumptions concerning the error terms: (1) the error term has mean zero, (2) the error term has constant variance independent of overall observations, and (3) the error terms corresponding to different points in time are not correlated. If a study requires precise decomposition of time series and examination of periodicities, one may wish to take advantage of spectral analysis. Its strength lies in its potential for providing better forecasts and its avoidance of the inaccuracies that arise from autocorrelation. However, the methods are untested in that relatively few studies exist to examine interpretations.

The selection and formulation of the problem are the most important steps in any research project. The chapter discusses a variety of issues related to problem-selection. Problem-formulation is a truly creative aspect of research; meticulous care is directed toward the effort. A particular theory makes sense because its logical consequences include predictions or sufficient explanations for the phenomena under consideration. Professional society meetings, at which explorers on the frontier give accounts of their latest expeditions, often yield a rich supply of research ideas, and provide the advantage of learning who is working in different areas. Rapid social or economic changes in a population or in regulatory mandates are expected to have manifold effects on community institutions. The chapter also provides an overview on the role of curiosity. It is a fundamental motivating force in the process of scientific inquiry, in that the entire process hinges on the desire to know more about something. Its presence is essential so that one can sustain the effort needed to pursue an investigation over a substantial period of time. Curiosity fuels one desire to reconcile discrepancies and repair omissions.

This chapter presents two principal goals: (1) it offers a general orientation to the philosophical and technical problems involved in measurement and a description of the sorts of instruments most commonly used in social or behavioral science research and (2) the data-collection procedures most frequently employed in such research. Investigators in every discipline tend to develop preferred techniques of data collection, which over a period of time come to characterize their respective fields. Like other decisions, the choices of instrumentation and, in turn, data collection type, must take into account feasibility and other factors. The acquired know-how mentors and colleagues is an invaluable resource in choosing and using appropriate procedures; excellent reference manuals are also available to provide guidance on technique and alternative approaches, particularly for survey studies. Measurement involves both philosophical and practical issues. Choice of variables and the nature of conjectures, the setting in which one plans to carry out a study, and constraints such as time, money, and available personnel will in part determine both instrumentation and procedures for data collection.

The computer is an important member of almost every research team; its role in processing and analyzing data may be crucial in the completion of a study. In recent years, fast and accurate computing and information retrieval have made data analysis vastly easier and has led to the extension and development of new applications. It is important to recognize that the availability of data processing at low cost can easily lure you into requesting information that may be trivial or useless. For pilot results, day-to-day monitoring of data, and calculations involving data from small studies, you may find a programmable hand or desk calculator very convenient, perhaps indispensable. The instruction manuals are extremely well prepared and easy-to-read and address the concerns of users, so the equipment can be mastered in a matter of hours. The capability to carry out computer-controlled experiments makes possible a creative and fruitful approach to the solution of a problem. The design of the study is the starting point for planning data analysis.

Multivariate analysis means any statistical analysis involving more than two variables or more than two groupings even if only one dependent variable is being considered at a time. The chapter examines several multivariate techniques, including multiple regression analysis, the analysis of variance, covariance analysis, factor analysis, discriminant function analysis, canonical correlation, chisquare, Cochran's Q, Friedman's two-way analysis, and the Kruskal–Wallis test. Most of the techniques involve great computational complexity and rigorous mathematical justification and require both training and know-how for successful application and interpretation. The greatest emphasis in standard texts is given to the techniques for presenting charts, graphs, and tables for univariate and bivariate data. A sheet of paper presents a two-dimensional surface and therefore, considerable ingenuity is required to deal with three or more variables. The possibilities for graphing and charting are very severely limited. At the heart of the use of multivariate analysis is the notion of multiple causality. Both the theoretical foundation and the practical application or interpretation of every technique reflects an attempt to formulate this notion in a systematic and mathematically manageable way.

