Geertz's wink interpretation is best expressed as a causal hypothesis (which we define precisely in section 3.1): the hypothetical causal effect of the wink on the other political actor is the other actor's response given the eyelid contraction minus his response if there were no movement (and no other changes). If the eyelid contraction were a wink, the causal effect would be positive; if it were only a twitch, the causal effect would be zero. If we decided to estimate this causal effect (and thus find out whether it was a wink or a twitch), all the problems of inference discussed at length in the rest of this book would need to be understood if we were to arrive at the best inference with respect to the interpretation of the observed behavior.

If what we interpret as winks were actually involuntary twitches, our attempts to derive causal inferences about eyelid contraction on the basis of a theory of voluntary social interaction would be routinely unsuccessful: we would not be able to generalize and we would know it.14 Designing research to distinguish winks and twitches is not likely to be a major part of most political science research, but the same methodological issue arises in much of the subject area in which political scientists work. We are often called on to interpret the meaning of an act. Foreign policy decision makers send messages to each other. Is a particular message a threat, a negotiating point, a statement aimed at appealing to a domestic audience? Knowledge of cultural norms, of conventions in international communications, and of the history of particular actors, as well as close observation of ancillary features of the communication, will all help us make such an interpretation. Or consider the following puzzle in quant.i.tative research: Voters in the United States seem to be sending a message by not turning out at the polls. But what does the low turnout mean? Does it reflect alienation with the political system? A calculation of the costs and benefits of voting with the costs being greater? Disappointment with recent candidates or recent campaigns? Could it be a consequence of a change in the minimum age of voting? Or a sign that nothing is sufficiently upsettingto get them to the polls? The decision of a citizen not to vote, like a wink or a diplomatic message, can mean many things. The sophisticated researcher should always work hard to ask the right questions and then carefully design scientific research to find out what the ambiguous act did in fact mean.

We would also like to briefly address the extreme claims of a few proponents of interpretation who argue that the goal of some research ought to be feelings and meanings with no observable consequences. This is hardly a fair characterization of all but a small minority of researchers in this tradition, but the claims are made sufficiently forcefully that they seem worth addressing explicitly. Like the over-enthusiastic claims of early positivists, who took the untenable position that un.o.bservable concepts had no place in scientific research, these arguments turn out to be inappropriate for empirical research. For example, Psathas (1968:510) argues thatany behavior by focusing only on that part which is overt and manifested in concrete, directly observable acts is naive, to say the least. The challenge to the social scientist who seeks to understand social reality, then, is to understand the meaning that the actor's act has for him.

Psathas may be correct that social scientists who focus on only overt, observable, behaviors are missing a lot, but how are we to know if we cannot see? For example, if two theories of self-conception have identical observable manifestations, then no observer will have sufficient information to distinguish the two. This is true no matter how clever or culturally sensitive the observer is, how skilled she is at interpretation, how well she "brackets" her own presuppositions, or how hard she tries. Interpretation, feeling, thick description, partic.i.p.ant observation, nonpartic.i.p.ant observation, depth interviewing, empathy, quantification and statistical a.n.a.lysis, and all other procedures and methods are inadequate to the task of distinguishing two theories without differing observable consequences. On the other hand, if the two theories have some observable manifestations that differ, then the methods we describe in this book provide ways to distinguish between them.

In practice, ethnographers (and all other good social scientists) do look for observable behavior in order to distinguish among their theories. They may immerse themselves in the culture, but they all rely on various forms of observation. Any further "understanding" of the cultural context comes directly from these or other comparable observations. Identifying relevant observations is not always easy. On the contrary, finding the appropriate observations is perhaps the most difficult part of a research project, especially (and necessarily) for those areas of inquiry traditionally dominated by qualitative research.

2.1.2 "Uniqueness," Complexity, and Simplification.

Some qualitatively oriented researchers would reject the position that general knowledge is either necessary or useful (perhaps even possible) as the basis for understanding a particular event. Their position is that the events or units they study are "unique." In one sense, they are right. There was only one French Revolution and there is only one Thailand. And no one who has read the biographical accounts or who lived through the 1960s can doubt the fact that there was only one Lyndon B. Johnson. But they go further. Explanation, according to their position, is limited to that unique event or unit: not why revolutions happen, but why the French Revolution happened; not why democratization sometimes seems to lag, but why it lags in Thailand; not why candidates win, but why LBJ won in 1948 or 1964. Researchers in this tradition believe that they would lose their ability to explain the specific if they attempted to deal with the general-with revolutions or democratization or senatorial primaries.

"Uniqueness," however, is a misleading term. The French Revolution and Thailand and LBJ are, indeed, unique. All phenomena, all events, are in some sense unique. The French Revolution certainly was; but so was the congressional election in the Seventh District of Pennsylvania in 1988 and so was the voting decision of every one of the millions of voters who voted in the presidential election that year. Viewed holistically, every aspect of social reality is infinitely complex and connected in some way to preceding natural and sociological events. Inherent uniqueness, therefore, is part of the human condition: it does not distinguish situations amenable to scientific generalizations from those about which generalizations are not possible. Indeed, as we showed in discussing theories of dinosaur extinction in chapter 1, even unique events can be studied scientifically by paying attention to the observable implications of theories developed to account for them.

