What is the discipline of collecting describing interpreting and presenting data?

This chapter concerns research on collecting, representing, and analyzing the data that underlie behavioral and social sciences knowledge. Such research, methodological in character, includes ethnographic and historical approaches, scaling, axiomatic measurement, and statistics, with its important relatives, econometrics and psychometrics. The field can be described as including the self-conscious study of how scientists draw inferences and reach conclusions from observations. Since statistics is the largest and most prominent of methodological approaches and is used by researchers in virtually every discipline, statistical work draws the lion’s share of this chapter’s attention.

Problems of interpreting data arise whenever inherent variation or measurement fluctuations create challenges to understand data or to judge whether observed relationships are significant, durable, or general. Some examples: Is a sharp monthly (or yearly) increase in the rate of juvenile delinquency (or unemployment) in a particular area a matter for alarm, an ordinary periodic or random fluctuation, or the result of a change or quirk in reporting method? Do the temporal patterns seen in such repeated observations reflect a direct causal mechanism, a complex of indirect ones, or just imperfections in the data? Is a decrease in auto injuries an effect of a new seat-belt law? Are the disagreements among people describing some aspect of a subculture too great to draw valid inferences about that aspect of the culture?

Such issues of inference are often closely connected to substantive theory and specific data, and to some extent it is difficult and perhaps misleading to treat methods of data collection, representation, and analysis separately. This report does so, as do all sciences to some extent, because the methods developed often are far more general than the specific problems that originally gave rise to them. There is much transfer of new ideas from one substantive field to another—and to and from fields outside the behavioral and social sciences. Some of the classical methods of statistics arose in studies of astronomical observations, biological variability, and human diversity. The major growth of the classical methods occurred in the twentieth century, greatly stimulated by problems in agriculture and genetics. Some methods for uncovering geometric structures in data, such as multidimensional scaling and factor analysis, originated in research on psychological problems, but have been applied in many other sciences. Some time-series methods were developed originally to deal with economic data, but they are equally applicable to many other kinds of data.

Within the behavioral and social sciences, statistical methods have been developed in and have contributed to an enormous variety of research, including:

  • In economics: large-scale models of the U.S. economy; effects of taxation, money supply, and other government fiscal and monetary policies; theories of duopoly, oligopoly, and rational expectations; economic effects of slavery.

  • In psychology: test calibration; the formation of subjective probabilities, their revision in the light of new information, and their use in decision making; psychiatric epidemiology and mental health program evaluation.

  • In sociology and other fields: victimization and crime rates; effects of incarceration and sentencing policies; deployment of police and fire-fighting forces; discrimination, antitrust, and regulatory court cases; social networks; population growth and forecasting; and voting behavior.

Even such an abridged listing makes clear that improvements in methodology are valuable across the spectrum of empirical research in the behavioral and social sciences as well as in application to policy questions. Clearly, methodological research serves many different purposes, and there is a need to develop different approaches to serve those different purposes, including exploratory data analysis, scientific inference about hypotheses and population parameters, individual decision making, forecasting what will happen in the event or absence of intervention, and assessing causality from both randomized experiments and observational data.

This discussion of methodological research is divided into three areas: design, representation, and analysis. The efficient design of investigations must take place before data are collected because it involves how much, what kind of, and how data are to be collected. What type of study is feasible: experimental, sample survey, field observation, or other? What variables should be measured, controlled, and randomized? How extensive a subject pool or observational period is appropriate? How can study resources be allocated most effectively among various sites, instruments, and subsamples?

The construction of useful representations of the data involves deciding what kind of formal structure best expresses the underlying qualitative and quantitative concepts that are being used in a given study. For example, cost of living is a simple concept to quantify if it applies to a single individual with unchanging tastes in stable markets (that is, markets offering the same array of goods from year to year at varying prices), but as a national aggregate for millions of households and constantly changing consumer product markets, the cost of living is not easy to specify clearly or measure reliably. Statisticians, economists, sociologists, and other experts have long struggled to make the cost of living a precise yet practicable concept that is also efficient to measure, and they must continually modify it to reflect changing circumstances.

Data analysis covers the final step of characterizing and interpreting research findings: Can estimates of the relations between variables be made? Can some conclusion be drawn about correlation, cause and effect, or trends over time? How uncertain are the estimates and conclusions and can that uncertainty be reduced by analyzing the data in a different way? Can computers be used to display complex results graphically for quicker or better understanding or to suggest different ways of proceeding?

Advances in analysis, data representation, and research design feed into and reinforce one another in the course of actual scientific work. The intersections between methodological improvements and empirical advances are an important aspect of the multidisciplinary thrust of progress in the behavioral and social sciences.

Designs for Data Collection

Four broad kinds of research designs are used in the behavioral and social sciences: experimental, survey, comparative, and ethnographic.

Experimental designs, in either the laboratory or field settings, systematically manipulate a few variables while others that may affect the outcome are held constant, randomized, or otherwise controlled. The purpose of randomized experiments is to ensure that only one or a few variables can systematically affect the results, so that causes can be attributed. Survey designs include the collection and analysis of data from censuses, sample surveys, and longitudinal studies and the examination of various relationships among the observed phenomena. Randomization plays a different role here than in experimental designs: it is used to select members of a sample so that the sample is as representative of the whole population as possible. Comparative designs involve the retrieval of evidence that is recorded in the flow of current or past events in different times or places and the interpretation and analysis of this evidence. Ethnographic designs, also known as participant-observation designs, involve a researcher in intensive and direct contact with a group, community, or population being studied, through participation, observation, and extended interviewing.

Experimental Designs

Laboratory Experiments

Laboratory experiments underlie most of the work reported in Chapter 1, significant parts of Chapter 2, and some of the newest lines of research in Chapter 3. Laboratory experiments extend and adapt classical methods of design first developed, for the most part, in the physical and life sciences and agricultural research. Their main feature is the systematic and independent manipulation of a few variables and the strict control or randomization of all other variables that might affect the phenomenon under study. For example, some studies of animal motivation involve the systematic manipulation of amounts of food and feeding schedules while other factors that may also affect motivation, such as body weight, deprivation, and so on, are held constant. New designs are currently coming into play largely because of new analytic and computational methods (discussed below, in “Advances in Statistical Inference and Analysis”).

Two examples of empirically important issues that demonstrate the need for broadening classical experimental approaches are open-ended responses and lack of independence of successive experimental trials. The first concerns the design of research protocols that do not require the strict segregation of the events of an experiment into well-defined trials, but permit a subject to respond at will. These methods are needed when what is of interest is how the respondent chooses to allocate behavior in real time and across continuously available alternatives. Such empirical methods have long been used, but they can generate very subtle and difficult problems in experimental design and subsequent analysis. As theories of allocative behavior of all sorts become more sophisticated and precise, the experimental requirements become more demanding, so the need to better understand and solve this range of design issues is an outstanding challenge to methodological ingenuity.

The second issue arises in repeated-trial designs when the behavior on successive trials, even if it does not exhibit a secular trend (such as a learning curve), is markedly influenced by what has happened in the preceding trial or trials. The more naturalistic the experiment and the more sensitive the meas urements taken, the more likely it is that such effects will occur. But such sequential dependencies in observations cause a number of important conceptual and technical problems in summarizing the data and in testing analytical models, which are not yet completely understood. In the absence of clear solutions, such effects are sometimes ignored by investigators, simplifying the data analysis but leaving residues of skepticism about the reliability and significance of the experimental results. With continuing development of sensitive measures in repeated-trial designs, there is a growing need for more advanced concepts and methods for dealing with experimental results that may be influenced by sequential dependencies.

Randomized Field Experiments

The state of the art in randomized field experiments, in which different policies or procedures are tested in controlled trials under real conditions, has advanced dramatically over the past two decades. Problems that were once considered major methodological obstacles—such as implementing randomized field assignment to treatment and control groups and protecting the randomization procedure from corruption—have been largely overcome. While state-of-the-art standards are not achieved in every field experiment, the commitment to reaching them is rising steadily, not only among researchers but also among customer agencies and sponsors.

