A typology is a multidimensional classification. The study of typological procedures is impeded by the use of a plethora of terms, some of which are used interchangeably. ”Classification” can be defined as the grouping of entities on the basis of similarity. For example, humans can be classified into female and male. A related term is ”taxonomy.” According to Simpson (1961, p. 11), taxonomy ”is the theoretical study of classification, including its bases, principles, procedures, and rules.” Interestingly, the term ”classification” has two meanings: One can speak of both the process of classification and its end product, a classification. The terms ”classification,” ”typology,” and ”taxonomy” are all used widely and somewhat interchangeably in sociology.
Any classification must be mutually exclusive and exhaustive. This requires that there be only one cell for each case. For example, if humans are being classified by sex, this requires that every case be placed in a cell (either male or female) but that no case be placed in more than one cell (no intermediate cases are allowed). It is assumed that the bases or dimensions for classification (such as sex) are clear and important (see Tiryakian 1968).
A type is one cell in a full typology. In sociology, emphasis often has been placed on one or a few types rather than on the full typology. The study of types developed largely as a verbal tradition in sociology and lately has been merged with a more recently developed quantitative approach.
In the verbal tradition, types were often defined as mental constructs or concepts, in contrast to empirically derived entities. Stinchcombe (1968, p. 43, original emphasis) says that ”a type concept in scientific discourse is a concept which is constructed out of a combination of the values of several variables.” Lazarsfeld (1937, p. 120) says that ”one is safe in saying that the concept of type is always used in referring to special compounds of attributes.” The variables that combine to form a type must be correlated or ”connected to each other” (Stinchcombe 1968, pp. 44-45).
An important function of a type is to serve as a criterion point (for comparative purposes) for the study of other types or empirical phenomena. In this case, only a single type is formulated. The most famous single-type formulation is Weber’s ideal type:
An ideal type is formed by the one-sided accentuation of one or more points of view. . . In its conceptual purity, this mental construct [Gedankenbild] cannot be found empirically anywhere in reality. It is a utopia. Historical research faces the task of determining in each individual case the extent to which this ideal-construct approximates to or diverges from reality, to what extent for example, the economic structure of a certain city is to be classified as a “city economy ” (1947, p. 90, original emphasis)
This strategy has been criticized. Martindale is startled by the suggestion that ”we compare actual individuals with the (admittedly imaginary) ideal typical individuals to see how much they deviate from them. This is nothing but a form of intellectual acrobatics, for actual individuals ought to deviate from the ideal type just as much as one made them deviate in the first place” (1960, p. 382).
Seizing on Weber’s statement that the pure ideal type ”cannot be found empirically anywhere in reality,” critics view the ideal type as hypothetical and thus without a fixed position, rendering it useless as a criterion point. A more realistic interpretation is that the ideal type represents a type that could be found empirically; it is simply that the purest case is the one most useful as a criterion, and this case is unlikely to be found empirically. As an example, a proof specimen of a coin is the best criterion for classifying or grading other coins, but it is not found empirically in the sense of being in circulation. If it were circulated, its features soon would be worn to the extent that its value for comparison with other coins would be greatly diminished.
The strategy of the ideal type is a sound one. Its logic is simple, and the confusion surrounding it is unfortunate, perhaps being due in part to the translation of Weber’s work. The genius of the ideal type lies in its parsimony. Instead of using a large full typology (say, of 144 cells, many of which may turn out to be empirically null or empty), a researcher can utilize a single ideal type. Then, instead of dealing needlessly with many null cells, the researcher need only fill in cells for which there are actual empirical cases and only as those cases are encountered. The ideal type is an accentuated or magnified version (or purest form) of the type. Although rarely found empirically in this pure form, the ideal type serves as a good comparison point. It usually represents the highest value on each of the intercorrelated variables or the end point of the continuum. While one could use the middle of the continuum as a referent (just as one uses the mean or median), it is convenient and perhaps clearer to use the end point (just as one measures from the end of a ruler rather than from its middle or another intermediate point).
Another single type that is used as a criterion is the constructed type. McKinney (1966, p. 3, original emphasis) defines the constructed type as ”a purposive, planned selection, abstraction, combination, and (sometimes) accentuation of a set of criteria with empirical referents that serves as a basis for comparison of empirical cases.” The constructed type is a more general form of the ideal type.