The real question that the issue of uniqueness raises is the problem of complexity. The point is not whether events are inherently unique, but whether the key features of social reality that we want to understand can be abstracted from a ma.s.s of facts. One of the first and most difficult tasks of research in the social sciences is this act of simplification. It is a task that makes us vulnerable to the criticism of oversimplification and of omitting significant aspects of the situation. Nevertheless, such simplication is inevitable for all researchers. Simplification has been an integral part of every known scholarly work-quant.i.tative and qualitative, anthropological and economic, in the social sciences and in the natural and physical sciences-and will probably always be. Even the most comprehensive description done by the best cultural interpreters with the most detailed contextual understanding will drastically simplify, reify, and reduce the reality that has been observed. Indeed, the difference between the amount of complexity in the world and that in the thickest of descriptions is still vastly larger than the difference between this thickest of descriptions and the most abstract quant.i.tative or formal a.n.a.lysis. No description, no matter how thick, and no explanation, no matter how many explanatory factors go into it, comes close to capturing the full "blooming and buzzing" reality of the world. There is no choice but to simplify. Systematic simplification is a crucial step to useful knowledge. As an economic historian has put it, if emphasis on uniqueness "is carried to the extreme of ignoring all regularities, the very possibility of social science is denied and historians are reduced to the aimlesssness of balladeers" (Jones 1981:160).

Where possible, a.n.a.lysts should simplify their descriptions only after they attain an understanding of the richness of history and culture. Social scientists may use only a few parts of the history of some set of events in making inferences. Nevertheless, rich, unstructured knowledge of the historical and cultural context of the phenomena with which they want to deal in a simplified and scientific way is usually a requisite for avoiding simplications that are simply wrong. Few of us would trust the generalizations of a social scientist about revolutions or senatorial elections if that investigator knew little and cared less about the French Revolution or the 1948 Texas election.

In sum, we believe that, where possible, social science research should be both general and specific: it should tell us something about cla.s.ses of events as well as about specific events at particular places. We want to be timeless and timebound at the same time. The emphasis on either goal may vary from research endeavor to research endeavor, but both are likely to be present. Furthermore, rather than the two goals being opposed to each other, they are mutually supportive. Indeed, the best way to understand a particular event may be by using the methods of scientific inference also to study systematic patterns in similar parallel events.

2.1.3 Comparative Case Studies.

Much of what political scientists do is describe politically important events systematically. People care about the collapse of the Soviet Union, the reactions of the public in Arab countries to the UN-authorized war to drive Iraq from Kuwait, and the results of the latest congressional elections in the United States. And they rely on political scientists for descriptions that reflect a more comprehensive awareness of the relationship between these and other relevant events-contemporary and historical-than is found in journalistic accounts. Our descriptions of events should be as precise and systematic as possible. This means that when we are able to find valid quant.i.tative measures of what we want to know, we should use them: What proportion of Soviet newspapers criticize government policy? What do public opinion polls in Jordan and Egypt reveal about Jordanian and Egyptian att.i.tudes toward the Gulf war? What percentage of congressional inc.u.mbents were reelected?

If quantification produces precision, it does not necessarily encourage accuracy, since inventing quant.i.tative indixes that do not relate closely to the concepts or events that we purport to measure can lead to serious measurement error and problems for causal inference (see section 5.1). Similarly, there are more and less precise ways to describe events that cannot be quantified. Disciplined qualitative researchers carefully try to a.n.a.lyze const.i.tutions and laws rather than merely report what observers say about them. In doing case studies of government policy, researchers ask their informants trenchant, well-specified questions to which answers will be relatively unambiguous, and they systematically follow up on off-hand remarks made by an interviewee that suggest relevant hypotheses. Case studies are essential for description, and are, therefore, fundamental to social science. It is pointless to seek to explain what we have not described with a reasonable degree of precision.

To provide an insightful description of complex events is no trivial task. In fields such as comparative politics or international relations, descriptive work is particularly important because there is a great deal we still need to know, because our explanatory abilities are weak, and because good description depends in part on good explanation. Some of the sources of our need-to-know and explanatory weaknesses are the same: in world politics, for instance, patterns of power, alignments, and international interdependence have all been changing rapidly recently, both increasing the need for good description of new situations, and altering the systemic context within which observed interactions between states take place. Since states and other actors seek to antic.i.p.ate and counter others' actions, causality is often difficult to establish, and expectations may play as important a part as observed actions in accounting for state behavior. A purported explanation of some aspect of world politics that a.s.sumes the absence of strategic interaction and antic.i.p.ated reactions will be much less useful than a careful description that focuses on events that we have reason to believe are important and interconnected. Good description is better than bad explanation.

One of the often overlooked advantages of the in-depth case-study method is that the development of good causal hypotheses is complementary to good description rather than compet.i.tive with it. Framing a case study around an explanatory question may lead to more focused and relevant description, even if the study is ultimately thwarted in its attempt to provide even a single valid causal inference.

Comparative case studies can, we argue, yield valid causal inferences when the procedures described in the rest of this book are used, even though as currently practiced they often do not meet the standards for valid inference (which we explicate in chapter 3). Indeed, much of what is called "explanatory" work by historically-oriented or interpretative social scientists remains essentially descriptive because it does not meet these universally applicable standards. From this perspective, the advice of a number of scholars that comparative case studies must be be more systematic for description or explanation is fundamental.