The health insurance experiment described in Chapter 2 is an example of a major randomized field experiment that has had and will continue to have important policy reverberations in the design of health care financing. Field experiments with the negative income tax (guaranteed minimum income) conducted in the 1970s were significant in policy debates, even before their completion, and provided the most solid evidence available on how tax-based income support programs and marginal tax rates can affect the work incentives and family structures of the poor. Important field experiments have also been carried out on alternative strategies for the prevention of delinquency and other criminal behavior, reform of court procedures, rehabilitative programs in mental health, family planning, and special educational programs, among other areas.

In planning field experiments, much hinges on the definition and design of the experimental cells, the particular combinations needed of treatment and control conditions for each set of demographic or other client sample characteristics, including specification of the minimum number of cases needed in each cell to test for the presence of effects. Considerations of statistical power, client availability, and the theoretical structure of the inquiry enter into such specifications. Current important methodological thresholds are to find better ways of predicting recruitment and attrition patterns in the sample, of designing experiments that will be statistically robust in the face of problematic sample recruitment or excessive attrition, and of ensuring appropriate acquisition and analysis of data on the attrition component of the sample.

Also of major significance are improvements in integrating detailed process and outcome measurements in field experiments. To conduct research on program effects under field conditions requires continual monitoring to determine exactly what is being done—the process—how it corresponds to what was projected at the outset. Relatively unintrusive, inexpensive, and effective implementation measures are of great interest. There is, in parallel, a growing emphasis on designing experiments to evaluate distinct program components in contrast to summary measures of net program effects.

Finally, there is an important opportunity now for further theoretical work to model organizational processes in social settings and to design and select outcome variables that, in the relatively short time of most field experiments, can predict longer-term effects: For example, in job-training programs, what are the effects on the community (role models, morale, referral networks) or on individual skills, motives, or knowledge levels that are likely to translate into sustained changes in career paths and income levels?

Survey Designs

Many people have opinions about how societal mores, economic conditions, and social programs shape lives and encourage or discourage various kinds of behavior. People generalize from their own cases, and from the groups to which they belong, about such matters as how much it costs to raise a child, the extent to which unemployment contributes to divorce, and so on. In fact, however, effects vary so much from one group to another that homespun generalizations are of little use. Fortunately, behavioral and social scientists have been able to bridge the gaps between personal perspectives and collective realities by means of survey research. In particular, governmental information systems include volumes of extremely valuable survey data, and the facility of modern computers to store, disseminate, and analyze such data has significantly improved empirical tests and led to new understandings of social processes.

Within this category of research designs, two major types are distinguished: repeated cross-sectional surveys and longitudinal panel surveys. In addition, and cross-cutting these types, there is a major effort under way to improve and refine the quality of survey data by investigating features of human memory and of question formation that affect survey response.

Repeated cross-sectional designs can either attempt to measure an entire population—as does the oldest U.S. example, the national decennial census—or they can rest on samples drawn from a population. The general principle is to take independent samples at two or more times, measuring the variables of interest, such as income levels, housing plans, or opinions about public affairs, in the same way. The General Social Survey, collected by the National Opinion Research Center with National Science Foundation support, is a repeated cross sectional data base that was begun in 1972. One methodological question of particular salience in such data is how to adjust for nonresponses and “don’t know” responses. Another is how to deal with self-selection bias. For example, to compare the earnings of women and men in the labor force, it would be mistaken to first assume that the two samples of labor-force participants are randomly selected from the larger populations of men and women; instead, one has to consider and incorporate in the analysis the factors that determine who is in the labor force.

In longitudinal panels, a sample is drawn at one point in time and the relevant variables are measured at this and subsequent times for the same people. In more complex versions, some fraction of each panel may be replaced or added to periodically, such as expanding the sample to include households formed by the children of the original sample. An example of panel data developed in this way is the Panel Study of Income Dynamics (PSID), conducted by the University of Michigan since 1968 (discussed in Chapter 3).

Comparing the fertility or income of different people in different circumstances at the same time to find correlations always leaves a large proportion of the variability unexplained, but common sense suggests that much of the unexplained variability is actually explicable. There are systematic reasons for individual outcomes in each person’s past achievements, in parental models, upbringing, and earlier sequences of experiences. Unfortunately, asking people about the past is not particularly helpful: people remake their views of the past to rationalize the present and so retrospective data are often of uncertain validity. In contrast, generation-long longitudinal data allow readings on the sequence of past circumstances uncolored by later outcomes. Such data are uniquely useful for studying the causes and consequences of naturally occurring decisions and transitions. Thus, as longitudinal studies continue, quantitative analysis is becoming feasible about such questions as: How are the decisions of individuals affected by parental experience? Which aspects of early decisions constrain later opportunities? And how does detailed background experience leave its imprint? Studies like the two-decade-long PSID are bringing within grasp a complete generational cycle of detailed data on fertility, work life, household structure, and income.

Advances in Longitudinal Designs

Large-scale longitudinal data collection projects are uniquely valuable as vehicles for testing and improving survey research methodology. In ways that lie beyond the scope of a cross-sectional survey, longitudinal studies can sometimes be designed—without significant detriment to their substantive interests—to facilitate the evaluation and upgrading of data quality; the analysis of relative costs and effectiveness of alternative techniques of inquiry; and the standardization or coordination of solutions to problems of method, concept, and measurement across different research domains.

Some areas of methodological improvement include discoveries about the impact of interview mode on response (mail, telephone, face-to-face); the effects of nonresponse on the representativeness of a sample (due to respondents’ refusal or interviewers’ failure to contact); the effects on behavior of continued participation over time in a sample survey; the value of alternative methods of adjusting for nonresponse and incomplete observations (such as imputation of missing data, variable case weighting); the impact on response of specifying different recall periods, varying the intervals between interviews, or changing the length of interviews; and the comparison and calibration of results obtained by longitudinal surveys, randomized field experiments, laboratory studies, onetime surveys, and administrative records.

It should be especially noted that incorporating improvements in methodology and data quality has been and will no doubt continue to be crucial to the growing success of longitudinal studies. Panel designs are intrinsically more vulnerable than other designs to statistical biases due to cumulative item non-response, sample attrition, time-in-sample effects, and error margins in repeated measures, all of which may produce exaggerated estimates of change. Over time, a panel that was initially representative may become much less representative of a population, not only because of attrition in the sample, but also because of changes in immigration patterns, age structure, and the like. Longitudinal studies are also subject to changes in scientific and societal contexts that may create uncontrolled drifts over time in the meaning of nominally stable questions or concepts as well as in the underlying behavior. Also, a natural tendency to expand over time the range of topics and thus the interview lengths, which increases the burdens on respondents, may lead to deterioration of data quality or relevance. Careful methodological research to understand and overcome these problems has been done, and continued work as a component of new longitudinal studies is certain to advance the overall state of the art.

Longitudinal studies are sometimes pressed for evidence they are not designed to produce: for example, in important public policy questions concerning the impact of government programs in such areas as health promotion, disease prevention, or criminal justice. By using research designs that combine field experiments (with randomized assignment to program and control conditions) and longitudinal surveys, one can capitalize on the strongest merits of each: the experimental component provides stronger evidence for casual statements that are critical for evaluating programs and for illuminating some fundamental theories; the longitudinal component helps in the estimation of long-term program effects and their attenuation. Coupling experiments to ongoing longitudinal studies is not often feasible, given the multiple constraints of not disrupting the survey, developing all the complicated arrangements that go into a large-scale field experiment, and having the populations of interest overlap in useful ways. Yet opportunities to join field experiments to surveys are of great importance. Coupled studies can produce vital knowledge about the empirical conditions under which the results of longitudinal surveys turn out to be similar to—or divergent from—those produced by randomized field experiments. A pattern of divergence and similarity has begun to emerge in coupled studies; additional cases are needed to understand why some naturally occurring social processes and longitudinal design features seem to approximate formal random allocation and others do not. The methodological implications of such new knowledge go well beyond program evaluation and survey research. These findings bear directly on the confidence scientists—and others—can have in conclusions from observational studies of complex behavioral and social processes, particularly ones that cannot be controlled or simulated within the confines of a laboratory environment.

Memory and the Framing of Questions

A very important opportunity to improve survey methods lies in the reduction of nonsampling error due to questionnaire context, phrasing of questions, and, generally, the semantic and social-psychological aspects of surveys. Survey data are particularly affected by the fallibility of human memory and the sensitivity of respondents to the framework in which a question is asked. This sensitivity is especially strong for certain types of attitudinal and opinion questions. Efforts are now being made to bring survey specialists into closer contact with researchers working on memory function, knowledge representation, and language in order to uncover and reduce this kind of error.

