From Ragin Charles, The Comparative Method, University of California Press, 1987.

Behind every research effort are general goals that extend beyond the specific goals of the study at hand. These goals are seldom stated explicitly, and they are rarely examined. The goal of most comparative social science is to produce explanations of macrosocial phenomena that are general but also show an appreciation of complexity. In other words, comparative social scientists recognize that a good social scientific explanation is relevant to a variety of cases but at the same time they recognize that social phenomena are complex and that a general explanation is a partial explanation at best. Thus, generality and complexity often compete with each other, even in a single study. An appreciation of complexity sacrifices generality; an emphasis on generality encourages a neglect of complexity. It is difficult to have both.

In the case-oriented strategies it is clear that the goal of appreciating complexity is given precedence over the goal of achieving generality. Invariant statements relevant to more narrowly defined categories of phenomena, for example, are preferred to probabilistic statements relevant to broadly defined categories. In variable-oriented strategies, by contrast, generality is given precedence over complexity. This is because investigators who use this approach are more interested in testing propositions derived from general theories than they are in unraveling the historical conditions that produce different historical outcomes. The case-oriented approach uses theory to aid historical interpretation and to guide the identification of important causal factors; the variable-oriented strategy, by contrast, usually tests hypotheses derived from theory.

When a theory is tested, it is necessary for the investigator to amass a substantial quantity of relevant evidence and to apply analytic techniques that are conservative by design. Because little attempt is made to gain concrete knowledge about specific cases or specific categories of historical outcomes (beyond that necessary to code variables), investigators cast a wide net; they avoid any unnecessary restriction of scope. Typically, a variable-oriented study begins by specifying the hypothesis to be tested and then delineating the widest possible population of relevant observations. The wider this population, the better. Not only does a wide population provide a basis for a more exacting test, but it also gives the investigator the opportunity to demonstrate the breadth of an argument.

In this approach, data on social units provide snapshots of instances of structural processes. Thus, structural features and their interrelations can be represented in terms of variables and inter-correlations, By studying the patterns that emerge from such snapshots of structural processes (that is, by studying correlations between variables), it is possible to derive empirical generalizations about structural processes relevant to large numbers of macrosocial units (usually nation-states). Thus, explanations in the variable-oriented strategy usually cite features of social structure.

The emphasis of the variable-oriented strategy on general features of social structure, conceived as variables, and on testing theory, as opposed to using theory to interpret cases historically, has allowed importation of quantitative methods, especially multiple regression techniques, from mainstream social science. These are powerful techniques. They allow investigators to make broad statements about cross-societal patterns on the basis of analyses of relatively small data sets (The typical quantitative cross-national data set contains fewer than eighty cases and ten variables - a tiny data set by the standards of mainstream social science.) Investigators are able to formulate broad generalizations about such important issues as international inequality on the basis of analyses of such data.

In the typical multivariate statistical analysis, the investigator attempts to assess the effect of an independent variable on a dependent variable net of the effects of control variables (that is, other independent variables). The basic idea is that even though the independent and control variables cannot be manipulated, as they are in an experiment, it is possible to subtract the effects of control variables on the dependent variable when estimating the effect of a specific causal variable.

In most statistical analyses, the effect of a control variable is its average effect on the dependent variable, across all cases, net of the effects of other variables. The subtraction of effects central to statistical control is a purely mechanical operation predicated on simplifying assumptions. It is assumed in multiple regression, for example, that a variable's effect is the same in each case - that a one-unit change in an independent variable has the same effect on the dependent variable regardless of context, that is, regardless of the values of the other independent variables. This makes it possible to estimate and then remove a variable's effect by simple subtraction. The result is a dependent variable whose values have been "corrected" for the effects of one or more independent variables.

The results of Bornschier and others (1978), for example, show that underdeveloped countries with higher levels of domestic investment grow faster. Specifically, for every percentage point increase in capital formation (computed as a percentage of GNP) underdeveloped countries increase their economic growth rates by about three-hundredths of a percentage point. Armed with this knowledge, it is possible to correct economic growth rates for the effects of domestic investment. To remove the effect of domestic investment, it is necessary simply to subtract the quantity - capital formation as a percentage of GNP multiplied by 0.03 - from each country's economic growth rate. The resulting values show economic growth rates corrected for the effect of domestic investment.

