Qualitative Comparative Analysis IS

(QCA) and Related Systematic

Comparative Methods
Recent Advances and Remaining Challenges for
Social Science Research

Benoît Rihoux
Université catholique de Louvain

abstract: During the past two decades, a set of systematic comparative case
analysis techniques has been developing at a steady pace. During the last few years
especially, the main initial technique, qualitative comparative analysis (QCA), has
been complemented by other related methods and techniques. The purpose of this
article is to critically assess some main recent developments in this field. QCA and
connected methods can be considered at two levels: as a research strategy and as
a set of concrete techniques. The author first argues that such a strategy displays
some decisive advantages in social science research, especially in small- and inter-
mediate-N research designs. Second, QCA as well as three other related techniques,
namely multi-value QCA (MVQCA), fuzzy sets and MSDO/MDSO, are presented
in brief, and some current debates with regard to these techniques are also summar-
ized. In the third section, the article surveys recent contributions and ongoing
efforts that have provided some advances in the application of these techniques,
around five key issues: case selection and model specification; measurement,
dichotomization and linkage with theory; contradictions and non-observed cases;
the time and process dimension; and the confrontation or combination with other
methods. Finally, the article discuss the potential for further development of these
methods in social science research broadly defined.

keywords: comparative methods ✦ fuzzy sets ✦ qualitative and quantitative

methods ✦ qualitative comparative analysis (QCA) ✦ small-N research design

Introduction
Following a seminal volume by Charles Ragin (1987), a set of systematic
comparative case analysis techniques has been developing at a steady

International Sociology ✦ September 2006 ✦ Vol 21(5): 679–706

© International Sociological Association
SAGE (London, Thousand Oaks, CA and New Delhi)
DOI: 10.1177/0268580906067836

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pace. During the last few years especially, the main initial technique,
qualitative comparative analysis (QCA), has been complemented by other
related methods and techniques. The purpose of this article is to critically
assess some main recent developments in this field.
QCA and connected methods can be considered at two levels: as a
research strategy, more at the epistemological level, and as a set of concrete
techniques. I first argue that such a strategy displays some decisive advan-
tages in social science research, especially in small- and intermediate-N
research designs. Second, QCA as well as three other related techniques,
namely multi-value QCA (MVQCA), fuzzy sets and MSDO/MDSO, are
briefly presented and some current debates with regard to these tech-
niques are also summarized. The third section surveys recent contri-
butions and ongoing efforts that have provided some advances in the
application of these methods, around five key issues: case selection and
model specification; measurement, dichotomization and linkage with
theory; contradictions and non-observed cases; the time and process
dimension; and the confrontation or combination with other methods.
Finally, we discuss the potential for further development of these methods
in social science research broadly defined.

Context: Systematic Comparative Case Analysis

During the last few years, an increasing proportion of social scientists
have been opting for multiple case studies as a research strategy – more
generally speaking, the explicitly comparative design is gaining
momentum. The choice of such a strategy often reflects the intention of
scholars to meet two apparently contradictory goals. On the one hand,
one seeks to gather in-depth insight in the different cases and capture the
complexity of the cases – to gain intimacy with the cases (Ragin and
Becker, 1992). On the other hand, one still wishes to produce some level
of generalization (Ragin, 1987). Indeed, in empirical social science, both
case-oriented work and techniques that allow one to generalize (typically
quantitative, i.e. statistical, techniques) are useful. One notes that the
increasing momentum of such methods also coincides with a renewed
interest in case-oriented research (Mahoney and Rueschemeyer, 2003;
George and Bennett, 2005; Gerring, 2004; Gerring, forthcoming), and also
in new attempts to engage in a well-informed dialogue between the
quantitative and qualitative empirical traditions (Brady and Collier, 2004;
Sprinz and Nahmias-Wolinsky, 2004; Moses et al., 2005).
In social science research, many relevant and interesting objects are natu-
rally limited in number. This is especially true at the mesosociological level
(e.g. specific sets of collective actors, of firms), and at the macrosociologi-
cal level (e.g. nation-states or regions, policy sectors). In such situations,

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we face naturally limited or ‘small-N’ (or ‘intermediate-N’) populations.

In some other circumstances, when the population of cases is larger, there
are still some good reasons for a researcher to pick out a more limited set
of cases. Indeed in comparative research, small-N situations may either be
the result of a limited number of cases, or of a deliberate choice of the
researcher to select a limited number of cases (De Meur and Rihoux, 2002).
Case studies constitute a very rich research tradition. Yet when it comes
to comparing, in many instances the comparison of the case study material
is rather loose or not formalized – hence the scientificity of case studies
is often questioned (Ragin and Becker, 1992; Gerring, 2004). This particu-
larly occurs when such comparisons occur ex post, and when the collec-
tion of the case study material has not been designed to be used for
subsequent comparative analysis.
During the last decade especially, following the launching of the QCA
technique, a set of specific methods, designed to address small-N and
intermediate-N research situations, has been further developed and
increasingly used, in various fields and disciplines. Of course, in any field
of study, when one engages in such an endeavour, one is bound to
encounter methodological difficulties and dilemmas. Hence, one of the
main topics in this contribution will be to demonstrate that such diffi-
culties can indeed be addressed.