Memory for events is often inaccurate, biased toward what respondents believe to be true—or should be true—about the world. In many cases in which data are based on recollection, improvements can be achieved by shifting to techniques of structured interviewing and calibrated forms of memory elicitation, such as specifying recent, brief time periods (for example, in the last seven days) within which respondents recall certain types of events with acceptable accuracy.

Experiments on individual decision making show that the way a question is framed predictably alters the responses. Analysts of survey data find that some small changes in the wording of certain kinds of questions can produce large differences in the answers, although other wording changes have little effect. Even simply changing the order in which some questions are presented can produce large differences, although for other questions the order of presentation does not matter. For example, the following questions were among those asked in one wave of the General Social Survey:

  • “Taking things altogether, how would you describe your marriage? Would you say that your marriage is very happy, pretty happy, or not too happy?”

  • “Taken altogether how would you say things are these days—would you say you are very happy, pretty happy, or not too happy?”

Presenting this sequence in both directions on different forms showed that the order affected answers to the general happiness question but did not change the marital happiness question: responses to the specific issue swayed subsequent responses to the general one, but not vice versa. The explanations for and implications of such order effects on the many kinds of questions and sequences that can be used are not simple matters. Further experimentation on the design of survey instruments promises not only to improve the accuracy and reliability of survey research, but also to advance understanding of how people think about and evaluate their behavior from day to day.

Comparative Designs

Both experiments and surveys involve interventions or questions by the scientist, who then records and analyzes the responses. In contrast, many bodies of social and behavioral data of considerable value are originally derived from records or collections that have accumulated for various nonscientific reasons, quite often administrative in nature, in firms, churches, military organizations, and governments at all levels. Data of this kind can sometimes be subjected to careful scrutiny, summary, and inquiry by historians and social scientists, and statistical methods have increasingly been used to develop and evaluate inferences drawn from such data. Some of the main comparative approaches are cross-national aggregate comparisons, selective comparison of a limited number of cases, and historical case studies.

Among the more striking problems facing the scientist using such data are the vast differences in what has been recorded by different agencies whose behavior is being compared (this is especially true for parallel agencies in different nations), the highly unrepresentative or idiosyncratic sampling that can occur in the collection of such data, and the selective preservation and destruction of records. Means to overcome these problems form a substantial methodological research agenda in comparative research. An example of the method of cross-national aggregative comparisons is found in investigations by political scientists and sociologists of the factors that underlie differences in the vitality of institutions of political democracy in different societies. Some investigators have stressed the existence of a large middle class, others the level of education of a population, and still others the development of systems of mass communication. In cross-national aggregate comparisons, a large number of nations are arrayed according to some measures of political democracy and then attempts are made to ascertain the strength of correlations between these and the other variables. In this line of analysis it is possible to use a variety of statistical cluster and regression techniques to isolate and assess the possible impact of certain variables on the institutions under study. While this kind of research is cross-sectional in character, statements about historical processes are often invoked to explain the correlations.

More limited selective comparisons, applied by many of the classic theorists, involve asking similar kinds of questions but over a smaller range of societies. Why did democracy develop in such different ways in America, France, and England? Why did northeastern Europe develop rational bourgeois capitalism, in contrast to the Mediterranean and Asian nations? Modern scholars have turned their attention to explaining, for example, differences among types of fascism between the two World Wars, and similarities and differences among modern state welfare systems, using these comparisons to unravel the salient causes. The questions asked in these instances are inevitably historical ones.

Historical case studies involve only one nation or region, and so they may not be geographically comparative. However, insofar as they involve tracing the transformation of a society’s major institutions and the role of its main shaping events, they involve a comparison of different periods of a nation’s or a region’s history. The goal of such comparisons is to give a systematic account of the relevant differences. Sometimes, particularly with respect to the ancient societies, the historical record is very sparse, and the methods of history and archaeology mesh in the reconstruction of complex social arrangements and patterns of change on the basis of few fragments.

Like all research designs, comparative ones have distinctive vulnerabilities and advantages: One of the main advantages of using comparative designs is that they greatly expand the range of data, as well as the amount of variation in those data, for study. Consequently, they allow for more encompassing explanations and theories that can relate highly divergent outcomes to one another in the same framework. They also contribute to reducing any cultural biases or tendencies toward parochialism among scientists studying common human phenomena.

One main vulnerability in such designs arises from the problem of achieving comparability. Because comparative study involves studying societies and other units that are dissimilar from one another, the phenomena under study usually occur in very different contexts—so different that in some cases what is called an event in one society cannot really be regarded as the same type of event in another. For example, a vote in a Western democracy is different from a vote in an Eastern bloc country, and a voluntary vote in the United States means something different from a compulsory vote in Australia. These circumstances make for interpretive difficulties in comparing aggregate rates of voter turnout in different countries.

The problem of achieving comparability appears in historical analysis as well. For example, changes in laws and enforcement and recording procedures over time change the definition of what is and what is not a crime, and for that reason it is difficult to compare the crime rates over time. Comparative researchers struggle with this problem continually, working to fashion equivalent measures; some have suggested the use of different measures (voting, letters to the editor, street demonstration) in different societies for common variables (political participation), to try to take contextual factors into account and to achieve truer comparability.

A second vulnerability is controlling variation. Traditional experiments make conscious and elaborate efforts to control the variation of some factors and thereby assess the causal significance of others. In surveys as well as experiments, statistical methods are used to control sources of variation and assess suspected causal significance. In comparative and historical designs, this kind of control is often difficult to attain because the sources of variation are many and the number of cases few. Scientists have made efforts to approximate such control in these cases of “many variables, small N.” One is the method of paired comparisons. If an investigator isolates 15 American cities in which racial violence has been recurrent in the past 30 years, for example, it is helpful to match them with 15 cities of similar population size, geographical region, and size of minorities—such characteristics are controls—and then search for systematic differences between the two sets of cities. Another method is to select, for comparative purposes, a sample of societies that resemble one another in certain critical ways, such as size, common language, and common level of development, thus attempting to hold these factors roughly constant, and then seeking explanations among other factors in which the sampled societies differ from one another.

Ethnographic Designs

Traditionally identified with anthropology, ethnographic research designs are playing increasingly significant roles in most of the behavioral and social sciences. The core of this methodology is participant-observation, in which a researcher spends an extended period of time with the group under study, ideally mastering the local language, dialect, or special vocabulary, and participating in as many activities of the group as possible. This kind of participant-observation is normally coupled with extensive open-ended interviewing, in which people are asked to explain in depth the rules, norms, practices, and beliefs through which (from their point of view) they conduct their lives. A principal aim of ethnographic study is to discover the premises on which those rules, norms, practices, and beliefs are built.

The use of ethnographic designs by anthropologists has contributed significantly to the building of knowledge about social and cultural variation. And while these designs continue to center on certain long-standing features—extensive face-to-face experience in the community, linguistic competence, participation, and open-ended interviewing—there are newer trends in ethnographic work. One major trend concerns its scale. Ethnographic methods were originally developed largely for studying small-scale groupings known variously as village, folk, primitive, preliterate, or simple societies. Over the decades, these methods have increasingly been applied to the study of small groups and networks within modern (urban, industrial, complex) society, including the contemporary United States. The typical subjects of ethnographic study in modern society are small groups or relatively small social networks, such as outpatient clinics, medical schools, religious cults and churches, ethnically distinctive urban neighborhoods, corporate offices and factories, and government bureaus and legislatures.

As anthropologists moved into the study of modern societies, researchers in other disciplines—particularly sociology, psychology, and political science—began using ethnographic methods to enrich and focus their own insights and findings. At the same time, studies of large-scale structures and processes have been aided by the use of ethnographic methods, since most large-scale changes work their way into the fabric of community, neighborhood, and family, affecting the daily lives of people. Ethnographers have studied, for example, the impact of new industry and new forms of labor in “backward” regions; the impact of state-level birth control policies on ethnic groups; and the impact on residents in a region of building a dam or establishing a nuclear waste dump. Ethnographic methods have also been used to study a number of social processes that lend themselves to its particular techniques of observation and interview—processes such as the formation of class and racial identities, bureaucratic behavior, legislative coalitions and outcomes, and the formation and shifting of consumer tastes.