The principal purposes of data analysis are to reveal patterns, differences, and relationships, which might not be evident from direct inspection of the data, and to permit making the decision regarding whether observational evidence supports hypotheses. The most important task in data analysis is to decide the technique that will do the best job, but before this decision can be made, it is important to know two things: (1) the nature of the problem and (2) the nature of conjectures. The choice of an appropriate statistical technique is then largely determined by the specific questions one is trying to answer and by the sort of data one has. Many beginning researchers are apprehensive about planning the statistical portion of their projects, but familiarity with the range of available techniques dispels some of these terrors. Statistical techniques permit the summarization of many kinds of numerical data and the description of certain kinds of relationships or comparisons among two or more sets of data in a neat and mathematically manageable fashion. Techniques serve their useful purpose if and only if in the company of appropriately formulated hypotheses, they assist in reaching a decision about the compatibility of observations and the propositions sought to establish.

This chapter presents definitions and major research hypothesis. The tasks of science include the building of theory and the systematic gathering and evaluating of evidence to support or refute such theory. If the study is exploratory, its goal includes the formulation of hypotheses. The discussion of definitions, operationalizing, and the different roles of variables is pertinent. A substantive or research hypothesis is a statement of what is expected to observe, the conditions of such observations, and the way other events affect the outcome. The statement is first posed as a conjecture in the language of the theory, that is, the construct language. It must then be operationalized, that is, translated into the data language. The data language uses the vocabulary of measurements, records of observations and manipulations, and outcomes of other procedures including computations. The record of the observations constitutes the evidence to justify or refute expectation. This part of the research process is called hypothesis testing. Thus, the next step is the formulation of your major research hypotheses. It is often assumed that it is possible and appropriate to restate the substantive hypotheses in statistically testable form and to invoke the conventional machinery of significance testing.

This chapter describes an assortment of deterministic techniques for problem analysis, which have been rapidly increasing in number and range of application. Much research in the social and behavioral sciences is directed toward the formulation of theory and its translation into a mathematical model. Such a model involves a formula; it may make use of a mathematical structure such as a finite group or a connected graph. Predictive deterministic models are always warmly received, and if such a model is available for the research problem, it should be taken advantage of. The chapter also provides an overview of the mathematical and related procedures used for analysis of deterministic models. It presents an assortment of five types of techniques designed to optimize decisions: (1) linear programming, (2) integer programming, (3) parametric programming, (4) dynamic programming, and (5) nonlinear programming. Despite their labels, they have nothing in common with computer programming. They all deal with the problem of allocating limited resources among competing activities in the best possible way. For each, there exists an algorithm that leads to the solution, providing the assumptions are satisfied and a solution exists at all.

This chapter provides an overview on sampling. The first step in a discussion of sampling is the identification of the target population or universe from which a sample is to be drawn. A population is the totality of all the cases, called population elements, or units, that meet some designated set of specifications. When one population is included in another, the former is called a subpopulation or a stratum. It is essential that the population units be clearly definable. Identifying the population properly is a difficult problem in itself. In any study, the choice of sample determines the generalizability of the results. To be useful, a sample must satisfy three criteria: (1) the sample must represent the population, (2) the sampling procedure must be efficient and economical, and (3) the estimates of population characteristics obtained from the sample must be precise and testable for reliability. The basic distinction in sampling is between probability and nonprobability samples. A probability sample is one in which the probability that any element of the population is included can be specified; in the simplest case, each element is equiprobable, but this is not necessary. It is only necessary that the probability of inclusion be knowable. In contrast, the probability of any element's inclusion in a nonprobability sample is unknown. The chapter also discusses the advantages and disadvantages of sampling.

This chapter highlights the review process of the literature in research. A review of the literature is an ongoing enterprise. It takes place in several phases as one develops a clearer, better-focused understanding of the problem. Each modification of the problem suggests further reading of relevant sources. The review process enables one to hook the study onto the chain of scientific knowledge; in isolation, one's work might not be of interest to other researchers, or its importance might be overlooked. Presenting the problem background, thus, serves two main purposes: (1) proper placement of study in the context of current theory—the consumer of research should be able to identify its theoretical base and the implications of this theory which one has pursued in formulating testable propositions and (2) appropriate connection of one's study to prior studies—the consumer of the research will see clearly in what ways it extends, contradicts, or complements already-existing knowledge, fills in gaps identified by other researchers, and opens new lines of investigation. The place of one's study in its overall disciplinary setting will be clear, as will its connection to work in related fields.