QCA and Recently Developed Connected Methods: Some

Key Features
The first specific technique, qualitative comparative analysis (QCA), was
launched in the late 1980s by Charles Ragin. It has now been applied in
a broad variety of fields and disciplines (Ragin, 1987; De Meur and
Rihoux, 2002; Rihoux, 2003; Ragin and Rihoux, 2004a; Rihoux and Ragin,
forthcoming). In this section, I discuss some key features of this technique,
as well as of three related techniques: multi-value QCA (MVQCA), fuzzy
sets and MSDO/MDSO.
On a more general level, QCA is first of all an approach, i.e. a way to
envisage the confrontation between theory and data (Ragin, 1987). Ragin
contends that it is possible to develop an original ‘synthetic strategy’ as
a middle way between the case-oriented, or qualitative, and the variable-
oriented, or quantitative approaches (Ragin, 1987, 1997). The goal of this
strategy is to ‘integrate the best features of the case-oriented approach
with the best features of the variable-oriented approach’ (Ragin, 1987: 84).
This statement has been criticized (e.g. Berg-Schlosser, 2004; Swyngedouw,
2004). As a response to these critiques, QCA and connected methods are
now more often presented instead as a specific family of configurational
comparative methods (Ragin, 2004; Ragin and Rihoux, 2004a).

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In spite of these critiques, Ragin’s initial statement can, altogether, be

confirmed, provided some qualifications and nuances are added. On the
one hand, indeed, QCA embodies some key strengths of the qualitative,
case-oriented approach (Ragin, 1987; De Meur and Rihoux, 2002). To start
with, it is a holistic approach, in the sense that each individual case is
considered as a complex entity, as a whole that needs to be compre-
hended and which should not be forgotten in the course of the analysis.
Thus, QCA is in essence a case-sensitive approach. From a mainstream
statistical viewpoint, this might be considered a weakness; quite the
contrary, from a qualitativist, case-based perspective, this is a strength of
QCA.
Furthermore, QCA develops a conception of causality that leaves room
for complexity (Ragin, 1987). In most hard sciences, complexity is neutral-
ized by experimental design – something that is not usually available to
us in the social sciences. QCA’s strategic response to this is the concept
of multiple conjunctural causation. This implies that: (1) most often, it is
a combination of conditions (independent variables) that eventually
produces a phenomenon – the outcome (dependent variable); (2) several
different combinations of conditions may produce the same outcome; and
(3) depending on the context, on the conjuncture, a given condition may
very well have a different impact on the outcome. Thus different causal
paths – each path being relevant, in a distinct way – may lead to the same
outcome (De Meur and Rihoux, 2002). As J. S. Mill, Ragin rejects any form
of permanent causality (Ragin, 1987) since causality is context- and
conjuncture-sensitive. Bottom line: by using QCA, the researcher is urged
not to specify a single causal model that fits the data best, as one usually
does with statistical techniques, but instead to determine the number and
character of the different causal models that exist among comparable cases
(Ragin, 1987).
On the other hand, QCA indeed embodies some key strengths of the
quantitative approach. First, it allows one to analyse more than just a
handful of cases, which is seldom done in case-oriented studies. This is
a key asset, as it opens up the possibility to produce generalizations.
Moreover, its key operations rely on Boolean algebra, which requires that
each case be reduced to a series of variables (conditions and an outcome).
Hence, it is an analytic approach, which allows replication (De Meur and
Rihoux, 2002). This replicability enables other researchers to eventually
corroborate or falsify the results of the analysis, a key condition for
progress in scientific knowledge (Popper, 1963). This being said, QCA is
not radically analytic, as it leaves some room for the holistic dimension
of phenomena. Finally, the Boolean algorithms allow one to identify
(causal) regularities that are parsimonious, i.e. that can be expressed with
the fewest possible conditions within the whole set of conditions that are

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considered in the analysis – though a maximum level of parsimony should