In addition to formulations that use a single type, there are formulations that use two or more types. One strategy involves the use of two ”polar” types (as in the North and South poles). These types serve as two bracketing criteria for the comparison of cases. A famous set of types is Tonnies’s (1957) Gemeinschaft and Gesellschaft (”community” and ”society”). Another is introvert and extrovert. Still others are primary and secondary groups and localistic and cosmopolitan communities (see McKinney 1966, p. 101, for these and other examples).
SUBSTRUCTION
One problem with the common practice of using only a single type or a few types is that the underlying correlated dimensions on which they are based may not be clear. In some cases, it is possible to make these dimensions clear and extend them all to form a property space or attribute space; a set of axes representing the full range of values on each dimension. Then the existence of other potential related types that were not originally formulated, can be discerned. This process of extending the full property space and the resulting full typology from a single type or a few types is called substruction and was developed by Lazarsfeld (1937; Barton 1955). As an example, Barton (1955, pp. 51-52) performed a substruction in which the attributes underlying the four types of folkways, mores, law, and custom were extended to form a full property space. Barton found three underlying dimensions of the four types (”how originated,” ”how enforced,” and ”strength of group feeling”) and combined them to form the property space.
REDUCTION
The opposite of substruction is reduction. Reduction is used when one has a full typology that is unmanageable because of its size. The three basic forms of reduction presented by Lazarsfeld (1937, p. 127) are functional, arbitrary numerical, and pragmatic. Lazarsfeld’s functional reduction consists of discarding from the typology all empirically null and thus unnecessary cells.
The second form of reduction is arbitrary numerical. Lazarsfeld (1937, p. 128) provides an example: In constructing an index of housing conditions, one might weight plumbing without central heat or a refrigerator as being equal to the other two without plumbing. Coding the existence of an attribute by 1 and the lack of it by 0 and taking variables in this order (plumbing, central heat, refrigerator), Lazarsfeld is saying that (1, 0, 0) = (0, 1, 1). Thus, two previously different three-dimensional cells are equated and reduced to one.
Lazarsfeld’s third form of reduction is pragmatic reduction. It consists of collapsing contiguous cells together to make one larger (but generally more heterogeneous) cell. As Lazarsfeld (1937, p. 128) says, ”in the case of pragmatic reduction, certain groups of combinations are contracted to one class in view of the research purpose.” For examples of these three forms of reduction, see Bailey (1973).
With Lazarsfeld’s rigorous work as a notable exception, it can be said that most work in the typological tradition has been qualitative. Blalock, commenting on McKinney’s (1966) constructive typology, says:
He [McKinney] also claims that there is nothing inherently anti-quantitative in the use of typologies. He notes that historically, however, researchers skilled in the use of typologies have not been statistically or mathematically inclined, and vice-versa. This may be one of the reasons for the existing gap between sociological theory and research. (1969, p. 33)
A persistent problem in the qualitative typological tradition has been the confusion over the status of the type as a heuristic device, a mental construct, or an empirical entity. Winch (1947) distinguished between heuristic and empirical types. He said that heuristic types are conceptually derived and may not have empirical examples. Empirical types, in contrast, result solely from data analysis, without prior conceptualization. A persistent problem with the conceptual types, such as the ideal type, has been the problem of inappropriate reification. If a type is a construct, concept, or model, it may not be found empirically but is designed only to be heuristically used in developing theory. However, there is often a tendency over time to reify the type or act as though it were actually found empirically. Figure 1 shows that the qualitative tradition has both heuristic and empirical types, while the quantitative tradition (discussed below) has primarily empirical types, as its types are derived from data analysis.
In other cases in the qualitative typological tradition, types are meant as empirical phenomena rather than heuristic devices. This is particularly true in the area of social ethnography or field research, where researchers eschew statistical analysis but analyze data resulting from field studies by developing typologies based on observations recorded in their field notes (see Spradley and McCurdy 1972). Typologies in this case take the form of tables with names or labels in the cells rather than frequencies of occurrence as in statistical tables. Here the labels or types are generally inductively or empirically derived through intensive study of groups in the field. However, even here there may be a distinction between the types derived by the researcher and the types actually used by the people being studied. For example, the types that tramps identify among themselves (mission stiff, bindle stiff) may be different from the types identified by researchers or the lay public (bums, winos, homeless persons). For a discussion of taxonomies in ethnographic research and a number of examples of actual taxonomies (inducting the tramp example), see Spradley and McCurdy (1972).
