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?

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.

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.

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.

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.

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.

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.