For example, Alexander George recommends a method of "structured, focused comparison" that emphasizes discipline in the way one collects data (George and McKeown 1985; see also Verba 1967). George and his collaborators stress the need for a systematic collection of the same information-the same variables-across carefully selected units. And they stress the need for theoretical guidance-for asking carefully thought-out explanatory questions-in order to accomplish this systematic description, if causal inference is to be ultimately possible.15 The method of structured, focused comparison is a systematic way to employ what George and McKeown call the congruence procedure. Using this method, the investigator "defines and standardizes the data requirements of the case studies ... by formulating theoretically relevant general questions to guide the examination of each case" (George and McKeown 1985:41). The point that George and McKeown (1985: 43) make is well-taken: "Controlled comparison of a small n should follow a procedure of systematic data compilation." Such "structured-focused comparison" requires collecting data on the same variables across units. Thus, it is not a different method from the one that we emphasize here so much as it is a way of systematizing the information in descriptive case studies in such a way that it could conceivably be used for descriptive or causal inference. Much valuable advice about doing comparative case studies, such as this, is rudimentary but often ignored.

2.2 INFERENCE: THE SCIENTIFIC PURPOSE OF DATA COLLECTION.

Inference is the process of using the facts we know to learn about facts we do not know. The facts we do not know are the subjects of our research questions, theories, and hypotheses. The facts we do know form our (quant.i.tative or qualitative) data or observations.

In seeking general knowledge, for its own sake or to understand particular facts better, we must somehow avoid being overwhelmed by the ma.s.sive cacophony of potential and actual observations about the world. Fortunately, the solution to that problem lies precisely in the search for general knowledge. That is, the best scientific way to organize facts is as observable implications of some theory or hypothesis. Scientific simplification involves the productive choice of a theory (or hypothesis) to evaluate; the theory then guides us to the selection of those facts that are implications of theory. Organizing facts in terms of observable implications of a specific theory produces several important and beneficial results in designing and conducting research. First, with this criterion for the selection of facts, we can quickly recognize that more observations of the implications of a theory will only help in evaluating the theory in question. Since more information of this sort cannot hurt, such data are never discarded, and the process of research improves.

Second, we need not have a complete theory before collecting data nor must our theory remain fixed throughout. Theory and data interact. As with the chicken and the egg, some theory is always necessary before data collection and some data are required before any theorizing. Textbooks on research tell us that we use our data to test our theories. But learning from the data may be as important a goal as evaluating prior theories and hypotheses. Such learning involves reorganizing our data into observable implications of the new theory. This reorganizing is very common early in many research processes, usually after some preliminary data have been collected; after the reorganization, data collection then continues in order to evaluate the new theory. We should always try to continue to collect data even after the reorganization in order to test the new theory and thus avoid using the same data to evaluate the theory that we used to develop it.16 Third, the emphasis on gathering facts as observable implications of a hypothesis makes the common ground between the quant.i.tative and qualitative styles of research much clearer. In fact, once we get past thinking of cases or units or records in the usual very narrow or even naive sense, we realize that most qualitative studies potentially provide a very large number of observable implications for the theories being evaluated, yet many of these observations may be overlooked by the investigator. Organizing the data into a list of the specific observable implications of a theory thus helps reveal the essential scientific purpose of much qualitative research. In a sense, we are asking the scholar who is studying a particular event-a particular government decision, perhaps-to ask: "If my explanation is correct of why the decision came out the way it did, what else might I expect to observe in the real world?" These additional observable implications might be found in other decisions, but they might also be found in other aspects of the decision being studied: for instance, when it was made, how it was made, how it was justified. The crucial maxim to guide both theory creation and data gathering is: search for more observable implications of the theory.

Each time we develop a new theory or hypothesis, it is productive to list all implications of the theory that could, in principle, be observed. The list, which could then be limited to those items for which data have been or could easily be collected, then forms the basic operational guide for a research project. If collecting one additional datum will help provide one additional way to evaluate a theory, then (subject to the usual time, money, and effort constraints) it is worth doing. If an interview or other observation might be interesting but is not a potential observable implication of this (or some other relevant) theory, then it should be obvious that it will not help us evaluate our theory.

As part of the simplification process accomplished by organizing our data into observable implications of a theory, we need to systematize the data. We can think about converting the raw material of real-world phenomena into "cla.s.ses" that are made up of "units" or "cases" which are, in turn, made up of "attributes" or "variables" or "parameters." The cla.s.s might be "voters"; the units might be a sample of "voters" in several congressional districts; and the attributes or variables might be income, party identification, or anything that is an observable implication of the theory being evaluated. Or the cla.s.s might be a particular kind of collectivity such as communities or countries, the units might be a selection of these, and the attributes or variables might be their size, the type of government, their economic circ.u.mstances, their ethnic composition, or whatever else is measureable and of interest to the researcher. These concepts, as well as various other constructs such as typologies, frameworks, and all manner of cla.s.sifications, are useful as temporary devices when we are collecting data but have no clear hypothesis to be evaluated. However, in general, we encourage researchers not to organize their data in this way. Instead, we need only the organizing concept inherent in our theory. That is, our observations are either implications of our theory or irrelevant. If they are irrelevant or not observable, we should ignore them. If they are relevant, then we should use them. Our data need not all be at the same level of a.n.a.lysis. Disaggregated data, or observations from a different time period, or even from a different part of the world, may provide additional observable implications of a theory. We may not be interested at all in these subsidiary implications, but if they are consistent with the theory, as predicted, they will help us build confidence in the power and applicability of the theory. Our data also need not be "symmetric": we can have a detailed study of one province, a comparative study of two countries, personal interviews with government leaders from only one policy sector, and even a quant.i.tative component-just so long as each is an observable consequence of our theory. In this process, we go beyond the particular to the general, since the characterization of particular units on the basis of common characteristics is a generalizing process. As a result, we learn a lot more about both general theories and particular facts.