not be pursued at all costs.
On a more specific level, QCA is also a technique based on the formal
logic of Boolean algebra1 and implemented by a set of computer programs,
so as to identify so-called ‘prime implicants’ in a truth table.2 The key phil-
osophy of QCA as a technique is to ‘[start] by assuming causal complex-
ity and then [mount] an assault on that complexity’ (Ragin, 1987: x).
The researcher must first produce a raw data table, in which each case
displays a specific combination of conditions (with 0 or 1 values) and an
outcome (with 0 or 1 values). The software then produces a truth table
that displays the data as a list of configurations. A configuration is a given
combination of some conditions and an outcome. A specific configuration
may correspond to several observed cases.
The key following step of the analysis is Boolean minimization – that
is, reducing the long Boolean expression, which consists in the long
description of the truth table, to the shortest possible expression (the
minimal formula, which is the list of the prime implicants) that unveils
the regularities in the data. It is then up to the researcher to interpret this
minimal formula, possibly in terms of causality.
Far from being a push-button-type technique, the use of QCA is an iter-
ative and creative process. The researcher must first gain enough famil-
iarity with each of the cases examined, and then produce a good-quality
truth table – that is, a table devoid of contradictory configurations. These
are configurations whose outcome is, in some cases, equal to [1] and in
some cases equal to [0], while displaying the same values on the
conditions. Such contradictions must thus be resolved before moving
ahead with the analysis. This involves frequent returns to the cases, to the
initial qualitative or quantitative data. This must also be done at the end
of the analysis, when one finally obtains the minimal formula: the
researcher must then make sense out of the solution, interpret it by rein-
terrogating the cases. This involves going back to the cases and examin-
ing each case as a whole. This also means that QCA can be a very
labour-intensive technique – which, from a case-oriented perspective,
should rather be seen as a strength.
As a technique, QCA displays three further qualities. First, it can be
used for at least five different purposes (De Meur and Rihoux, 2002:
78–80). The most basic use is simply to summarize data, i.e. to describe
cases in a synthetic way by producing a truth table, as a tool for data
exploration and typology-building. This use is basic in the sense that it
does not rely on a more elaborate, step-wise design of typology-building,
such as recently developed by George and Bennett (2005). It can also be
used to check coherence within the data: the detection of contradictions
allows one to learn more about the individual cases. The third use is to

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test existing theories or assumptions, to corroborate or refute these

theories or assumptions. QCA is hence a particularly powerful tool for
theory-testing (e.g. Sager, 2004; Goertz and Mahoney, 2005). Fourth, it can
be used to test some new ideas or assumptions formulated by the
researcher, and not embodied in an existing theory; this can also be useful
for data exploration. Finally, QCA allows one to elaborate new assump-
tions or theories: the minimal formula ultimately obtained can be inter-
preted – i.e. confronted with the cases examined – and lead the researcher
to formulate new segments of theory. This is probably why QCA is some-
times referred to as a kind of analytic induction (e.g. Hicks, 1994). QCA
is indeed inductive, to the extent that it allows the researcher to discover
more through a dialogue with the data. However, there is also a signifi-
cant input of theory in QCA. For instance, the selection of variables that
will be used in the analysis, and the way each variable is operationalized,
must be theoretically informed (De Meur and Rihoux, 2002). Arguably,
though, a more inductive use of QCA raises more methodological diffi-
culties than a simple, deductive theory-testing (Ebbinghaus, 2005).
Second, QCA is a particularly transparent technique, insofar as it forces
the researcher not only to make choices on his or her own (that is, the
researcher decides, not the computer), but also to justify these choices,
from a theoretical and/or empirical perspective. In the course of the
procedure, at several stages, the researcher is confronted with choices. For
instance, he or she must decide whether or not he or she wants to obtain
the shortest solution possible, to achieve a maximal level of parsimony.
If this choice is made, some cases that exist logically, but that have not
been observed in the data, will be included in the Boolean minimization.
In practice, the software will attribute a [0] or [1] outcome value to these
logical cases, thus making ‘simplifying assumptions’ about these cases.
The researcher may reject this option, privileging complexity over parsi-
mony. One also has to make clear choices as to the way each variable is
dichotomized, and as far as the choice of variables is concerned.
Third and not least, QCA allows one to consider phenomena that vary
both qualitatively and quantitatively. Both of these phenomena can be
operationalized in the conditions and outcome variables used for software
treatment (De Meur and Rihoux, 2002). Ragin uses the term ‘qualitative’
to indicate that QCA enables the researcher to analyse phenomena that
vary in nature, that are present or absent, and not only in degree (Ragin,
2002), that each case is considered as a complex and specific combination
of features (Ragin et al., 1996), and that QCA allows examination of
constellations, configurations and conjunctures (Ragin, 1987).
Because of some of its limitations, some of which are discussed in more
detail later, and also due to the diversifying demands of a broadening
community of users, three connected techniques have been developing