Figure 1. A Typology of Typologies
EMPIRICAL DERIVATION
Computerization has brought on a new era of quantitative typology construction, which now coexists with the older qualitative tradition. This new approach often is called numerical taxonomy, cluster analysis, or pattern recognition (see Sneath and Sokal 1973; Bailey 1974). In contrast to the earlier verbal approach, which largely dealt with concepts and mental constructs, the newer quantitative approach is largely empirical and inductive.
It begins with a data set and derives empirical types from the data through a variety of quantitative procedures, many of them computerized.
This newer statistical approach to classification can be elucidated through the monothetic-polythetic distinction. A typology is monothetic if the possession of a unique set of features is both necessary and sufficient for identifying a specimen as belonging to a particular cell in the typology. That is, each feature is necessary and the set is sufficient. Thus, no specimen can be assigned to a particular type unless it possesses all the features (and no others) required of that type. This means that all the specimens in a given type are identical in every way (at least in all the features specified).
In contrast, a polythetic typology is constructed by grouping together the individuals within a sample that have the greatest number of shared features. No single feature is either necessary or sufficient (Sokal and Sneath 1963, p. 14). The objects or specimens are grouped to maximize overall similarity within each group. In a polythetic type, each individual possesses a large number of the classifying properties and each property is possessed by a large number of individuals. In the case where no single property is possessed by every individual in the group, the type is said to be fully polythetic.
While a verbal type (such as the ideal type) may be purely homogeneous (i.e., monothetic), it is unlikely that an empirically constructed type will be monothetic (except for some divisively derived types), especially if it contains a large number of cases grouped on a large number of variables. Thus, most empirically constructed types are polythetic, and some may be fully polythetic, without even a single feature being common to all the members of the group.
A basic distinction for all empirical classification techniques is whether one groups objects or variables. The former is known as Q-analysis, and the latter as R-analysis (Sokal and Sneath 1963, p. 124). In R-analysis, one computes coefficients (either similarity or distance coefficients) down the columns of the basic score matrix, which includes objects and variables (see Table 1 in Bailey 1972). In Q-analysis, one correlates rows. The interior data cells are the same in any case, and one form is the simple matrix transposition of the other. The difference is that Q-analysis correlates the objects (e.g., persons), while R-analysis correlates the variables (e.g., age). While Q-analysis is the most common form in biology (see Sneath and Sokal 1973), it rarely is used in sociology (for an example, see Butler and Adams 1966). One problem is that Q-analysis requires a small sample of cases measured on a large number of variables, while R-analysis requires a large sample of cases with a smaller number of variables. Biology has the former sort of data; sociology, the latter.
Most sociologists have had little experience with Q-analysis. Most statistical analysis in sociology is concerned with relationships between two or more variables, with few studies making inferences concerning individuals rather than variables. Thus, the very notion of correlating individuals is alien to many sociologists.
Once the researcher has decided whether to pursue Q-analysis or R-analysis, the next step is to decide which measure of similarity to use. A researcher can measure similarity either directly, with a correlation coefficient, or indirectly, with a distance coefficient. While similarity coefficients show how close together two objects or variables are in the property space, distance coefficients show how far apart they are in that space. For a discussion of these measures, see Bailey (1974).
The next task of empirical typology construction is to parsimoniously group the cases into homogeneous types. There are two chief ways to proceed. One can envision all N cases as forming a single type. This is maximally parsimonious but maximizes within-group or internal variance. Grouping proceeds ”from above” by dividing the cases into smaller groups that are more homogeneous. This is called the divisive strategy. Divisive classification generally proceeds by dividing the group on the basis of similarity on one or more variables, either simultaneously or sequentially. According to Sokal and Sneath (1963, p. 16), divisive classification is ”inevitably largely monothetic.”
The alternative strategy (the agglomerative strategy) is to envision the N cases as forming N separate groups of one case each. Then each group is homogeneous (including only a single case), but parsimony is minimal. The strategy here is ”classification from below” by agglomerating or grouping the most similar cases together, yielding some loss of internal homogeneity but gaining parsimony (as N groups are generally too unwieldy).
Unlike divisively formed types, agglomeratively formed types are generally polythetic and often fully polythetic.
The basic typological strategy is very straightforward and logically simple for divisive methods. All one must do is partition the set of cases in all possible ways and choose the grouping that maximizes internal homogeneity in a sufficiently small number of clusters. The problem is that the computation is prohibitive even for a modest number of cases measured on a modest number of variables.