In general, we wish to bring as much information to bear on our hypothesis as possible. This may mean doing additional case studies, but that is often too difficult, time consuming, or expensive. We obviously should not bring in irrelevant information. For example, treating the number of conservative-held seats in the British House of Commons as a monthly variable instead of one which changes at each national election, would increase the number of observations substantially but would make no sense since little new information would be added. On the other hand, disaggregating U.S. presidential election results to the state or even county level increases both the number of cases and the amount of information brought to bear on the problem.

Such disaggregated information may seem irrelevant since the goal is to learn about the causes of a particular candidate's victory in a race for the presidency-a fundamentally aggregate-level question. However, most explanations of the outcome of the presidential election have different observable implications for the disaggregated units. If, for instance, we predict the outcome of the presidential election on the basis of economic variables such as the unemployment rate, the use of the unemployment rates on a state-by-state basis provides many more observations of the implications of our theory than does the aggregate rate for the nation as a whole. By verifying that the theory holds in these other situations-even if these other situations are not of direct interest-we increase the confidence that the theory is correct and that it correctly explains the one observable consequence of the theory that is of interest.

2.3 FORMAL MODELS OF QUALITATIVE RESEARCH.

A model is a simplification of, and approximation to, some aspect of the world. Models are never literally "true" or "false," although good models abstract only the "right" features of the reality they represent.

For example, consider a six-inch toy model of an airplane made of plastic and glue. This model is a small fraction of the size of the real airplane, has no moving parts, cannot fly, and has no contents. None of us would confuse this model with the real thing; asking whether any aspect of the model is true is like asking whether the model who sat for Leonardo DaVinci's Mona Lisa really had such a beguiling smile. Even if she did, we would not expect Leonardo's picture to be an exact representation of anyone, whether the actual model or the Virgin Mary, any more than we would expect an airplane model fully to reflect all features of an aircraft. However, we would like to know whether this model abstracts the correct features of an airplane for a particular problem. If we wish to communicate to a child what a real airplane is like, this model might be adequate. If built to scale, the model might also be useful to airplane designers for wind tunnel tests. The key feature of a real airplane that this model abstracts is its shape. For some purposes, this is certainly one of the right features. Of course, this model misses myriad details about an airplane, including size, color, the feeling of being on the plane, strength of its various parts, number of seats on board, power of its engines, fabric of the seat cushions, and electrical, air, plumbing, and numerous other critical systems. If we wished to understand these aspects of the plane, we would need an entirely different set of models.

Can we evaluate a model without knowing which features of the subject we wish to study? Clearly not. For example, we might think that a model that featured the amount of dirt on an airplane would not be of much use. Indeed, for the purposes of teaching children or wind tunnel tests, it would be largely irrelevant. However, since even carpet dust can cause a plane to weigh more and thus use more expensive fuel, models of this sort are important to the airline industry and have been built (and saved millions of dollars).

All models range between restrictive and unrestrictive versions. Restrictive models are clearer, more parsimonious, and more abstract, but they are also less realistic (unless the world really is parsimonious). Models which are unrestrictive are detailed, contextual, and more realistic, but they are also less clear and harder to estimate with precision (see King 1989: section 2.5). Where on this continuum we choose to construct a model depends on the purpose for which it is to be put and on the complexity of the problem we are studying.

Whereas some models are physical, others are pictorial, verbal, or algebraic. For example, the qualitative description of European judicial systems in a book about that subject is a model of that event. No matter how thick the description or talented the author, the book's account will always be an abstraction or simplification compared to the actual judicial system. Since understanding requires some abstraction, the sign of a good book is as much what is left out as what is included.

While qualitative researchers often use verbal models, we will use algebraic models in our discussion below to study and improve these verbal models. Just as with models of toy airplanes and book-long studies of the French Revolution, our algebraic models of qualitative research should not be confused with qualitative research itself. They are only meant to provide especially clear statements of problems to avoid and opportunities to exploit. In addition, we often find that they help us to discover ideas that we would not have thought of otherwise.

We a.s.sume that readers have had no previous experience with algebraic models, although those with exposure to statistical models will find some of the models that follow familiar. But the logic of inference in these models applies to both quant.i.tative and qualitative research. Just because quant.i.tative researchers are probably more familiar with our terminology does not mean that they are any better at applying the logic of scientific inference. Moreover, these models do not apply more closely to quant.i.tative than to qualitative research; in both cases, the models are useful abstractions of the research to which they are applied. To ease their introduction, we introduce all algebraic models with verbal descriptions, followed by a box where we use standard algebraic notation. Although we discourage it, the boxes may be skipped without loss of continuity.