Note that the comparisons that are performed in statistical analyses such as the one described here involve contrasts between cases' scores on the relevant variables with average or mean scores. This makes it possible to compute simple and partial correlations and to calculate the relevant effects. No attempt is made to compare cases directly to each other. Only broad patterns of covariation are assessed. When quantitatively oriented researchers examine individual cases, it is usually by plotting the residuals from a multivariate regression analysis and then devoting special attention to the cases that deviate strongly from predicted patterns. Thus, the particularity of a case is defined relative to a general pattern specified through multivariate analysis.

Consider a more elaborate example of variable-oriented research. An investigator might wish to test the argument that the presence of democratic institutions gives polities greater longevity. To test the effect of the presence of democratic institutions on years of polity existence (measured as number of years without a major regime change; see Gurr 1974), it would be necessary to remove the effect of confounding variables in order to have a proper assessment of the effect of democratic institutions. For example, wealth of the nation-state might correlate with the presence of democratic institutions and also increase polity longevity. The effect of wealth, therefore, should be removed when estimating the effect of democratic institutions. Another factor which might increase polity longevity and correlate with the presence of democratic institutions is scope of state action. Scope of state action refers to the government's degree of involvement in the lives of its subjects. Because many polities with democratic institutions have states that are broad in scope, and scope is a plausible cause of longevity, the effect of scope also should be removed. And other causes of polity longevity, including such factors as period of initial polity formation, that might be confounded with the presence of democratic institutions could be identified. Measures of all such factors should be included in the statistical analysis of polity longevity and should be controlled statistically when the assessment of the effect ofdemocratic institutions is made.

Notthat to estimate these effects it is not necessary to have data on all logically possible combinations of values of the independent variables. (This is impossible, of course, if the measures are continuous.) This is one of the major attractions of statistical control. With these techniques it is possible to infer a variable's effect in all contexts simply by assessing its effect in existing settings. Thus, broad claims can be made on the basis of data that are very incomplete relative to the experimental design standard.

The mechanics of statistical control are relatively straightforward. Effect parameters for independent variables are calculated so that the correlation of the dependent variable with an additive (or, in a few studies, logarithmic) combination of the independent variables is maximized. The effect parameters (say, standardized regression coefficients) indicate the relative importance of the different independent variables. The larger the effect parameter, the more important the variable. If the control variables are the most important variables in the additive combination of independent variables, then the variable of theoretical interest (in this example, presence of democratic institutions) may have no significant effect. If this occurs, the investigator may conclude that it is not an important cause of variation in the phenomenon of interest.

A statistical analysis of polity longevity might show that the presence of democratic institutions - on the average, controlling for wealth of the nation-state, the scope of its government, and its date of origin - increases polity longevity by five years. The investigator would conclude that democracy contributes moderately to longevity. The relative impact of the three control variables on the effect of democratic institutions can be assessed by comparing the estimated effect of the variable of theoretical interest in the absence of the controls. For example, if an analysis excluding control variables were to show that the presence of democratic institutions increases polity longevity by twenty-five years, the investigator might argue that much of the apparent effect of democratic institutions on longevity is actually due to variables it is confounded with, such as the wealth of nations.

This example illustrates the broad sweep afforded by a multivariate statistical approach. By making the appropriate simplifying assumptions about unit changes and additivity, investigators can use methods that digest data on many countries and culminate in general statements of empirical regularity.

But is an estimate of population parameters, per se, desirable? The estimation of such parameters is powerfully influenced by the relative frequency of different types of cases. Suppose, for example, that the data set contains a large number of (1) poor, recent, democratic polities with governments of wide scope and (2) rich, democratic polities in countries from a much earlier period of initial formation, with governments of narrower scope, and that both of these polity types are relatively short-lived.(Remember that most countries have experienced aseries of polities.) The estimate of the effect of democratic institutions on polity longevity would be negative. This finding would be obtained regardless of other patterns in the data. (Other patterns might be revealed, of course, if the investigator were to examine residuals.) Paired comparisons, such as those used in case-oriented investigations, of the remaining cases might show, however, that the presence of democratic institutions consistently increases longevity in a variety of settings. The much greater relative frequency of the first two types mentioned above would statistically outweigh the positive contributions of democratic institutions in other types of settings.