Advances in structured interviewing (see above) have proven especially powerful in the study of culture. Techniques for understanding kinship systems, concepts of disease, color terminologies, ethnobotany, and ethnozoology have been radically transformed and strengthened by coupling new interviewing methods with modem measurement and scaling techniques (see below). These techniques have made possible more precise comparisons among cultures and identification of the most competent and expert persons within a culture. The next step is to extend these methods to study the ways in which networks of propositions (such as boys like sports, girls like babies) are organized to form belief systems. Much evidence suggests that people typically represent the world around them by means of relatively complex cognitive models that involve interlocking propositions. The techniques of scaling have been used to develop models of how people categorize objects, and they have great potential for further development, to analyze data pertaining to cultural propositions.

Ideological Systems

Perhaps the most fruitful area for the application of ethnographic methods in recent years has been the systematic study of ideologies in modern society. Earlier studies of ideology were in small-scale societies that were rather homogeneous. In these studies researchers could report on a single culture, a uniform system of beliefs and values for the society as a whole. Modern societies are much more diverse both in origins and number of subcultures, related to different regions, communities, occupations, or ethnic groups. Yet these subcultures and ideologies share certain underlying assumptions or at least must find some accommodation with the dominant value and belief systems in the society.

The challenge is to incorporate this greater complexity of structure and process into systematic descriptions and interpretations. One line of work carried out by researchers has tried to track the ways in which ideologies are created, transmitted, and shared among large populations that have traditionally lacked the social mobility and communications technologies of the West. This work has concentrated on large-scale civilizations such as China, India, and Central America. Gradually, the focus has generalized into a concern with the relationship between the great traditions—the central lines of cosmopolitan Confucian, Hindu, or Mayan culture, including aesthetic standards, irrigation technologies, medical systems, cosmologies and calendars, legal codes, poetic genres, and religious doctrines and rites—and the little traditions, those identified with rural, peasant communities. How are the ideological doctrines and cultural values of the urban elites, the great traditions, transmitted to local communities? How are the little traditions, the ideas from the more isolated, less literate, and politically weaker groups in society, transmitted to the elites?

India and southern Asia have been fruitful areas for ethnographic research on these questions. The great Hindu tradition was present in virtually all local contexts through the presence of high-caste individuals in every community. It operated as a pervasive standard of value for all members of society, even in the face of strong little traditions. The situation is surprisingly akin to that of modern, industrialized societies. The central research questions are the degree and the nature of penetration of dominant ideology, even in groups that appear marginal and subordinate and have no strong interest in sharing the dominant value system. In this connection the lowest and poorest occupational caste—the untouchables—serves as an ultimate test of the power of ideology and cultural beliefs to unify complex hierarchical social systems.

Historical Reconstruction

Another current trend in ethnographic methods is its convergence with archival methods. One joining point is the application of descriptive and interpretative procedures used by ethnographers to reconstruct the cultures that created historical documents, diaries, and other records, to interview history, so to speak. For example, a revealing study showed how the Inquisition in the Italian countryside between the 1570s and 1640s gradually worked subtle changes in an ancient fertility cult in peasant communities; the peasant beliefs and rituals assimilated many elements of witchcraft after learning them from their persecutors. A good deal of social history—particularly that of the family—has drawn on discoveries made in the ethnographic study of primitive societies. As described in Chapter 4, this particular line of inquiry rests on a marriage of ethnographic, archival, and demographic approaches.

Other lines of ethnographic work have focused on the historical dimensions of nonliterate societies. A strikingly successful example in this kind of effort is a study of head-hunting. By combining an interpretation of local oral tradition with the fragmentary observations that were made by outside observers (such as missionaries, traders, colonial officials), historical fluctuations in the rate and significance of head-hunting were shown to be partly in response to such international forces as the great depression and World War II. Researchers are also investigating the ways in which various groups in contemporary societies invent versions of traditions that may or may not reflect the actual history of the group. This process has been observed among elites seeking political and cultural legitimation and among hard-pressed minorities (for example, the Basque in Spain, the Welsh in Great Britain) seeking roots and political mobilization in a larger society.

Ethnography is a powerful method to record, describe, and interpret the system of meanings held by groups and to discover how those meanings affect the lives of group members. It is a method well adapted to the study of situations in which people interact with one another and the researcher can interact with them as well, so that information about meanings can be evoked and observed. Ethnography is especially suited to exploration and elucidation of unsuspected connections; ideally, it is used in combination with other methods—experimental, survey, or comparative—to establish with precision the relative strengths and weaknesses of such connections. By the same token, experimental, survey, and comparative methods frequently yield connections, the meaning of which is unknown; ethnographic methods are a valuable way to determine them.

Models for Representing Phenomena

The objective of any science is to uncover the structure and dynamics of the phenomena that are its subject, as they are exhibited in the data. Scientists continuously try to describe possible structures and ask whether the data can, with allowance for errors of measurement, be described adequately in terms of them. Over a long time, various families of structures have recurred throughout many fields of science; these structures have become objects of study in their own right, principally by statisticians, other methodological specialists, applied mathematicians, and philosophers of logic and science. Methods have evolved to evaluate the adequacy of particular structures to account for particular types of data. In the interest of clarity we discuss these structures in this section and the analytical methods used for estimation and evaluation of them in the next section, although in practice they are closely intertwined.

A good deal of mathematical and statistical modeling attempts to describe the relations, both structural and dynamic, that hold among variables that are presumed to be representable by numbers. Such models are applicable in the behavioral and social sciences only to the extent that appropriate numerical measurement can be devised for the relevant variables. In many studies the phenomena in question and the raw data obtained are not intrinsically numerical, but qualitative, such as ethnic group identifications. The identifying numbers used to code such questionnaire categories for computers are no more than labels, which could just as well be letters or colors. One key question is whether there is some natural way to move from the qualitative aspects of such data to a structural representation that involves one of the well-understood numerical or geometric models or whether such an attempt would be inherently inappropriate for the data in question. The decision as to whether or not particular empirical data can be represented in particular numerical or more complex structures is seldom simple, and strong intuitive biases or a priori assumptions about what can and cannot be done may be misleading.

Recent decades have seen rapid and extensive development and application of analytical methods attuned to the nature and complexity of social science data. Examples of nonnumerical modeling are increasing. Moreover, the widespread availability of powerful computers is probably leading to a qualitative revolution, it is affecting not only the ability to compute numerical solutions to numerical models, but also to work out the consequences of all sorts of structures that do not involve numbers at all. The following discussion gives some indication of the richness of past progress and of future prospects although it is by necessity far from exhaustive.

In describing some of the areas of new and continuing research, we have organized this section on the basis of whether the representations are fundamentally probabilistic or not. A further useful distinction is between representations of data that are highly discrete or categorical in nature (such as whether a person is male or female) and those that are continuous in nature (such as a person’s height). Of course, there are intermediate cases involving both types of variables, such as color stimuli that are characterized by discrete hues (red, green) and a continuous luminance measure. Probabilistic models lead very naturally to questions of estimation and statistical evaluation of the correspondence between data and model. Those that are not probabilistic involve additional problems of dealing with and representing sources of variability that are not explicitly modeled. At the present time, scientists understand some aspects of structure, such as geometries, and some aspects of randomness, as embodied in probability models, but do not yet adequately understand how to put the two together in a single unified model. Table 5-1 outlines the way we have organized this discussion and shows where the examples in this section lie.

What is the discipline of collecting describing interpreting and presenting data?

Table 5-1

A Classification of Structural Models.

Probability Models

Some behavioral and social sciences variables appear to be more or less continuous, for example, utility of goods, loudness of sounds, or risk associated with uncertain alternatives. Many other variables, however, are inherently categorical, often with only two or a few values possible: for example, whether a person is in or out of school, employed or not employed, identifies with a major political party or political ideology. And some variables, such as moral attitudes, are typically measured in research with survey questions that allow only categorical responses. Much of the early probability theory was formulated only for continuous variables; its use with categorical variables was not really justified, and in some cases it may have been misleading. Recently, very significant advances have been made in how to deal explicitly with categorical variables. This section first describes several contemporary approaches to models involving categorical variables, followed by ones involving continuous representations.