2.4 A FORMAL MODEL OF DATA COLLECTION.

Before formalizing our presentation of descriptive and causal inference-the two primary goals of social science research-we will develop a model for the data to be collected and for summarizing these data. This model is quite simple, but it is a powerful tool for a.n.a.lyzing problems of inference. Our algebraic model will not be as formal as that in statistics but nevertheless makes our ideas clearer and easier to convey. By data collection, we refer to a wide range of methods, including observation, partic.i.p.ant observation, intensive interviews, large-scale sample surveys, history recorded from secondary sources, randomized experiments, ethnography, content a.n.a.lyses, and any other method of collecting reliable evidence. The most important rule for all data collection is to report how the data were created and how we came to possess them. Every piece of information that we gather should contribute to specifying observable implications of our theory. It may help us develop a new research question, but it will be of no use in answering the present question if it is not an observable implication of the question we seek to answer.

We model data with variables, units, and observations. One simple example is the annual income of each of four people. The data might be represented simply by four numbers: $9,000, $22,000, $21,000, and $54,292. In the more general case, we could label the income of four people (numbered 1, 2, 3, and 4) as y1, y2, y3 and y4 One variable coded for two unstructured interviews might take on the values "partic.i.p.atory," "cooperative," or "intransigent," and might be labeled y1 and y2. In these examples, the variable is y; the units are the individual people; and the observations are the values of the variables for each unit (income for dollars or degree of cooperation). The symbol y is called a variable because its values vary over the units, and in general, a variable can represent anything whose values change over a set of units. Since we can collect information over time or across sectional areas, units may be people, countries, organizations, years, elections, or decades, and often, some combination of these or other units. Observations can be numerical, verbal, visual, or any other type of empirical data.

For example, suppose we are interested in international organizations since 1945. Before we collect our data, we need to decide what outcomes we want to explain. We could seek to understand the size distribution of international organizational activity (by issue area or by organization) in 1990; changes in the aggregate size of international organizational activity since 1945; or changes in the size distribution of international organizational activity since 1945. Variables measuring organizational activity could include the number of countries belonging to international organizations at a given time, the number of tasks performed by international organizations, or the sizes of budgets and staffs. In these examples, the units of a.n.a.lysis would include international organizations, issue areas, country memberships, and time periods such as years, five-year periods, or decades. At the data-collection stage, no formal rules apply as to what variables to collect, how many units there should be, whether the units must outnumber the variables, or how well variables should be measured. The only rule is our judgment as to what will prove to be important. When we have a clearer idea of how the data will be used, the rule becomes finding as many observable implications of a theory as possible. As we emphasized in chapter 1, empirical research can be used both to evaluate a priori hypotheses or to suggest hypotheses not previously considered; but if the latter approach is followed, new data must be collected to evaluate these hypotheses.

It should be very clear from our discussion that most works labeled "case studies" have numerous variables measured over many different types of units. Although case-study research rarely uses more than a handful of cases, the total number of observations is generally immense. It is therefore essential to distinguish between the number of cases and the number of observations. The former may be of some interest for some purposes, but only the latter is of importance in judging the amount of information a study brings to bear on a theoretical question. We therefore reserve the commonly used n to refer only to the number of observations and not to the number of cases. Only occasionally, such as when individual observations are partly dependent, will we distinguish between information and the number of observations. The terminology of the number of observations comes from survey sampling where n is the number of persons to be interviewed, but we apply it much more generally. Indeed, our definition of an "observation" coincides exactly with Harry Eckstein's (1975:85) definition of what he calls a "case." As Eckstein argues, "A study of six general elections in Britain may be, but need not be, an n = 1 study. It might also be an n = 6 study. It can also be an n = 120,000,000 study. It depends on whether the subject of study is electoral systems, elections, or voters." The "ambiguity about what const.i.tutes an 'individual' (hence 'case') can only be dispelled by not looking at concrete ent.i.ties but at the measures made of them. On this basis, a 'case' can be defined technically as a phenomenon for which we report and interpret only a single measure on any pertinent variable." The only difference in our usage is that since Eckstein's article, scholars have continued to use the word "case" to refer to a full case study, which still has a fairly imprecise definition. Therefore, wherever possible we use the word "case" as most writers do and reserve the word "observation" to refer to measures of one or more variables on exactly one unit.

We attempt in the rest of this chapter to show how concepts like variables and units can increase the clarity of our thinking about research design even when it may be inappropriate to rely on quant.i.tative measures to summarize the information at our disposal. The question we pose is: How can we make descriptive inferences about "history as it really was" without getting lost in a sea of irrelevant detail? In other words, how can we sort out the essential from the ephemeral?

2.5 SUMMARIZING HISTORICAL DETAIL.

After data are collected, the first step in any a.n.a.lysis is to provide summaries of the data. Summaries describe what may be a large amount of data, but they are not directly related to inference. Since we are ultimately interested in generalization and explanation, a summary of the facts to be explained is usually a good place to start but is not a sufficient goal of social science scholarship.

Summarization is necessary. We can never tell "all we know" about any set of events; it would be meaningless to try to do so. Good historians understand which events were crucial, and therefore construct accounts that emphasize essentials rather than digressions. To understand European history during the first fifteen years of the nineteenth century, we may well need to understand the principles of military strategy as Napoleon understood them, or even to know what his army ate if it "traveled on its stomach," but it may be irrelevant to know the color of Napoleon's hair or whether he preferred fried to boiled eggs. Good historical writing includes, although it may not be limited to, a compressed verbal summary of a welter of historical detail.