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during the last few years: respectively fuzzy sets, MVQCA and MSDO/
MDSO.
Fuzzy sets, currently developed by Ragin (2000), prolong and expand
the logic of QCA, but allow the researcher to analyse not only crisp
dichotomous variables, but also fuzzy variables, which can be defined in
terms of degree of membership in a well-defined set. On the one hand,
fuzzy sets can be regarded as a response from Ragin, in the view of some
critiques vis-a-vis QCA, notably around the limits of crisp sets analysis.
In this sense, they can be viewed, to a certain extent, as a prolongation of
QCA. However, on the other hand, they are quite distinct from QCA, tech-
nically and in terms of approach. Indeed, in technical terms, fuzzy sets
are not restricted to small-N situations. They are actually quite well suited
to large-N situations, i.e. to research designs in which the comprehension
of each individual case matters much less. In terms of approach, it may
be argued that they are a somewhat distinct route to attempt to bridge
the gap between qualitative and quantitative approaches: QCA’s starting
point lies more in cases (more in the qualitative world), whereas fuzzy
sets’ starting point lies more in variables and generalization (i.e. in the
quantitative world). Hence, fuzzy sets should rather be considered more
as a challenge towards conventional statistical and correlational quanti-
tative analysis.
In contrast with fuzzy sets, multi-value QCA (MVQCA) (Cronqvist and
Berg-Schlosser, forthcoming; Cronqvist, 2005), can be considered as a
direct extension of QCA. Indeed MVQCA retains the main idea of QCA:
it performs a minimization of a data set with the result that cases with
the same value of the outcome variable are covered by a parsimonious
solution. As with QCA, the solution contains one or several prime impli-
cants, each one of which covers a number of cases with this outcome,
while no cases with a different outcome are explained by any of the impli-
cants. The major difference, though, is that while QCA only allows
dichotomous variables to be processed, MVQCA also includes multi-
value variables in the analysis. This is a response to one of the recurrent
critiques of QCA, that the constraint to use only dichotomous variables
causes two key problems: information loss and risk of obtaining a large
number of contradictory configurations.3 Actually, ‘MVQCA is a gener-
alisation of QCA, and each dichotomous variable is a multi-value variable
(with two possible values)’ (Cronqvist, 2005: 2).
Finally, MSDO/MDSO (most similar, different outcome/most differ-
ent, similar outcome) is the most recent linked technique, at least in the
form of software4 tools – some applications of this technique have already
been performed in the 1990s (Berg-Schlosser and De Meur, 1994; De Meur
and Berg-Schlosser, 1996; Berg-Schlosser and De Meur, 1997; Bursens,
1999; De Meur et al., 2006). It is meant to be a help in the prior steps of

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the comparative research design, more precisely in model specification,

so as to take into account many potential explanatory variables or
conditions that are systematically grouped into categories, producing a
reduction in complexity.
In conclusion, one could say that dichotomous QCA is more specifi-
cally designed to address small-N situations, say: less than 30–40 cases,5
with a key emphasis laid on case-based knowledge. Conversely, fuzzy
sets are more targeted at larger-N situations, as a challenge to main-
stream statistical data treatment. Finally, MVQCA lies in some sort of
middle ground between QCA and fuzzy sets – it is more powerful in
medium-N situations. Herrmann and Cronqvist (2005) have recently
confronted the three techniques, and have refined this general argument.
According to them, the three respective techniques are best used in
different research situations, following two dimensions. The first dimen-
sion is the sheer number of cases – the size of the data set. The second
dimension is the necessity to preserve the richness of the data infor-
mation in the raw data set. Figure 1 summarizes situations in which each
one of the three techniques is best used. I have also picked out two other

High

Quantitative Fuzzy
methods sets
Size of data set (number of cases)

Medium MVQCA

Robust
statistics

Qualitative
QCA methods

Low
Single case studies

Low Medium High

Need to preserve richness of information of data set

Figure 1 Best Use of QCA, MVQCA and Fuzzy Sets

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specific sets of techniques and placed them on these two dimensions. On

the one hand, single, in-depth case studies probably constitute the most
demanding form of empirical qualitative methods with regard to the
requested richness of case information. On the other hand, robust statis-
tics are designed to tackle small-N situations (Hampel et al., 1986). As far
as we know, QCA and robust statistics haven’t been thoroughly confronted
so far.
Of course there are some overlaps between these techniques. For
instance, if the number of cases is low to medium (say, between 40 and
50 cases), one will have the possibility to choose between dichotomous
QCA and MVQCA. It is probably advisable to try first with dichotomous
QCA, provided that the model doesn’t display too many contradictions
and that some conditions don’t obviously require a non-dichotomous
treatment. For instance, in a social stratification study, a researcher may
not find it acceptable, from a theoretical and/or empirical perspective, to
transform a three-value working-class–middle-class–upper-class variable
into a dichotomous variable, thereby losing too much information.

Key Issues and Recent Advances

During the last 15 years, and more so during the last few years, these
methods have been applied in a variety of ways, in a growing number of
disciplines, covering various topics as well. Naturally, in that process,
scholars have encountered difficulties and have developed strategies to
overcome these difficulties, thereby improving the use of these techniques.
In this section, I attempt to survey and comment on some of the most
important recent advances, in a more detailed way for dichotomous QCA.

Case Selection and Model Specification

In any comparative research effort, one is confronted with two classical
research design issues. The first is case selection: how to select genuinely
comparable cases? The second one is variable selection, which of course
refers to model specification. Actually, these two issues are quite closely
linked.
With regard to case selection, in any small-N or medium-N design,
arguably, one should not broaden too much the variety of cases. In other
words, the quest for generalization should always be bounded, by
comparing cases that share a sufficient number of features and that
operate within sufficiently comparable contexts (Lijphart, 1971; Collier,
1993; Ragin et al., 1996). By contrast to most large-N research, in this effort,
one should treat cases as singular, whole entities purposefully defined
and selected, not as homogeneous observations drawn at random from a
pool of equally plausible selections (Ragin, 2004). Hence in such a research