A basic problem with empirically derived typologies is that they are generally static because the measures of similarity or distance that are used are synchronic rather than diachronic. While this is a problem, it is not a problem unique to classification but is shared by almost all forms of sociological analysis. Further, it is possible to deal with this issue by using diachronic data such as change coefficients or time series data.
Despite procedural differences, there are clear congruences between the qualitative and quantitative typological approaches. The ideal type is essentially monothetic, as are some types produced by quantitative divisive procedures. Quantitative procedures produce types that are polythetic, even fully polythetic. The results of quantitative procedures are generally not full typologies but reduced form that include fewer than the potential maximum number of types. Such polythetic types can be seen as analogous to the result of subjecting full monothetic typologies to reduction (either pragmatic or arbitrary numerical). Thus, contemporary typologists meet the need for reduction by using quantitative methods. Any correlational method of typology construction is by definition a method of functional reduction.
Further, the method usually will perform pragmatic reduction along with the functional reduction. Remember that pragmatic reduction collapses monothetic cells. The correlation coefficients utilized in typological methods are never perfect. The lower the correlations are, the more diverse the individuals in a group are. Placing diverse individuals in one group is tantamount to collapsing monothetic cells by means of pragmatic reduction. Thus, there are two basic avenues for constructing reduced types: Begin with monothetic types (such as ideal types) and subject them to the various forms of reduction to yield polythetic types or construct polythetic types directly by using quantitative methods. Thus, the qualitative and quantitative procedures can produce similar results.
Given the breadth and diversity of sociological typologies (for example, from quantitative to qualitative procedures and from heuristic to empirical types), it is not surprising that there have been a number of criticisms of typologies. Some alleged problems are that typologies are not mutually exclusive and exhaustive, are treated as ends in themselves rather than as means to an end, are not parsimonious, are based on arbitrary and ad hoc criteria, are essentially static, rely on dichotomized rather than internally measured variables, yield types that are subject to reification, and are basically descriptive rather than explanatory or predictive. All these factors can be problems but are relatively easy for a knowledgeable typologist to avoid. The ones that cannot be easily avoided (such as the problem of cross-sectional data) often are seen as general problems for sociology as a whole and are not specific to typology construction.
MERITS
Even if pitfalls remain, the merits of carefully constructed typologies make them well worth the effort. One of the chief merits of a typology is parsimony. A researcher who is overwhelmed by thousands or even millions of individual cases can work comfortably with those cases when they are grouped into a few main types. A related merit is the emphasis on bringing simplicity and order out of complexity and chaos. A focus on the relative homogeneity of types provides an emphasis on order in contrast to the emphasis on diversity and complexity that is paramount in untyped phenomena. A third merit of a full typology is its comprehensiveness. There is no other tool available that can show not only all relevant dimensions but also the relationships between them and the categories created by the intersections. Such a typology shows the entire range of every variable and all their confluences. A fourth merit (as was noted above) is a typology’s use of a type or types for comparative purposes. A fifth merit is a typology’s use as a heuristic tool to highlight the relevant theoretical dimensions of a type. A sixth is a typology’s ability to show which cells have empirical examples and which are empirically null. This can aid in hypothesis testing, especially when a large number of variables have a small number of values that actually occur (Stinchcombe 1968, p. 47). A seventh merit is a typology’s ability to combine two or more variables in such a way that interaction effects can be analyzed (Stinchcombe 1968, pp. 46-47).
TYPOLOGIES AND CONTINUOUS DATA
A clear but sometimes unstated goal of scientific development is to move past simple, nominal-variable analysis to the use of complex continuous-data models by employing ratio or interval variables. This has clearly been the case in sociology, which now depends on sophisticated regression models that work best with ratio (or at least interval) variables. Thus, some might argue that as science moves away from types toward the use of variables, typology construction becomes secondary.
Although the logic of moving from a reliance on types to a reliance on interval and ratio variables may seem irrefutable, this transition is not as smooth as some might wish. In fact, a number of obstacles to the transition from types to variables have arisen. Some researchers feel that once they have adopted sophisticated statistical techniques that use ratio variables, typologies are no longer needed. The reasoning here is that typologies are chiefly descriptive, arise at an early level of scientific analysis, and are essentially crude or unsophisticated formulations. In contrast, later models focus on explanation and prediction rather than description.