Our model of the process of summarizing historical detail is a statistic. A statistic is an expression of data in abbreviated form. Its purpose is to display the appropriate characteristics of the data in a convenient format.17 For example, one statistic is the sample mean, or average:

whereis a convenient way of writing y1 + y2 + y3 + ... + yn. Another statistic is the sample maximum, labeled ymax:.

(2.1).

The sample mean of the four incomes from the example in section 2.4 ($9,000, $22,000, $21,000, and $54,292) is $26,573. The sample maximum is $54,292. We can summarize the original data containing four numbers with these two numbers representing the sample mean and maximum. We can also calculate other sample characteristics, such as the minimum, median, mode, or variance.

Each summary in this model reduces all the data (four numbers in this simple example, or our knowledge of some aspect of European history in the other) to a single number. Communicating with summaries is often easier and more meaningful to a reader than using all the original data. Of course, if we had only four numbers in a data set, then it would make little sense to use five different summaries; presenting the four original numbers would be simpler. Interpreting a statistic is generally easier than understanding the entire data set, but we necessarily lose information by describing a large set of numbers with only a few.

What rules govern the summary of historical detail? The first rule is that summaries should focus on the outcomes that we wish to describe or explain. If we were interested in the growth of the average international organization, we would not be wise to focus on the United Nations; but if we were concerned about the size distribution of international organizations, from big to small, the United Nations would surely be one of the units on which we ought to concentrate. The United Nations is not a representative organization, but it is an important one. In statistical terms, to investigate the typical international organization, we would examine mean values (of budgets, tasks, memberships, etc.), but to understand the range of activity, we would want to examine the variance. A second, equally obvious precept is that a summary must simplify the information at our disposal. In quant.i.tative terms, this rule means that we should always use fewer summary statistics than units in the original data, otherwise, we could as easily present all the original data without any summary at all.18 Our summary should also be sufficiently simple that it can be understood by our audience. No phenomenon can be summarized perfectly, so standards of adequacy must depend on our purposes and on the audience. For example,a scientific paper on wars and alliances might include data involving 10,000 observations. In such a paper, summaries of the data using fifty numbers might be justified; however, even for an expert, fifty separate indicators might be incomprehensible without some further summary. For a lecture on the subject to an undergraduate cla.s.s, three charts might be superior.

2.6 DESCRIPTIVE INFERENCE.

Descriptive inference is the process of understanding an un.o.bserved phenomenon on the basis of a set of observations. For example, we may be interested in understanding variations in the district vote for the Conservative, Labour, and Social Democratic parties in Britain in 1979. We presumably have some hypotheses to evaluate; however, what we actually observe is 650 district elections to the House of Commons in that year.

Naively, we might think that we were directly observing the electoral strength of the Conservatives by recording their share of the vote by district and their overall share of seats. But a certain degree of randomness or unpredictability is inherent in politics, as in all of social life and all of scientific inquiry.19 Suppose that in a sudden fit of absentmindedness (or in deference to social science) the British Parliament had agreed to elections every week during 1979 and suppose (counter-factually) that these elections were independent of one another. Even if the underlying support for the Conservatives remained constant, each weekly replication would not produce the same number of votes for each party in each district. The weather might change, epidemics might break out, vacations might be taken-all these occurrences would affect voter turnout and electoral results. Additionally, fortuitous events might happen in the international environment, or scandals might reach the ma.s.s media; even if these had no long-term significance, they could affect the weekly results. Thus, numerous, transitory events could effect slightly different sets of election returns. Our observation of any one election would not be a perfect measure of Conservative strength after all.

As another example, suppose we are interested in the degree of conflict between Israelis (police and residents) and Palestinians in communities on the Israeli-occupied West Bank of the Jordan River. Official reports by both sides seem suspect or are censored, so we decide to conduct our own study. Perhaps we can ascertain the general level of conflict in different communities by intensive interviews or partic.i.p.ationin family or group events. If we do this for a week in each community, our conclusions about the level of conflict in each one will be a function in part of whatever chance events occur the week we happen to visit. Even if we conduct the study over a year, we still will not perfectly know the true level of conflict, even though our uncertainty about it will drop.

In these examples, the variance in the Conservative vote across districts or the variance in conflict between West Bank communities can be conceptualized as arising from two separate factors: systematic and nonsystematic differences. Systematic differences in our voter example include fundamental and predictable characteristics of the districts, such as differences in ideology, in income, in campaign organization, or in traditional support for each of the parties. In hypothetical weekly replications of the same elections, systematic differences would persist, but the nonsytematic differences such as turnout variations due to the weather, would vary. In our West Bank example, systematic differences would include the deep cultural differences between Israelis and Palestinians, mutual knowledge of each other, and geographic patterns of residential housing segregation. If we could start our observation week a dozen different times, these systematic differences between communities would continue to affect the observed level of conflict. However, nonsystematic differences, such as terrorist incidents or instances of Israeli police brutality, would not be predictable and would only affect the week in which they happened to occur. With appropriate inferential techniques, we can usually learn about the nature of systematic differences even with the ambiguity that occurs in one set of real data due to nonsystematic, or random, differences.