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design, in contrast, the population of cases is not a given; it is actually

delimited by the researcher, informed by theory and empirical knowl-
edge. As social science theories are not always so consolidated, this
process is often iterative. This being said, it is of vital importance that
these comparable cases display enough diversity with regard to the
conditions which will be included in the model, and also with regard to
the outcome variable.
This first view is in line with the ‘most similar systems design’ as
defined by Przeworski and Teune (1970): as one matches similar cases as
much as possible, most of the variables can be controlled, which allows
one, following Mill’s indirect method of difference, to attribute different
outcome values to the remaining factors – to those factors which are
included as conditions in the QCA model. In medium-N settings,
however, the opposite strategy defined by Przeworski and Teune, the
most different systems design, also makes sense. It seeks maximal hetero-
geneity in the selection of cases that share an identical outcome. This
allows one to eliminate all factors that are not linked to an identical
outcome. In this way, more general explanations can be reached (Berg-
Schlosser, forthcoming).
The recent development of MSDO/MDSO is a first attempt to system-
atically combine these two designs. Hence MSDO/MDSO is a tool which
assists both case selection and model specification (De Meur et al., 2006;
Berg-Schlosser, forthcoming; De Meur, forthcoming). This technique is to
be used as a prior step before using a technique such as QCA and its
extensions, so as to take into account many potential explanatory vari-
ables, which are grouped into categories, producing a reduction in
complexity. This is done through the step-wise elaboration of distance
matrices and (dis)similarity graphs, which allow one to identify the most
similar pairs of cases that display a different outcome, as well as the most
different pairs of cases that display a similar outcome. This, in turn,
enables the researcher to select the key conditions to be used further, typi-
cally for a QCA-type analysis. De Meur et al. (2006) have applied
MSDO/MDSO in the field of policy-making processes in EU institutions,
using material from a study performed by Bursens (1999). Their main goal
is to identify the variables that explain why certain types of policy
networks develop through the elaboration of EU legislative proposals.
MSDO/MDSO ultimately enables them to narrow down the number of
conditions in a systematic way, and then to perform a QCA that yields
empirically robust conclusions on how institutions matter in the forma-
tion of EU policy networks.
In spite of the development of tools such as MSDO/MDSO, case selec-
tion and model specification are still very difficult tasks. One of the key
remaining problems is how to increase the number of cases, without

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losing in-depth case knowledge. Building upon Lijphart’s (1971, 1975) and
King et al.’s (1994) advocated designs, which meet respectively the contra-
dictory needs of internal validity by control and comparison and external
validity by correlation and broadening of the scope, Levi-Faur (2006) puts
forward an original strategy. More precisely, he first develops four case-
based strategies, each one of which consists of a two-by-two combination
of, respectively, Przeworski and Teune’s most-similar system design
(MSSD) or most different system design (MDSD), and Mill’s method of
difference or method of agreement. They are to be used in a step-wise
and iterative model.
These developments are pretty much in line with some other recent
contributions on case selection in small- and medium-N research designs,
especially through two major books (Mahoney and Rueschemeyer, 2003;
George and Bennett, 2005). Both Mahoney (2003b) and Ebbinghaus (2005)
refine the initial argument made by Ragin and by others, according to
which, in qualitative comparative research, cases are selected both for
intensive within-case analysis and systematic cross-case analysis. To put
it more precisely: sufficiently detailed within-case studies are a condition
sine qua non for successful cross-case comparison. Ebbinghaus (2005) also
examines a third research design besides MSDO and MDSO, namely
MSSO (most similar, same outcome), which obviously raises difficulties
if one aims at establishing patterns of causality. However, provided some
care is taken in the definition of necessary conditions (Braumoeller and
Goertz, 2000) such a design can be useful in the process of model-building,
in particular to eliminate some non-necessary conditions. Thus, especi-
ally at the first stages of a comparative research enterprise, cases with a
similar outcome variable can be used as a heuristic device to pick out the
most interesting potential conditions. Later on in the research process,
such a model can then be tested against cases with different outcome
values (George and Bennett, 2005) – this is also in line with Mahoney and
Goertz’s (2004) demonstration on the usefulness and importance of select-
ing negative cases as well. QCA and its parent techniques are very much
in line with a step-wise, case-oriented research design, as convincingly
advocated by George and Bennett (2005).
Still with regard to model-building, another promising avenue is being
developed by Schneider and Wagemann (forthcoming), who draw a
useful distinction between remote and proximate conditions, and who
also apply a practical two-step procedure to implement this distinction.
Such a strategy also allows one to filter out some more remote (i.e. distant,
more contextual) conditions, and hence to encompass more conditions in
exploratory (MV)QCA or fuzzy sets tests. One further interest of this is
that the remoteness/proximity distinction could also be a way to tap time
and sequence (as discussed here later).

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Of course, whatever design is used with QCA, one still bumps into the
contradictions/uniqueness trade-off. If one includes too many variables,
a problem of uniqueness might occur, i.e. each case is then simply described
as a distinct configuration of variables, which results in full complexity
and no parsimony. On the other hand, if one uses too few variables the
probability of contradictions increases. Varone et al. (2006) discuss some
possibilities to deal with this trade-off.