To the extent that comparative researchers are more interested in the effect of a variable in different settings or in different types of cases - and less interested in its average, net effect in a population of observations techniques of statistical control produce findings that are of unknown value. Use of these techniques, therefore, must be predicated on an interest in population parameters - the average effect of a cause in a theoretically defined set of observations.

An investigator might determine, for example, that the presence of X1 increases the probability of Y by 10 percent, while the presence of X2 increases the probability of Y by 15 percent, while X3, and X4 have no effect on the probability of Y. Together X1 and X2 might increase the probability of Y by 25 percent. This goal of estimating each cause's independent contribution to the probability of Y is inconsistent with the goal of determining the different combinations of conditions that cause Y. An examination of combinations might show, for example, that X1 causes Y only when it coincides with both X3 and X4, and that X2 causes Y only when it coincides with an absence of X4, and that these two patterns are invariant. Estimation of the independent contribution of different causes to the probability of an outcome does not address concerns for multiple conjunctural causation.

From the perspective of mainstream social science the first two problems presented above plague all nonexperimental investigations and cannot be addressed within a statistical framework. Multivariate techniques were developed in the social sciences precisely because social phenomena are difficult to study experimentally, and naturally occurring data that approximate data resulting from experimental designs are extremely rare. Techniques of statistical control, therefore, should not be criticized because the data sets analyzed by social scientists are deficient. In other words, techniques of statistical control should not be criticized for their failure to address problems they were designed to circumvent.

The remaining deficiencies of multivariate statistical control outlined above can be remedied through more sophisticated techniques. However, the data used by comparativists often are not strong enough to permit these remedies. For example, the third problem listed above concerns the likelihood that a certain independent variable will have different effects on the outcome variable depending on the values of other independent variables. In short, the effect of a variable (say, the effect of democratic institutions on polity longevity) may depend on context (whether the country is rich or poor, whether its government is active in many spheres or few, and so on).

Most experts in multivariate techniques would suggest that researchers who suspect such patterns of contextuality test for them by using interaction models. These models allow investigators to assess the different effects of one variable on another within categories of a third variable. In other words, experts would argue that investigators should use statistical models that do not assume additivity.

Most data used by comparative social scientists, even data used by comparativists devoted to the use of techniques of statistical control, do not meet these requirements. For example, the use of interaction models to examine multiple conjunctural causation is difficult because of an insufficiency of cases and because the interaction terms used to assess the intersection of different causal conditions usually are highly collinear with each other. An examination of different combinations of six different causal conditions, for example, would require an equation with sixty-four terms, many of which would be highly collinear because of their common component terms. Even if such an equation could be estimated, it would be very difficult to decipher because the coefficients could be interpreted only in groups. The data used in most comparative investigations are simply not strong enough to support tests for complex patterns of interaction. (Of course, roughly parallel problems exist in case-oriented research, where there is a corresponding limited variety of cases).

The fourth problem with statistical control mentioned above concerns the distorting effect that the relative frequency of different types of cases has on the estimation of population parameters. This problem can also be addressed with more sophisticated statistical techniques. One simple way to address this issue is to estimate different models for different sub-populations and test the statistical significance of the differences obtained. In an analysis of polity longevity, for example, an investigator might hypothesize that polities created before World War II are qualitatively different from polities created after World War II and that, accordingly, different models of polity longevity should estimated for the two sub-populations. The population of polities also could be divin other ways, depending on which sub-population differences concern the investigator. (In essence, this is a type of interaction model.)

Again, however, the fact that most quantitative cross-national studies have relatively few cases (around fifty to one hundred) discourages investigators from splitting their samples. The greater the specificity of an argument, the fewer the number of cases available for statistical analysis. These limitations discourage the kind of specificity associated with sample splitting. Furthermore, some methodologists argue that it is necessary for the investigator to specify sub-populations in advance of data analysis. Sub-population differences do surface in the course of variable-oriented analyses as they do in case-oriented studies (where the search for invariance forces investigators to differentiate types), but there are strong pressures on the variable-oriented researcher to keep sample splitting to a minimum.