Thus, one of the fundamental goals of inference is to distinguish the systematic component from the nonsystematic component of the phenomena we study. The systematic component is not more important than the nonsystematic component, and our attention should not be focused on one to the exclusion of the other. However, distinguishing between the two is an essential task of social science. One way to think about inference is to regard the data set we compile as only one of many possible data sets-just as the actual 1979 British election returns const.i.tute only one of many possible sets of results for different hypothetical days on which elections could have been held, or just as our one week of observation in one small community is one of many possible weeks.

In descriptive inference, we seek to understand the degree to which our observations reflect either typical phenomena or outliers. Had the 1979 British elections occurred during a flu epidemic that swept through working-cla.s.s houses but tended to spare the rich, our observations might be rather poor measures of underlying Conservative strength, precisely because the nonsystematic, chance element in the data would tend to overwhelm or distort the systematic element. If our observation week had occurred immediately after the Israeli invasion of Southern Lebanon, we would similarly not expect results that are indicative of what usually happens on the West Bank.

The political world is theoretically capable of producing multiple data sets for every problem but does not always follow the needs of social scientists. We are usually only fortunate enough to observe one set of data. For purposes of a model, we will let this one set of data be represented by one variable y (say, the vote for Labor) measured over all n = 650 units (districts): y1, y2, ... , yn (for example, y1 might be 23,562 people voting for Labor in district 1). The set of observations which we label y is a realized variable. Its values vary over the n units. In addition, we define Y as a random variable because it varies randomly across hypothetical replications of the same election. Thus, y5 is the number of people voting for Labor in district 5, and Y5 is the random variable representing the vote across many hypothetical elections that could have been held in district 5 under essentially the same conditions. The observed votes for the Labor party in the one sample we observe, y1, y2, ... , yn, differ across const.i.tuencies because of systematic and random factors. That is, to distinguish the two forms of "variables," we often use the term realized variable to refer to y and random variable to refer to Y.

The same arrangement applies to our qualitative example. We would have no hope or desire of quantifying the level of tension between Israelis and Palestinians, in part because "conflict" is a complicated issue that involves the feelings of numerous individuals, organizational oppositions, ideological conflicts, and many other features. In this situation, y5 is a realized variable which stands for the total conflict observed during our week in the fifth community, say El-Bireh.20 The random variable 5 represents both what we observe in El-Bireh and what we could have observed; the randomness comes from the variation in chance events over the possible weeks we could have chosen to observe.21 One goal of inference is to learn about systematic features of the random variables 1, ... , n. (Note the contradictory, but standard, terminology: although in general we wish to distinguish systematic from nonsystematic components in our data, in a specific case we wish to take a random variable and extract its systematic features.) For example, we might wish to know the expected value of the Labor vote in district 5 (the average Labor vote 5 across a large number of hypothetical elections in this district). Since this is a systematic feature of the underlying electoral system, the expected value is of considerable interest to social scientists. In contrast, the Labor vote in one observed election, 5, is of considerably less long-term interest since it is a function of systematic features and random error.22 The expected value (one feature of the systematic component) in the fifth West Bank community, El-Bireh, is expressed formally as follows:E(5) = 5

where E() is the expected value operation, producing the average across an infinite number of hypothetical replications of the week we observe in community 5, El-Bireh. The parameter 5 (the Greek letter mu with a subscript 5) represents the answer to the expected value calculation (a level of conflict between Palestinians and Israelis) for community 5. This parameter is part of our model for a systematic feature of the random variable 5. One might use the observed level of conflict, y5, as an estimate of 5, but because y5 contains many chance elements along with information about this systematic feature, better estimators usually exist (see section 2.7).

Another systematic feature of these random variables which we might wish to know is the level of conflict in the average West Bank community: (2.2).

One estimator of might be the average of the observed levels of conflict across all the communities studied,, but other estimators for this systematic feature exist, too. (Note that the same summary of data in our discussion of summarizing historical detail from section 2.5 is used for the purpose of estimating a descriptive inference.) Other systematic features of the random variables include the variance and a variety of causal parameters introduced in section 3.1.

Still another systematic feature of these random variables that might be of interest is the variation in the level of conflict within a communityeven when the systematic features do not change: the extent to which observations over different weeks (different hypothetical realizations of the same random variable) produce divergent results. This is, in other words, the size of the nonsystematic component. Formally, this is calculated for a single community by using the variance (instead of the expectation): (2.3).

where 2 (the Greek letter sigma) denotes the result of applying the variance operator to the random variable i. Living in a West Bank community with a high level of conflict between Israelis and Palestinians would not be pleasant, but living in a community with a high variance, and thus unpredictability, might be worse. In any event, both may be of considerable interest for scholarly researchers.

To understand these issues better, we distinguish two fundamental views of random variation.23 These two perspectives are extremes on a continuum. Although significant numbers of scholars can be found who are comfortable with each extreme, most political scientists have views somewhere between the two.

Perspective 1: A Probabilistic World. Random variation exists in nature and the social and political worlds and can never be eliminated. Even if we measured all variables without error, collected a census (rather than only a sample) of data, and included every conceivable explanatory variable, our a.n.a.lyses would still never generate perfect predictions. A researcher can divide the world into apparently systematic and apparently nonsystematic components and often improve on predictions, but nothing a researcher does to a.n.a.lyze data can have any effect on reducing the fundamental amount of nonsystematic variation existing in various parts of the empirical world.