Log-Linear Models for Categorical Variables

Many recent models for analyzing categorical data of the kind usually displayed as counts (cell frequencies) in multidimensional contingency tables are subsumed under the general heading of log-linear models, that is, linear models in the natural logarithms of the expected counts in each cell in the table. These recently developed forms of statistical analysis allow one to partition variability due to various sources in the distribution of categorical attributes, and to isolate the effects of particular variables or combinations of them.

Present log-linear models were first developed and used by statisticians and sociologists and then found extensive application in other social and behavioral sciences disciplines. When applied, for instance, to the analysis of social mobility, such models separate factors of occupational supply and demand from other factors that impede or propel movement up and down the social hierarchy. With such models, for example, researchers discovered the surprising fact that occupational mobility patterns are strikingly similar in many nations of the world (even among disparate nations like the United States and most of the Eastern European socialist countries), and from one time period to another, once allowance is made for differences in the distributions of occupations. The log-linear and related kinds of models have also made it possible to identify and analyze systematic differences in mobility among nations and across time. As another example of applications, psychologists and others have used log-linear models to analyze attitudes and their determinants and to link attitudes to behavior. These methods have also diffused to and been used extensively in the medical and biological sciences.

Regression Models for Categorical Variables

Models that permit one variable to be explained or predicted by means of others, called regression models, are the workhorses of much applied statistics; this is especially true when the dependent (explained) variable is continuous. For a two-valued dependent variable, such as alive or dead, models and approximate theory and computational methods for one explanatory variable were developed in biometry about 50 years ago. Computer programs able to handle many explanatory variables, continuous or categorical, are readily available today. Even now, however, the accuracy of the approximate theory on given data is an open question.

Using classical utility theory, economists have developed discrete choice models that turn out to be somewhat related to the log-linear and categorical regression models. Models for limited dependent variables, especially those that cannot take on values above or below a certain level (such as weeks unemployed, number of children, and years of schooling) have been used profitably in economics and in some other areas. For example, censored normal variables (called tobits in economics), in which observed values outside certain limits are simply counted, have been used in studying decisions to go on in school. It will require further research and development to incorporate information about limited ranges of variables fully into the main multivariate methodologies. In addition, with respect to the assumptions about distribution and functional form conventionally made in discrete response models, some new methods are now being developed that show promise of yielding reliable inferences without making unrealistic assumptions; further research in this area promises significant progress.

One problem arises from the fact that many of the categorical variables collected by the major data bases are ordered. For example, attitude surveys frequently use a 3-, 5-, or 7-point scale (from high to low) without specifying numerical intervals between levels. Social class and educational levels are often described by ordered categories. Ignoring order information, which many traditional statistical methods do, may be inefficient or inappropriate, but replacing the categories by successive integers or other arbitrary scores may distort the results. (For additional approaches to this question, see sections below on ordered structures.) Regression-like analysis of ordinal categorical variables is quite well developed, but their multivariate analysis needs further research. New log-bilinear models have been proposed, but to date they deal specifically with only two or three categorical variables. Additional research extending the new models, improving computational algorithms, and integrating the models with work on scaling promise to lead to valuable new knowledge.

Models for Event Histories

Event-history studies yield the sequence of events that respondents to a survey sample experience over a period of time; for example, the timing of marriage, childbearing, or labor force participation. Event-history data can be used to study educational progress, demographic processes (migration, fertility, and mortality), mergers of firms, labor market behavior, and even riots, strikes, and revolutions. As interest in such data has grown, many researchers have turned to models that pertain to changes in probabilities over time to describe when and how individuals move among a set of qualitative states.

Much of the progress in models for event-history data builds on recent developments in statistics and biostatistics for life-time, failure-time, and hazard models. Such models permit the analysis of qualitative transitions in a population whose members are undergoing partially random organic deterioration, mechanical wear, or other risks over time. With the increased complexity of event-history data that are now being collected, and the extension of event-history data bases over very long periods of time, new problems arise that cannot be effectively handled by older types of analysis. Among the problems are repeated transitions, such as between unemployment and employment or marriage and divorce; more than one time variable (such as biological age, calendar time, duration in a stage, and time exposed to some specified condition); latent variables (variables that are explicitly modeled even though not observed); gaps in the data; sample attrition that is not randomly distributed over the categories; and respondent difficulties in recalling the exact timing of events.

Models for Multiple-Item Measurement

For a variety of reasons, researchers typically use multiple measures (or multiple indicators) to represent theoretical concepts. Sociologists, for example, often rely on two or more variables (such as occupation and education) to measure an individual’s socioeconomic position; educational psychologists ordinarily measure a student’s ability with multiple test items. Despite the fact that the basic observations are categorical, in a number of applications this is interpreted as a partitioning of something continuous. For example, in test theory one thinks of the measures of both item difficulty and respondent ability as continuous variables, possibly multidimensional in character.

Classical test theory and newer item-response theories in psychometrics deal with the extraction of information from multiple measures. Testing, which is a major source of data in education and other areas, results in millions of test items stored in archives each year for purposes ranging from college admissions to job-training programs for industry. One goal of research on such test data is to be able to make comparisons among persons or groups even when different test items are used. Although the information collected from each respondent is intentionally incomplete in order to keep the tests short and simple, item-response techniques permit researchers to reconstitute the fragments into an accurate picture of overall group proficiencies. These new methods provide a better theoretical handle on individual differences, and they are expected to be extremely important in developing and using tests. For example, they have been used in attempts to equate different forms of a test given in successive waves during a year, a procedure made necessary in large-scale testing programs by legislation requiring disclosure of test-scoring keys at the time results are given.

An example of the use of item-response theory in a significant research effort is the National Assessment of Educational Progress (NAEP). The goal of this project is to provide accurate, nationally representative information on the average (rather than individual) proficiency of American children in a wide variety of academic subjects as they progress through elementary and secondary school. This approach is an improvement over the use of trend data on university entrance exams, because NAEP estimates of academic achievements (by broad characteristics such as age, grade, region, ethnic background, and so on) are not distorted by the self-selected character of those students who seek admission to college, graduate, and professional programs.

Item-response theory also forms the basis of many new psychometric instruments, known as computerized adaptive testing, currently being implemented by the U.S. military services and under additional development in many testing organizations. In adaptive tests, a computer program selects items for each examinee based upon the examinee’s success with previous items. Generally, each person gets a slightly different set of items and the equivalence of scale scores is established by using item-response theory. Adaptive testing can greatly reduce the number of items needed to achieve a given level of measurement accuracy.

Nonlinear, Nonadditive Models

Virtually all statistical models now in use impose a linearity or additivity assumption of some kind, sometimes after a nonlinear transformation of variables. Imposing these forms on relationships that do not, in fact, possess them may well result in false descriptions and spurious effects. Unwary users, especially of computer software packages, can easily be misled. But more realistic nonlinear and nonadditive multivariate models are becoming available. Extensive use with empirical data is likely to force many changes and enhancements in such models and stimulate quite different approaches to nonlinear multivariate analysis in the next decade.

Geometric and Algebraic Models

Geometric and algebraic models attempt to describe underlying structural relations among variables. In some cases they are part of a probabilistic approach, such as the algebraic models underlying regression or the geometric representations of correlations between items in a technique called factor analysis. In other cases, geometric and algebraic models are developed without explicitly modeling the element of randomness or uncertainty that is always present in the data. Although this latter approach to behavioral and social sciences problems has been less researched than the probabilistic one, there are some advantages in developing the structural aspects independent of the statistical ones. We begin the discussion with some inherently geometric representations and then turn to numerical representations for ordered data.

Although geometry is a huge mathematical topic, little of it seems directly applicable to the kinds of data encountered in the behavioral and social sciences. A major reason is that the primitive concepts normally used in geometry—points, lines, coincidence—do not correspond naturally to the kinds of qualitative observations usually obtained in behavioral and social sciences contexts. Nevertheless, since geometric representations are used to reduce bodies of data, there is a real need to develop a deeper understanding of when such representations of social or psychological data make sense. Moreover, there is a practical need to understand why geometric computer algorithms, such as those of multidimensional scaling, work as well as they apparently do. A better understanding of the algorithms will increase the efficiency and appropriateness of their use, which becomes increasingly important with the widespread availability of scaling programs for microcomputers.