Measurement, Dichotomization and Linkage with Theory

In spite of the analytical strength of dichotomization (De Meur and
Rihoux, 2002), the progress made on the issue of dichotomization and
categorization of the data, and the development of new tools such as
MVQCA and fuzzy sets, which enable one to process finer grained data,
there is still a lot to be discussed on how and why to categorize data. This
issue is quite important, as QCA and related techniques are evidently
case-sensitive and variable-sensitive. Hence modifying the operational-
ization even only on one single condition, in dichotomous QCA for
instance, may very well bring profound modifications to the minimal
formulae. Some good practices have been recently laid out. One of them
is that one should only use statistical criteria (mean, median, etc.) in the
last resort (Ragin and Rihoux, 2004a). Attention must also be paid to the
size of the two subsets (Herrmann and Cronqvist, 2005), a current rule of
thumb being that each subset should contain at least one-third of the cases.
Of course, dichotomization should not be pursued at any cost. Brau-
moeller and Goertz (2000) argue that the forced dichotomization of
fundamentally non-dichotomous phenomena can introduce problematic
measurement biases. MVQCA is one of the obvious alternative strategies.
Some first real-life applications are indeed promising in this respect.
Cronqvist and Berg-Schlosser (2006), for instance, confront mainstream
quantitative methods with dichotomous QCA and with MVQCA. Their
goal is to explore the causes in the differences of HIV prevalence rates
between Sub-Saharan African countries. While regression tests and factor
analysis show that the religious context and colonial history have had a
strong impact on the spread of HIV, the popular thesis, according to which
high education prevents high HIV prevalence rates, is invalidated.
Further, they perform some dichotomous QCA tests, which are not unin-
teresting, but which still contain some contradictory configurations – this
problem is precisely solved with MVQCA. In countries with a high HIV
prevalence rate, MVQCA then allows them to find connections between
the mortality rate and the increase of the prevalence rate, as well as
between the economical structure and the increase of the prevalence rate,
which might be of interest for further HIV prevention policies. Method-
ologically, the introduction of finer graded scales with MVQCA is proved

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useful, also in empirical terms, as it allows a more genuine categorization

of the data.
QCA is also designed for more theory-driven work. If it is well used,
QCA allows for a three-way comparison. First and more obviously, it is
designed for cross-case analysis. Second, it is also a tool for within-case
analysis, in the phase of interpretation of the minimal formulae. Third
and not least, it allows one to perform comparisons between empirical
reality and theoretical ideal types (Varone et al., 2006). This more theory-
oriented use of QCA has been explored in different, promising ways. For
instance, Watanabe (2003), Peillon (1996) and Yamasaki (2003) have used
more advanced features of the software to examine the Boolean intersec-
tions between theory and empirical observations. Befani and Sager (2006),
and Befani et al. (forthcoming) have also begun to develop an original
theory-driven QCA strategy in the field of policy evaluation. They have
modelled a ‘realist’ theory (Pawson and Tilley, 1997) consisting of
context–mechanism–outcome (CMO) configurations, which explain the
different types of policy results. A model deriving from this initial theor-
etical construct is then elaborated, and empirical data are collected in
order to fill in a data matrix on which QCA is performed. The QCA
produces minimal combinations of conditions, which are, in turn, used to
refine the initial theory. The theory refinement made possible by QCA
covers both directions on the abstraction to specification scale: downward,
it offers more elaborate configurations able to account for a certain
outcome; upward, it aggregates relatively specific elements into more
abstract ones (realist synthesis).
Last but not least, it is obvious that fuzzy sets offer some interesting
alternatives when one is confronted with coding problems, in particular
linked with dichotomization.. The conception of variables in terms of
fuzzy set membership (Ragin, 2000) provides a way to operationalize and
typologize phenomena that sticks closer to theoretical discourse (see also
Goertz and Mahoney, 2005; Goertz, 2006). Indeed Kvist (2006) demon-
strates how fuzzy sets can be used to perform a more precise operational-
ization of theoretical concepts. He further shows how to configure
concepts into analytical concepts. Using unemployment insurance and
child family policies in four Scandinavian countries as test cases, he
exemplifies these approaches by using fuzzy memberships indicating the
orientation towards specific policy ideal types.
Another advantage of fuzzy sets is that they provide some flexibility
in the hard deterministic nature of QCA and MVQCA – indeed the crisp
QCA does not leave room for manoeuvre: either a specific condition (or
a specific combination of conditions) is sufficient to produce the outcome
of interest, or it is not. By allowing some input of probabilistic proposi-
tions more precisely (through statistical tests with predefined benchmarks

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that can be adjusted by the researcher) one may produce propositions in

terms of ‘quasi-sufficiency’ (Ragin, 2000). This is a response to criticisms
on the deterministic nature of Boolean algorithms (e.g. Dion, 1998).