Perspective 2: A Deterministic World. Random variation is only that portion of the world for which we have no explanation. The division between systematic and stochastic variation is imposed by the a.n.a.lyst and depends on what explanatory variables are available and included in the a.n.a.lysis. Given the right explanatory variables, the world is entirely predictable.

These differing perspectives produce various ambiguities in the inferences in different fields of inquiry.24 However, for most purposes these two perspectives can be regarded as observationally equivalent. This is especially true if we a.s.sume, under Perspective 2, that at least some explanatory variables remain unknown. Thus, observational equivalence occurs when these unknown explanatory variables in Perspective 2 become the interpretation for the random variation in Perspective 1. Because of the lack of any observable implications with which to distinguish between them, a choice between the two perspectives depends on faith or belief rather than on empirical verification.

As another example, with both perspectives, distinguishing whether a particular political or social event is the result of a systematic or nonsystematic process depends upon the choices of the researcher. From the point of view of Perspective 1, we may tentatively cla.s.sify an effect as systematic or nonsystematic. But unless we can find another set of data (or even just another case) to check for the persistence of an effect or pattern, it is very difficult to make the right judgment.

From the extreme version of Perspective 2, we can do no more than describe the data-"incorrectly" judging an event as stochastic or systematic is impossible or irrelevant. A more realistic version of this perspective admits to Perspective 1's correct or incorrect attribution of a pattern as random or systematic, but it allows us some lat.i.tude in deciding what will be subject to examination in any particular study and what will remain unexplained. In this way, we begin any a.n.a.lysis with all observations being the result of "nonsystematic" forces. Our job is then to provide evidence that particular events or processes are the result of systematic forces. Whether an unexplained event or process is a truly random occurrence or just the result of as yet unidentified explanatory variables is left as a subject for future research.

This argument applies with equal force to qualitative and quant.i.tative researchers. Qualitative research is often historical, but it is of most use as social science when it is also explicitly inferential. To conceptualize the random variables from which observations are generated and to attempt to estimate their systematic features-rather than merely summarizing the historical detail-does not require large-scale data collections. Indeed, one mark of a good historian is the ability to distinguish systematic aspects of the situation being described from idiosyncratic ones. This argument for descriptive inference, therefore, is certainly not a criticism of case studies or historical work. Instead, any kind of social science research should satisfy the basic principles of inference discussed in this book. Finding evidence of systematic features will be more difficult with some kinds of evidence, but it is no less important.

As an example of problems of descriptive inference in historical research, suppose that we are interested in the outcomes of U.S.-Soviet summit meetings between 1955 and 1990. Our ultimate purpose is to answer a causal question: under what conditions and to what extent did the summits lead to increased cooperation? Answering that question requires resolving a number of difficult issues of causal a.n.a.lysis, particularly those involving the direction of causality among a set of systematically related variables.25 In this section, however, we restrict ourselves to problems of descriptive inference.

Let us suppose that we have devised a way of a.s.sessing-through historical a.n.a.lysis, surveying experts, counting "cooperative" and "conflictual" events or a combination of these measurement techniques-the extent to which summits were followed by increased superpower cooperation. And we have some hypotheses about the conditions for increased cooperation-conditions that concern shifts in power, electoral cycles in the United States, economic conditions in each country, and the extent to which previous expectations on both sides have been fulfilled. Suppose also that we hope to explain the underlying level of cooperation in each year, and to a.s.sociate it somehow with the presence or absence of a summit meeting in the previous period, as well as with our other explanatory factors.

What we observe (even if our indices of cooperation are perfect) is only the degree of cooperation actually occurring in each year. If we observe high levels of cooperation in years following summit meetings, we do not know without further study whether the summits and subsequent cooperation are systematically related to one another. With a small number of observations, it could be that the a.s.sociation between summits and cooperation reflects randomness due to fundamental uncertainty (good or bad luck under Perspective 1) or to as yet unidentified explanatory variables (under Perspective 2). Examples of such unidentified explanatory variables include weather fluctuations leading to crop failures in the Soviet Union, shifts in the military balance, or leadership changes, all of which could account for changes in the extent of cooperation. If identified, these variables are alternative explanations-omitted variables that could be collected or examined to a.s.sess their influence on the summit outcome. If unidentified, these variables may be treated as nonsystematic events that could account for the observed high degree of superpower cooperation. To provide evidence against the possibility that random events (unidentified explanatory variables) account for the observed cooperation, we might look at many other years. Since random events and processes are by definition not persistent, they will be extremely unlikely to produce differential cooperation in years with and without superpower summits. Once again, we are led to the conclusion that only repeated tests in different contexts (years, in this case) enable us to decide whether to define a pattern as systematic or just due to the transient consequences of random processes.

Distinguishing systematic from nonsystematic processes is often difficult. From the perspective of social science, a flu epidemic that strikes working-cla.s.s voters more heavily than middle-cla.s.s ones is an unpredictable (nonsystematic) event that in one hypothetical replication of the 1979 election would decrease the Labor vote. But a persistent pattern of cla.s.s differences in the incidence of a disabling illness would be a systematic effect lowering the average level of Labor voting across many replications.