Thus, while it is possible to answer the criticisms of statistical control and to point to more sophisticated techniques, investigator's typically cannot take advantage of these techniques. Investigators are not limited to simple, linear additive models; in practice, however, they usually stick fairly close to such formulations. If any tests for interaction or for population differences are performed, they are very simple in nature. This is because most data sets used by compararivists place serious constraints on statistical sophistication.

Techniques of statistical control, and multivariate analysis in general, exercise a powerful influence on the dialogue of ideas and evidence in quantitative cross-national research. The basic building blocks of this strategy are variables and their intercorrelation. Discussions of specification issues, therefore, dominate the dialogue of ideas and evidence. Is the theory to be tested properly operationalized? Have all the appropriate control variables and competing theories been specified? Is the population of relevant observations accurately delineated? Is the sample appropriate? Has there been any unwarranted restriction of scope? Does an adequate basis for generalization exist? Are the functional forms correct? Does a plot of the residuals show that anything major has been missed? In short, the methodological issues that dominate variable-oriented investigations converge with those of mainstream social science.

How do investigators who use the variable-oriented strategy respond to rejections of initial hypotheses? In case-oriented studies, investigators typically propose more intricate conjunctural arguments or they attempt to differentiate subtypes of the phenomenon of interest and elaborate subtype - specific causal arguments. In variable-oriented studies, the response usually is quite different. Formally at least, a rejection is a rejection, and the logic of hypothesis testing central to the variable-oriented approach dictates "failure to reject" the null hypothesis. In practice, however, investigators usually try different specifications of the same argument in the hope that one will support the favored theory. Usually, this process involves adding or subtracting control variables, or re-conceptualizing the key concepts of the theoretical model that is being tested, or devising new measures, or redefining control variables as theoretical variables. In short, the dialogue usually stays focused on variables and their interrelations.

Sometimes investigators using the variable-oriented strategy follow the lead of case-oriented investigators and differentiate subtypes or construct conjunctural arguments. But the pressure to use these strategies is less acute because there is no expectation that the research will culminate with an identification of invariant relationships. In any event, these case-oriented techniques sacrifice precious degrees of freedom and weaken the variable-oriented approach. Differentiating subtypes entails sample splitting and a consequent reduction of the total degrees of freedom. Likewise, constructing elaborate interaction models to test conjunctural arguments exacts a severe toll on degrees of freedom and creates an indecipherable mass of multi-collinearity. The number of terms in an equation increases exponentially as the complexity of the interaction terms to be tested increases.

At this point, the limitations of the variable-oriented strategy converge morphologically with the limitations of the case-oriented strategy in a peculiar manner. Recall that the case-oriented strategy, because it is holistic, becomes more difficult to use as the number of cases increases. The volume of comparison explodes as the number of empirical and hypothetical cases is expanded. The method simply becomes unwieldy. A morphologically parallel problem incapacitates the variable-oriented strategy. As the complexity of the causal argument to be tested increases, intractable methodological problems are introduced. Complex conjunctural arguments cannot be tested, nor can subtypes be differentiated, in the absence of sufficient cases to permit statistical manipulation. The assumptions of statistical models become more strained in the face of intricate causal arguments, given a restricted sample size. In some investigations the number of parameters to be estimated can easily exceed the number of cases, and the possibility of estimating parameters is closed off.

The next reading assignment discusses strategies, which combine the two main approaches. Combined strategies have emerged in part because of the limitations inherent in these two approaches.

Bornschier, Volker et al., "Cross-national Evidence of the Effects of Foreign Investment and Aid on Economic Growth and Inequality", American Journal of Sociology, Vol. 84, 1978, pp. 651-683.

Gurr, Ted Robert, "Persistence and Change in Political Systems, 1800-1971" American Political Science Review, Vol. 68, 1974, pp. 1482-1504.

Liberson, Stanley, Making it Count: The Improvement of Social Research and Theory, Berkeley, University of California Press.

Ragin, Charles and Zaret David, "Theory and Method in Comparative Research: Two Strategies", Social Forces, Vol. 61, 1983, pp. 731-754.