On Contradictions and Non-Observed Cases

It is actually good to obtain contradictory configurations with observed
cases, at some stages of the analysis: the researcher can learn from these
contradictions, as it forces him or her to go back to the empirical cases
and to theory. In practical, real-life research, one of the potential signals
of the existence of such contradictions is that, most probably, the
researcher has forgotten to include at least one key condition so as to
explain variation in the outcome of interest. Another original way to treat
these contradictions has been developed by Roscigno and Hodson
(Roscigno and Hodson, 2004; Hodson and Roscigno, 2004), in their meta-
analysis of organizational ethnographies. For each configuration of
observed cases, they consider the relative frequency of the cases with [1]
and with [0] outcomes, respectively, and then use a conventional statisti-
cal method (t-tests) to make comparisons between the distribution of
outcomes for that configuration, on the one hand, and that of the
outcomes for cases not captured by the configuration, on the other hand.
With this technique, they are able to demonstrate that, from a statistical
– i.e. probabilistic – perspective, some of the contradictory configurations
that would otherwise be unconsidered with a standard QCA minimiza-
tion procedure, do indeed enable one to discriminate the outcome, to a
certain extent at least.
On the other hand, when one uses a small-N research design, a problem
of limited diversity is raised with QCA, as the number of logically possible
combinations of conditions quickly overwhelms the number of empiri-
cally observed combinations (Ragin, 1987). An early answer of QCA to
this has been to allow the software to use non-observed cases (called
‘remainders’, ‘logical cases’ or ‘counterfactuals’). The software then makes
simplifying assumptions on these additional cases, which produces
shorter, more parsimonious minimal formulae. To a certain extent, the use
of logical cases can be justified (De Meur and Rihoux, 2002; Ragin and
Rihoux, 2004b; Rihoux et al., 2004). This has however been criticized,
especially if one includes some logical cases that would be empirically or
theoretically very unlikely, or even inconceivable (Markoff, 1990; Romme,
1995). Actually, the epistemological issue at stake here is the arbitration
between parsimony and complexity, or, to put it differently, the level of
reduction of complexity one should aim at.
During the last few years, different responses to these critiques have
been developed. The first strategy has been to draw a distinction between
‘easy’ and ‘hard’ simplifying assumptions (Ragin and Sonnett, 2004; Ragin

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and Rihoux, 2004a). The former are counterfactuals, which can be

sustained from an empirical and/or theoretical perspective, whereas the
latter are more counterintuitive. For instance, if one would consider a non-
observed case with a [1] value on all conditions, assuming that such a
case would have a [0] outcome value would constitute a hard simplify-
ing assumption. The strategy is then quite straightforward: allow the
software to consider only easy, simplifying assumptions, empirically
and/or theoretically qualified. A quite parallel strategy has been pursued
by Grassi (2004) in his analysis of democratic consolidation in Latin
American political systems, and by Clément (2004) in her exploration on
the causes of state collapse in Somalia, Lebanon and former Yugoslavia.
Another strategy has consisted not in putting restrictions on non-
observed cases, but in providing a treatment of contradictory simplifying
assumptions. In short, such contradictions appear when the software uses
the same non-observed combinations of conditions for both the minimiza-
tion of [0] outcome cases and [1] outcome cases – i.e. it allocates two differ-
ent outcome values on the same combination of conditions. The quite
labour-intensive solution that has been applied so far consists of three
main phases. First, the respective minimal formulae for the [0] and [1]
outcomes are systematically intersected, to detect the presence of contra-
dictory simplifying assumptions. Second, the non-observed cases that
create such contradictions are included in the data set, with the allocation
of a [0] or [1] outcome value. This step necessitates some empirical and/or
theoretical justifications. Third, the minimizations are run again, in the
hope that at least one intersection of the minimal formulae for the [0] and
[1] outcomes, respectively, will not display contradictions anymore. With
real-life data, this procedure must often be replicated two or three times,
in a more iterative way. This strategy has been successfully implemented
in a few applications, e.g. on the determinants of organizational change
in Green parties (Rihoux, 2001) and on agenda-setting processes with
regard to basic income proposals (Vanderborght and Yamasaki, 2004).
The bottom line is that, by explicitly tackling contradictions and non-
observed cases, one actually gains a lot in the understanding of the
phenomena of interest.

Bringing in the Time and Process Dimension

At first sight, there is a stark contrast between the wealth of recent
developments, both epistemological and methodological, with regard to
the time and process dimension, and the apparently static character of
QCA. Indeed, in its Boolean treatment, QCA is not designed to explicitly
integrate the time and process dimension, and seems to provide only a
form of static comparison (Boswell and Brown, 1999). This may seem
surprising, as QCA is after all more a case-oriented method.