Scaling

Over the past 50 years several kinds of well-understood scaling techniques have been developed and widely used to assist in the search for appropriate geometric representations of empirical data. The whole field of scaling is now entering a critical juncture in terms of unifying and synthesizing what earlier appeared to be disparate contributions. Within the past few years it has become apparent that several major methods of analysis, including some that are based on probabilistic assumptions, can be unified under the rubric of a single generalized mathematical structure. For example, it has recently been demonstrated that such diverse approaches as nonmetric multidimensional scaling, principal-components analysis, factor analysis, correspondence analysis, and log-linear analysis have more in common in terms of underlying mathematical structure than had earlier been realized.

Nonmetric multidimensional scaling is a method that begins with data about the ordering established by subjective similarity (or nearness) between pairs of stimuli. The idea is to embed the stimuli into a metric space (that is, a geometry with a measure of distance between points) in such a way that distances between points corresponding to stimuli exhibit the same ordering as do the data. This method has been successfully applied to phenomena that, on other grounds, are known to be describable in terms of a specific geometric structure; such applications were used to validate the procedures. Such validation was done, for example, with respect to the perception of colors, which are known to be describable in terms of a particular three-dimensional structure known as the Euclidean color coordinates. Similar applications have been made with Morse code symbols and spoken phonemes. The technique is now used in some biological and engineering applications, as well as in some of the social sciences, as a method of data exploration and simplification.

One question of interest is how to develop an axiomatic basis for various geometries using as a primitive concept an observable such as the subject’s ordering of the relative similarity of one pair of stimuli to another, which is the typical starting point of such scaling. The general task is to discover properties of the qualitative data sufficient to ensure that a mapping into the geometric structure exists and, ideally, to discover an algorithm for finding it. Some work of this general type has been carried out: for example, there is an elegant set of axioms based on laws of color matching that yields the three-dimensional vectorial representation of color space. But the more general problem of understanding the conditions under which the multidimensional scaling algorithms are suitable remains unsolved. In addition, work is needed on understanding more general, non-Euclidean spatial models.

Ordered Factorial Systems

One type of structure common throughout the sciences arises when an ordered dependent variable is affected by two or more ordered independent variables. This is the situation to which regression and analysis-of-variance models are often applied; it is also the structure underlying the familiar physical identities, in which physical units are expressed as products of the powers of other units (for example, energy has the unit of mass times the square of the unit of distance divided by the square of the unit of time).

There are many examples of these types of structures in the behavioral and social sciences. One example is the ordering of preference of commodity bundles—collections of various amounts of commodities—which may be revealed directly by expressions of preference or indirectly by choices among alternative sets of bundles. A related example is preferences among alternative courses of action that involve various outcomes with differing degrees of uncertainty; this is one of the more thoroughly investigated problems because of its potential importance in decision making. A psychological example is the trade-off between delay and amount of reward, yielding those combinations that are equally reinforcing. In a common, applied kind of problem, a subject is given descriptions of people in terms of several factors, for example, intelligence, creativity, diligence, and honesty, and is asked to rate them according to a criterion such as suitability for a particular job.

In all these cases and a myriad of others like them the question is whether the regularities of the data permit a numerical representation. Initially, three types of representations were studied quite fully: the dependent variable as a sum, a product, or a weighted average of the measures associated with the independent variables. The first two representations underlie some psychological and economic investigations, as well as a considerable portion of physical measurement and modeling in classical statistics. The third representation, averaging, has proved most useful in understanding preferences among uncertain outcomes and the amalgamation of verbally described traits, as well as some physical variables.

For each of these three cases—adding, multiplying, and averaging—researchers know what properties or axioms of order the data must satisfy for such a numerical representation to be appropriate. On the assumption that one or another of these representations exists, and using numerical ratings by subjects instead of ordering, a scaling technique called functional measurement (referring to the function that describes how the dependent variable relates to the independent ones) has been developed and applied in a number of domains. What remains problematic is how to encompass at the ordinal level the fact that some random error intrudes into nearly all observations and then to show how that randomness is represented at the numerical level; this continues to be an unresolved and challenging research issue.

During the past few years considerable progress has been made in understanding certain representations inherently different from those just discussed. The work has involved three related thrusts. The first is a scheme of classifying structures according to how uniquely their representation is constrained. The three classical numerical representations are known as ordinal, interval, and ratio scale types. For systems with continuous numerical representations and of scale type at least as rich as the ratio one, it has been shown that only one additional type can exist. A second thrust is to accept structural assumptions, like factorial ones, and to derive for each scale the possible functional relations among the independent variables. And the third thrust is to develop axioms for the properties of an order relation that leads to the possible representations. Much is now known about the possible nonadditive representations of both the multifactor case and the one where stimuli can be combined, such as combining sound intensities.

Closely related to this classification of structures is the question: What statements, formulated in terms of the measures arising in such representations, can be viewed as meaningful in the sense of corresponding to something empirical? Statements here refer to any scientific assertions, including statistical ones, formulated in terms of the measures of the variables and logical and mathematical connectives. These are statements for which asserting truth or falsity makes sense. In particular, statements that remain invariant under certain symmetries of structure have played an important role in classical geometry, dimensional analysis in physics, and in relating measurement and statistical models applied to the same phenomenon. In addition, these ideas have been used to construct models in more formally developed areas of the behavioral and social sciences, such as psychophysics. Current research has emphasized the communality of these historically independent developments and is attempting both to uncover systematic, philosophically sound arguments as to why invariance under symmetries is as important as it appears to be and to understand what to do when structures lack symmetry, as, for example, when variables have an inherent upper bound.

Clustering

Many subjects do not seem to be correctly represented in terms of distances in continuous geometric space. Rather, in some cases, such as the relations among meanings of words—which is of great interest in the study of memory representations—a description in terms of tree-like, hierarchial structures appears to be more illuminating. This kind of description appears appropriate both because of the categorical nature of the judgments and the hierarchial, rather than trade-off, nature of the structure. Individual items are represented as the terminal nodes of the tree, and groupings by different degrees of similarity are shown as intermediate nodes, with the more general groupings occurring nearer the root of the tree. Clustering techniques, requiring considerable computational power, have been and are being developed. Some successful applications exist, but much more refinement is anticipated.

Network Models

Several other lines of advanced modeling have progressed in recent years, opening new possibilities for empirical specification and testing of a variety of theories. In social network data, relationships among units, rather than the units themselves, are the primary objects of study: friendships among persons, trade ties among nations, cocitation clusters among research scientists, interlocking among corporate boards of directors. Special models for social network data have been developed in the past decade, and they give, among other things, precise new measures of the strengths of relational ties among units. A major challenge in social network data at present is to handle the statistical dependence that arises when the units sampled are related in complex ways.

Statistical Inference and Analysis

As was noted earlier, questions of design, representation, and analysis are intimately intertwined. Some issues of inference and analysis have been discussed above as related to specific data collection and modeling approaches. This section discusses some more general issues of statistical inference and advances in several current approaches to them.

Causal Inference

Behavioral and social scientists use statistical methods primarily to infer the effects of treatments, interventions, or policy factors. Previous chapters included many instances of causal knowledge gained this way. As noted above, the large experimental study of alternative health care financing discussed in Chapter 2 relied heavily on statistical principles and techniques, including randomization, in the design of the experiment and the analysis of the resulting data. Sophisticated designs were necessary in order to answer a variety of questions in a single large study without confusing the effects of one program difference (such as prepayment or fee for service) with the effects of another (such as different levels of deductible costs), or with effects of unobserved variables (such as genetic differences). Statistical techniques were also used to ascertain which results applied across the whole enrolled population and which were confined to certain subgroups (such as individuals with high blood pressure) and to translate utilization rates across different programs and types of patients into comparable overall dollar costs and health outcomes for alternative financing options.

A classical experiment, with systematic but randomly assigned variation of the variables of interest (or some reasonable approach to this), is usually considered the most rigorous basis from which to draw such inferences. But random samples or randomized experimental manipulations are not always feasible or ethically acceptable. Then, causal inferences must be drawn from observational studies, which, however well designed, are less able to ensure that the observed (or inferred) relationships among variables provide clear evidence on the underlying mechanisms of cause and effect.