This notion belies the fact that science must constantly develop new ideas and theories to regenerate itself. As it does so, it must repeat the process of providing sound typologies that facilitate research by aiding in concept development and clarification and provide a comprehensive overview. Thus, it is a dangerous myth to think that sociology has ”outgrown” the need for typologies. In fact, new ideas, theories, and sociological areas of research continually require new typologies. Even researchers in older, more mature sociological areas that have based their theory and research on inadequate typologies may find that the foundations of their field are crumbling, requiring new attempts to provide sound typological reinforcements.
In addition to the constant need for typological renewal and rejuvenation, some sociologists find that attempts to move past types to sophisticated statistical analyses of ratio variables are confronted with a bewildering array of obstacles. Contemporary sociological statisticians who wish to rely on ratio variables are faced with a classic paradox. On the one hand, their regression models assume (or even demand) at least interval, or ideally ratio, variables. On the other hand, sociological theory is dependent on empirically important concepts, many of which are found to be essentially nominal or ordinal in their measurement levels. These include central ascribed or achieved statuses such as gender, race, religion, geographic region, nationality, occupation, and political affiliation.
Other important variables, such as income, education, and age, are more suitable for sophisticated statistical models. However, even these variables often are utilized theoretically in a limited ordinal form (young-old, high income-low income, etc.). Thus, there may be an empirical dis-juncture between the type of variable needed for regression analysis (or other modern statistical techniques) and the type required by empirical sociological theory. Theory needs concepts such as race, gender, and religion, and these concepts are more suited for typological analysis than for regression analysis.
This suggests two areas of future research. One is to modify regression models to accommodate categorical variables, and this has been done (Aldrich and Nelson 1984). However, such accommodation may be costly, as it is unclear whether modified models operate efficiently or significantly underestimate the degree of explained variance. The second avenue is to rely more heavily on typological analysis. Although this may not seem as ”sophisticated,” it may prove more compatible with theory and thus facilitate theoretical development more than statistical models do.
TYPOLOGIES IN THE AGE OF STATISTICS
If one has to choose between a sophisticated statistical analysis with variables that are not central to sociological theory and a typological analysis that accommodates theoretically important variables, it is foolish to rule out the latter in the name of scientific progress. Such progress would be false if the use of sophisticated techniques proved theoretically vacuous. This would be a classic case of the statistical tale wagging the theoretical dog. A wiser course is to recognize the complementarity between typologies and statistics. Statistics need not be viewed as necessarily or inevitably supplanting typologies; instead, each can be used when it proves valuable.
The conclusion to this point is that sociological progress has not rendered typological analysis obsolete by emphasizing statistical techniques such as multiple regression analysis. Thus, it may prove useful to look further at the epistemological foundations of contemporary sociology to see what the role of typologies is in an era when statistical analysis dominates. Consider the gap between the language of theory construction and the language of statistical data analysis. Imagine that a sociologist is interested in the type concept of ”underachieved’ and defines it as a person who has the ability to achieve at a higher level than is actualized.
When one substructs this type, it is clear that it is formed from two dimensions: (1) individual ability and (2) individual achievement. The sociologist can then theorize that an affluent childhood results in a particular type of personality. Individuals with that personality feel no pressing psychological need to achieve at a high level, since their needs continue to be met. This is an intriguing and ideographically rich sociological hypothesis. It involves images of a living person who has a particular type of childhood that leads to a particular type of adulthood. Thus, an earlier type concept (”the rich kid”) evolves into a later type concept (”the underachiever”). Conversely, one could hypothesize that the type concept of ”impoverished youth” leads to the subsequent adult concept of ”overachiever.”
The most direct way to test the hypothesis that the rich kid evolves into the adult underachiever is to identify a group of rich kids, follow them until adulthood, and then measure their subsequent achievement rates over a period of time. However, this is both tedious and time-consuming and is not the typical approach in social science. The most common approach is to gather cross-sectional survey data and then conduct a statistical analysis on the data. It is simple to select the two salient variables of parental wealth and adult achievement. Suppose one finds a negative correlation between parental wealth and adult achievement.
Since a negative correlation of achievement with wealth is not synonymous with the type concept of underachievement, the data analysis is not adequate to test the hypothesis.
Even if the statistical analysis were sufficient to test the hypothesis, a mere correlation value (e.g., r = .43) is very sterile and is isolated from both sociological reality and the richness of sociological theory. It fails to convey the richness of the type-concept description. While the type referent for the type concept of ”underachiever” is the holistic, living human individual, the referents for the statistical analysis are the variables of wealth and achievement, which seem artificially separated from the sociological reality the theory refers to and the type concept manages to capture.