Certain recurrent challenges have been identified in studying causal inference. One challenge arises from the selection of background variables to be measured, such as the sex, nativity, or parental religion of individuals in a comparative study of how education affects occupational success. The adequacy of classical methods of matching groups in background variables and adjusting for covariates needs further investigation. Statistical adjustment of biases linked to measured background variables is possible, but it can become complicated. Current work in adjustment for selectivity bias is aimed at weakening implausible assumptions, such as normality, when carrying out these adjustments. Even after adjustment has been made for the measured background variables, other, unmeasured variables are almost always still affecting the results (such as family transfers of wealth or reading habits). Analyses of how the conclusions might change if such unmeasured variables could be taken into account is essential in attempting to make causal inferences from an observational study, and systematic work on useful statistical models for such sensitivity analyses is just beginning.

The third important issue arises from the necessity for distinguishing among competing hypotheses when the explanatory variables are measured with different degrees of precision. Both the estimated size and significance of an effect are diminished when it has large measurement error, and the coefficients of other correlated variables are affected even when the other variables are measured perfectly. Similar results arise from conceptual errors, when one measures only proxies for a theoretical construct (such as years of education to represent amount of learning). In some cases, there are procedures for simultaneously or iteratively estimating both the precision of complex measures and their effect on a particular criterion.

Although complex models are often necessary to infer causes, once their output is available, it should be translated into understandable displays for evaluation. Results that depend on the accuracy of a multivariate model and the associated software need to be subjected to appropriate checks, including the evaluation of graphical displays, group comparisons, and other analyses.

New Statistical Techniques

Internal Resampling

One of the great contributions of twentieth-century statistics was to demonstrate how a properly drawn sample of sufficient size, even if it is only a tiny fraction of the population of interest, can yield very good estimates of most population characteristics. When enough is known at the outset about the characteristic in question—for example, that its distribution is roughly normal—inference from the sample data to the population as a whole is straightforward, and one can easily compute measures of the certainty of inference, a common example being the 95 percent confidence interval around an estimate. But population shapes are sometimes unknown or uncertain, and so inference procedures cannot be so simple. Furthermore, more often than not, it is difficult to assess even the degree of uncertainty associated with complex data and with the statistics needed to unravel complex social and behavioral phenomena.

Internal resampling methods attempt to assess this uncertainty by generating a number of simulated data sets similar to the one actually observed. The definition of similar is crucial, and many methods that exploit different types of similarity have been devised. These methods provide researchers the freedom to choose scientifically appropriate procedures and to replace procedures that are valid under assumed distributional shapes with ones that are not so restricted. Flexible and imaginative computer simulation is the key to these methods. For a simple random sample, the “bootstrap” method repeatedly resamples the obtained data (with replacement) to generate a distribution of possible data sets. The distribution of any estimator can thereby be simulated and measures of the certainty of inference be derived. The “jackknife” method repeatedly omits a fraction of the data and in this way generates a distribution of possible data sets that can also be used to estimate variability. These methods can also be used to remove or reduce bias. For example, the ratio-estimator, a statistic that is commonly used in analyzing sample surveys and censuses, is known to be biased, and the jackknife method can usually remedy this defect. The methods have been extended to other situations and types of analysis, such as multiple regression.

There are indications that under relatively general conditions, these methods, and others related to them, allow more accurate estimates of the uncertainty of inferences than do the traditional ones that are based on assumed (usually, normal) distributions when that distributional assumption is unwarranted. For complex samples, such internal resampling or subsampling facilitates estimating the sampling variances of complex statistics.

An older and simpler, but equally important, idea is to use one independent subsample in searching the data to develop a model and at least one separate subsample for estimating and testing a selected model. Otherwise, it is next to impossible to make allowances for the excessively close fitting of the model that occurs as a result of the creative search for the exact characteristics of the sample data—characteristics that are to some degree random and will not predict well to other samples.

Robust Techniques

Many technical assumptions underlie the analysis of data. Some, like the assumption that each item in a sample is drawn independently of other items, can be weakened when the data are sufficiently structured to admit simple alternative models, such as serial correlation. Usually, these models require that a few parameters be estimated. Assumptions about shapes of distributions, normality being the most common, have proved to be particularly important, and considerable progress has been made in dealing with the consequences of different assumptions.

More recently, robust techniques have been designed that permit sharp, valid discriminations among possible values of parameters of central tendency for a wide variety of alternative distributions by reducing the weight given to occasional extreme deviations. It turns out that by giving up, say, 10 percent of the discrimination that could be provided under the rather unrealistic assumption of normality, one can greatly improve performance in more realistic situations, especially when unusually large deviations are relatively common.

These valuable modifications of classical statistical techniques have been extended to multiple regression, in which procedures of iterative reweighting can now offer relatively good performance for a variety of underlying distributional shapes. They should be extended to more general schemes of analysis.

In some contexts—notably the most classical uses of analysis of variance—the use of adequate robust techniques should help to bring conventional statistical practice closer to the best standards that experts can now achieve.

Many Interrelated Parameters

In trying to give a more accurate representation of the real world than is possible with simple models, researchers sometimes use models with many parameters, all of which must be estimated from the data. Classical principles of estimation, such as straightforward maximum-likelihood, do not yield reliable estimates unless either the number of observations is much larger than the number of parameters to be estimated or special designs are used in conjunction with strong assumptions. Bayesian methods do not draw a distinction between fixed and random parameters, and so may be especially appropriate for such problems.

A variety of statistical methods have recently been developed that can be interpreted as treating many of the parameters as or similar to random quantities, even if they are regarded as representing fixed quantities to be estimated. Theory and practice demonstrate that such methods can improve the simpler fixed-parameter methods from which they evolved, especially when the number of observations is not large relative to the number of parameters. Successful applications include college and graduate school admissions, where quality of previous school is treated as a random parameter when the data are insufficient to separately estimate it well. Efforts to create appropriate models using this general approach for small-area estimation and undercount adjustment in the census are important potential applications.

Missing Data

In data analysis, serious problems can arise when certain kinds of (quantitative or qualitative) information is partially or wholly missing. Various approaches to dealing with these problems have been or are being developed. One of the methods developed recently for dealing with certain aspects of missing data is called multiple imputation: each missing value in a data set is replaced by several values representing a range of possibilities, with statistical dependence among missing values reflected by linkage among their replacements. It is currently being used to handle a major problem of incompatibility between the 1980 and previous Bureau of Census public-use tapes with respect to occupation codes. The extension of these techniques to address such problems as nonresponse to income questions in the Current Population Survey has been examined in exploratory applications with great promise.

Computing

Computer Packages and Expert Systems

The development of high-speed computing and data handling has fundamentally changed statistical analysis. Methodologies for all kinds of situations are rapidly being developed and made available for use in computer packages that may be incorporated into interactive expert systems. This computing capability offers the hope that much data analyses will be more carefully and more effectively done than previously and that better strategies for data analysis will move from the practice of expert statisticians, some of whom may not have tried to articulate their own strategies, to both wide discussion and general use.

But powerful tools can be hazardous, as witnessed by occasional dire misuses of existing statistical packages. Until recently the only strategies available were to train more expert methodologists or to train substantive scientists in more methodology, but without the updating of their training it tends to become outmoded. Now there is the opportunity to capture in expert systems the current best methodological advice and practice. If that opportunity is exploited, standard methodological training of social scientists will shift to emphasizing strategies in using good expert systems—including understanding the nature and importance of the comments it provides—rather than in how to patch together something on one’s own. With expert systems, almost all behavioral and social scientists should become able to conduct any of the more common styles of data analysis more effectively and with more confidence than all but the most expert do today. However, the difficulties in developing expert systems that work as hoped for should not be underestimated. Human experts cannot readily explicate all of the complex cognitive network that constitutes an important part of their knowledge. As a result, the first attempts at expert systems were not especially successful (as discussed in Chapter 1). Additional work is expected to overcome these limitations, but it is not clear how long it will take.

Exploratory Analysis and Graphic Presentation

The formal focus of much statistics research in the middle half of the twentieth century was on procedures to confirm or reject precise, a priori hypotheses developed in advance of collecting data—that is, procedures to determine statistical significance. There was relatively little systematic work on realistically rich strategies for the applied researcher to use when attacking real-world problems with their multiplicity of objectives and sources of evidence. More recently, a species of quantitative detective work, called exploratory data analysis, has received increasing attention. In this approach, the researcher seeks out possible quantitative relations that may be present in the data. The techniques are flexible and include an important component of graphic representations. While current techniques have evolved for single responses in situations of modest complexity, extensions to multiple responses and to single responses in more complex situations are now possible.

Graphic and tabular presentation is a research domain in active renaissance, stemming in part from suggestions for new kinds of graphics made possible by computer capabilities, for example, hanging histograms and easily assimilated representations of numerical vectors. Research on data presentation has been carried out by statisticians, psychologists, cartographers, and other specialists, and attempts are now being made to incorporate findings and concepts from linguistics, industrial and publishing design, aesthetics, and classification studies in library science. Another influence has been the rapidly increasing availability of powerful computational hardware and software, now available even on desktop computers. These ideas and capabilities are leading to an increasing number of behavioral experiments with substantial statistical input. Nonetheless, criteria of good graphic and tabular practice are still too much matters of tradition and dogma, without adequate empirical evidence or theoretical coherence. To broaden the respective research outlooks and vigorously develop such evidence and coherence, extended collaborations between statistical and mathematical specialists and other scientists are needed, a major objective being to understand better the visual and cognitive processes (see Chapter 1) relevant to effective use of graphic or tabular approaches.

Combining Evidence

Combining evidence from separate sources is a recurrent scientific task, and formal statistical methods for doing so go back 30 years or more. These methods include the theory and practice of combining tests of individual hypotheses, sequential design and analysis of experiments, comparisons of laboratories, and Bayesian and likelihood paradigms.

There is now growing interest in more ambitious analytical syntheses, which are often called meta-analyses. One stimulus has been the appearance of syntheses explicitly combining all existing investigations in particular fields, such as prison parole policy, classroom size in primary schools, cooperative studies of therapeutic treatments for coronary heart disease, early childhood education interventions, and weather modification experiments. In such fields, a serious approach to even the simplest question—how to put together separate estimates of effect size from separate investigations—leads quickly to difficult and interesting issues. One issue involves the lack of independence among the available studies, due, for example, to the effect of influential teachers on the research projects of their students. Another issue is selection bias, because only some of the studies carried out, usually those with “significant” findings, are available and because the literature search may not find out all relevant studies that are available. In addition, experts agree, although informally, that the quality of studies from different laboratories and facilities differ appreciably and that such information probably should be taken into account. Inevitably, the studies to be included used different designs and concepts and controlled or measured different variables, making it difficult to know how to combine them.

Rich, informal syntheses, allowing for individual appraisal, may be better than catch-all formal modeling, but the literature on formal meta-analytic models is growing and may be an important area of discovery in the next decade, relevant both to statistical analysis per se and to improved syntheses in the behavioral and social and other sciences.

Opportunities and Needs

This chapter has cited a number of methodological topics associated with behavioral and social sciences research that appear to be particularly active and promising at the present time. As throughout the report, they constitute illustrative examples of what the committee believes to be important areas of research in the coming decade. In this section we describe recommendations for an additional $16 million annually to facilitate both the development of methodologically oriented research and, equally important, its communication throughout the research community.

Methodological studies, including early computer implementations, have for the most part been carried out by individual investigators with small teams of colleagues or students. Occasionally, such research has been associated with quite large substantive projects, and some of the current developments of computer packages, graphics, and expert systems clearly require large, organized efforts, which often lie at the boundary between grant-supported work and commercial development. As such research is often a key to understanding complex bodies of behavioral and social sciences data, it is vital to the health of these sciences that research support continue on methods relevant to problems of modeling, statistical analysis, representation, and related aspects of behavioral and social sciences data. Researchers and funding agencies should also be especially sympathetic to the inclusion of such basic methodological work in large experimental and longitudinal studies. Additional funding for work in this area, both in terms of individual research grants on methodological issues and in terms of augmentation of large projects to include additional methodological aspects, should be provided largely in the form of investigator-initiated project grants.

Ethnographic and comparative studies also typically rely on project grants to individuals and small groups of investigators. While this type of support should continue, provision should also be made to facilitate the execution of studies using these methods by research teams and to provide appropriate methodological training through the mechanisms outlined below.

Overall, we recommend an increase of $4 million in the level of investigator-initiated grant support for methodological work. An additional $1 million should be devoted to a program of centers for methodological research.

Many of the new methods and models described in the chapter, if and when adopted to any large extent, will demand substantially greater amounts of research devoted to appropriate analysis and computer implementation. New user interfaces and numerical algorithms will need to be designed and new computer programs written. And even when generally available methods (such as maximum-likelihood) are applicable, model application still requires skillful development in particular contexts. Many of the familiar general methods that are applied in the statistical analysis of data are known to provide good approximations when sample sizes are sufficiently large, but their accuracy varies with the specific model and data used. To estimate the accuracy requires extensive numerical exploration. Investigating the sensitivity of results to the assumptions of the models is important and requires still more creative, thoughtful research. It takes substantial efforts of these kinds to bring any new model on line, and the need becomes increasingly important and difficult as statistical models move toward greater realism, usefulness, complexity, and availability in computer form. More complexity in turn will increase the demand for computational power. Although most of this demand can be satisfied by increasingly powerful desktop computers, some access to mainframe and even supercomputers will be needed in selected cases. We recommend an additional $4 million annually to cover the growth in computational demands for model development and testing.

Interaction and cooperation between the developers and the users of statistical and mathematical methods need continual stimulation—both ways. Efforts should be made to teach new methods to a wider variety of potential users than is now the case. Several ways appear effective for methodologists to communicate to empirical scientists: running summer training programs for graduate students, faculty, and other researchers; encouraging graduate students, perhaps through degree requirements, to make greater use of the statistical, mathematical, and methodological resources at their own or affiliated universities; associating statistical and mathematical research specialists with large-scale data collection projects; and developing statistical packages that incorporate expert systems in applying the methods.

Methodologists, in turn, need to become more familiar with the problems actually faced by empirical scientists in the laboratory and especially in the field. Several ways appear useful for communication in this direction: encouraging graduate students in methodological specialties, perhaps through degree requirements, to work directly on empirical research; creating postdoctoral fellowships aimed at integrating such specialists into ongoing data collection projects; and providing for large data collection projects to engage relevant methodological specialists. In addition, research on and development of statistical packages and expert systems should be encouraged to involve the multidisciplinary collaboration of experts with experience in statistical, computer, and cognitive sciences.

A final point has to do with the promise held out by bringing different research methods to bear on the same problems. As our discussions of research methods in this and other chapters have emphasized, different methods have different powers and limitations, and each is designed especially to elucidate one or more particular facets of a subject. An important type of interdisciplinary work is the collaboration of specialists in different research methodologies on a substantive issue, examples of which have been noted throughout this report. If more such research were conducted cooperatively, the power of each method pursued separately would be increased. To encourage such multidisciplinary work, we recommend increased support for fellowships, research workshops, and training institutes.

Funding for fellowships, both pre-and postdoctoral, should be aimed at giving methodologists experience with substantive problems and at upgrading the methodological capabilities of substantive scientists. Such targeted fellowship support should be increased by $4 million annually, of which $3 million should be for predoctoral fellowships emphasizing the enrichment of methodological concentrations. The new support needed for research workshops is estimated to be $1 million annually. And new support needed for various kinds of advanced training institutes aimed at rapidly diffusing new methodological findings among substantive scientists is estimated to be $2 million annually.

What is the study of using mathematical models to predict future events and to draw conclusions about a sample of a population?

statistical inference. The process of drawing a sample from a population and then carrying out statistical analysis on the sample in order to make conclusions about the entire population is called statistical inference.

What is it called when all the data you have fits into all the categories you have?

frequency. One feature that data analysts use frequently to summarize the data in a lengthy table is called a ______ table. pivot. What is it called when all the data you have fits into all the categories you have? Exhaustive.

What is the statistics term used for a property of an object that can be measured and recorded?

A variable is a characteristic that can be measured and that can assume different values. Height, age, income, province or country of birth, grades obtained at school and type of housing are all examples of variables.

What is the difference between descriptive statistics and inferential statistics quizlet?

Descriptive statistics are used to describe and summarize the data from a research sample. Inferential statistics help us make probability-based inferences about the wider population from which we obtained our sample.