The unfortunate aspect of this for sociological development is that it leaves theory construction and statistical analysis as two juxtaposed but separate entities with a clear disjuncture between them. This disjuncture results from the fact that theorizing is largely a conceptual undertaking. It involves both deductive and inductive reasoning, and its language is the holistic language of the individual actor. The prime theoretical referent is the object, not the variable. This object is usually the human individual but can be an alternative object, such as a group, city, or country. In any event, the primary focus is on the object, with variables receiving a secondary focus. However, even if variables have the primary focus, the focus remains on both object and the variables.
In statistics using R-analysis such as multiple regression, the epistemological focus is quite different. Here objects such as persons enter the analysis only as data carriers in the sample. As soon as the R-matrix of correlations among variables is established, it suffices for the remainder of the analysis. The result is that the individuals virtually disappear from the picture except in those rare instances in sociology where Q-correlations are used.
Thus, theory and statistical analysis remain two separate paradigms within sociology rather than two aspects of the same research process. This obviously hinders scientific progress sociology and stands in stark contrast to the physical sciences, where theory and method are not separated processes but are well integrated, enabling much swifter progress.
INTEGRATING TYPES AND TAXA
One way to bridge the dichotomy between theory and statistical method is to link qualitative type concepts with the empirical clusters derived quantitatively through methods of numerical taxonomy. Following the lead of Bailey (1994), these are called taxa. As was noted above, types are generally conceptual, monothetic, and based on underlying R-dimensions (although the cell entries are empirical objects). In contrast, taxa tend to be empirical, polythetic, and Q-analytic (based on individuals). While the differences may seem to mimic the differences between theory and statistics discussed above, both types and taxa can be seen primarily as mirror images of each other and thus as having structural similarities that allow a bridge to be built from one to the other.
Since much theorizing is done in terms of types, a needed first step is to move from the realm of type concepts to the realm of empirical data analysis. While this traditionally is accomplished by turning from theory to statistical analysis, an alternative is to link conceptually formed types with statistically derived taxa.
The first task is to move from the conceptual to the empirical. As outlined in Bailey (1994, p. 66), this is rather straightforward and merely involves the identification of empirical cases for each conceptual cell. An example would be to locate an actual ethnographic type such as ”bindle stiff’ (Spradley and McCurdy, 1972). The empirical cases found for each cell in a typology (such as Figure 1) are equivalent to the taxa formed through cluster analysis. The second task in bridging the gap between types and taxa is converting from monothetic to polythetic As was discussed above, this can be achieved in various ways, such as Lazarfeld’s (1937) process of pragmatic reduction. The third task is to connect the R-analysis of types with the Q-analysis of taxa. The easiest way to accomplish this is to use R-analysis for clustering.
In the other direction—from taxa to types— all the tasks are reversed and involve going from empirical to conceptual, from poythetic to monothetic, and from Q-analysis to R-analysis. Going from empirical to conceptual entails finding a concept to represent the statistically constructed group. For example, if the cluster analysis yields an empirical cluster composed primarily of people who scored very high on an exam, one could formulate the type concept of ”high achievers” to represent it.
The second task involves going from polythetic to monothetic. Technically speaking, this entails changing a heterogeneous empirical grouping to a homogeneous grouping and cannot be accomplished empirically except somewhat artificially. For example, Lockhart and Hartman (1963) constructed monothetic clusters by discarding all the characters that varied within the group. This is compensated for by the prior step, in which the conceptual type concept monothetically represents the empirical polythetic taxa. The third task is to achieve R-analytic clustering by using R-correla-tions rather than Q-correlations in the cluster analysis.
CONCLUSION
A well-constructed typology can bring order out of chaos. It can transform the overwhelming complexity of an apparently eclectic congeries of numerous apparently diverse cases into a well-ordered set of a few homogeneous types clearly situated in a property space of a few important dimensions. A sound typology forms a firm foundation and provides direction for both theorizing and empirical research. No other tool has as much power to simplify life for a sociologist.
The task for the future is the further elaboration of this crucial nexus between the qualitative and statistical approaches. This requires effort from sociologists with both theoretical and statistical talents. McKinney (1966, p. 49) recognizes the ”complementary relationship of quantitative and typological procedures” and advocates ”the emergence of a number of social scientists who are procedurally competent in both typology and statistical techniques.” Costner (1972, p. xi) also recognizes the basic unity of the qualitative and quantitative approaches to typology construction.