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This is only one part of the picture, though, which only looks at the
Boolean nuts and bolts of QCA. Already from the earlier applications
onwards, time and process have been – only to a certain extent admit-
tedly – taken into account in QCA. First and most obvious, in all well-
conducted QCA applications, the minimal formulae are not static: they
tell some bits of a thick story, which must be interpreted, obviously also
taking into account considerations of time and sequence (De Meur and
Rihoux, 2002; Cress and Snow, 2000). Second, it is possible, at the model-
building stage, to construct conditions that, themselves, integrate the time
dimension. For instance, one may operationalize a condition as follows:
‘an A-type of event has preceded a B-type of event: yes/no’. Third, follow-
ing the suggestion made by King et al. (1994), a case might also be
circumscribed a subunit of a case that displays a sufficient degree of differ-
entiation with the other subunits of that case. It is then possible to inte-
grate the time dimension in the definition of the cases themselves. For
instance, Rihoux (2001) has segmented party organizations through time,
using a chronological sequence and also relying on the sequence of [0]
and [1] outcomes as cut-off points, so as to produce several cases – or
rather units of observation – per party. The same has been done by
Clément (2004). Obviously, however, such a design raises some difficulties
as far as the independence of the cases is concerned.
These first responses are thus only partial, and do not respond to the
more ambitious challenge of really integrating time and process into
QCA itself. This opens up a huge methodological Pandora’s Box, as one
should then attempt to take into consideration concepts and phenom-
ena such as cumulative causes, threshold effects, causal chains, path
dependency, feedback processes (Pierson, 2003) and critical junctures
(Abbott, 1992), to mention but a few. One should also take into account
the complexity of causal processes (e.g. Mahoney, 2003a; Rueschemeyer
and Stephens, 1997; Stephens, 1998; George and Bennett, 2005; Gerring,
2005), which goes far beyond the rather simple QCA conceptualization
in terms of multiple conjunctural causation. If one wishes to address
these issues, several potential concrete paths open up, especially around
sequence analysis broadly defined (Krook, 2005). A first set of existing
or developing techniques concentrate on structures of whole sequences,
such as optimal matching (Abbott, 1995), comparative narrative analysis
(Abell, 1987, 2004) or Gibbs sampling (Abbott and Barman, 1997). A
second set of techniques breaks down the components of individual
sequences, such as event-structure analysis (ESA) (Griffin, 1992, 1993;
Heise, 1989), narrative analysis or process tracing (George and Bennett,
2005; Rueschemeyer and Stephens, 1997). There are also some other
formal techniques, such as game-theoretic interaction models, which
self-contain dynamic processes.

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Already quite a few attempts have been made so far. In an analysis of

the outcomes of local environmental policies in the US, Stevenson and
Greenberg (2000) have convincingly used, in their research design, both
QCA and ESA. Quite similarly, in a research on closure processes of non-
profit organizations, Duckles et al. (2005) have first elaborated an expected
sequence of events leading to the outcome of interest, i.e. organizational
closure. Then they have used thick case information (narratives, inter-
views) to reconstruct the actual sequence of events in the empirical cases.
With the help of ESA, they were then able to construct 31 event struc-
tures, some of which were operationalized in sequential submodels for
successive QCA minimization procedures. Eventually, they elaborated a
complete model that enabled them to identify some key precipitating
factors in the chain of events, at least for some clusters of cases. In another
vein, Brown and Boswell (1995) have combined QCA with game model-
ling, on their study of ethnic conflicts in split labour market conditions.
They use a game-theoretic – by definition dynamic – model to construct
dynamic hypotheses to be tested through QCA.
An attempt of another kind, by Caren and Panofsky (2005), consists in
integrating temporality directly into QCA. Using an hypothetically
constructed example, they argue that it is possible to develop an exten-
sion of QCA (TQCA – temporal QCA) to capture causal sequences. First,
they include sequence considerations as a specific case attribute, hence
increasing dramatically the number of possible configurations. Second,
they place theoretical restrictions to limit the number of possible config-
urations. Third, they perform a specific form of Boolean minimization;
this allows them to obtain richer minimal formulae, which also include
sequences and trajectories. This is an interesting attempt, although it
dramatically increases the problem of limited diversity, and it should still
be tested against real-life data.

Combining or Confronting QCA with Other Methods

Another series of innovations pertains to the confrontation (or dialogue,
rather) between QCA and connected techniques and other methods, be
they more qualitative or quantitative. This occurs as growing debates
develop on how to combine, or possibly even mix methods in real-life
empirical research (e.g. Tashakkori and Teddlie, 2003).
By definition, a vast number of QCA applications are de facto
developed in sequence with more qualitative, thick case-oriented
methods. Especially in the smaller-N analyses, with dichotomous QCA,
most consolidated applications stem from more qualitative case studies.
Most often, there is already a lot of upstream qualitative work involved
in the process of achieving an in-depth understanding of cases. One of
the recent illustrations is Grimm’s (2006) analysis on entrepreneurship

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policy and regional economic growth in the US and Germany. She uses
QCA in a more exploratory way, to enrich her qualitative knowledge of
the specific cases, by helping her to identify some particular contextual
factors that are influencing some cases while others are unaffected.
As for the connection with mainstream statistical methods, in numerous
recent contributions, especially in medium-N and larger-N settings,
researchers use both statistical techniques and QCA-type techniques to
analyse the same initial data, and confront the conclusions of both tech-
niques. Quite often, the empirical conclusion is that QCA-type techniques
allow one to learn more out of the data. For instance, by reanalysing with
fuzzy sets the bell curve data on social inequalities in the US, Ragin (2006)
demonstrates that there is much more to be found when one takes into
account the fundamentally configurational nature of social phenomena,
which cannot be grasped with standard statistical procedures. Another
example is Luoma’s (2006) study of social sustainability in local Finnish
communities, in which QCA enriches the conclusions reached by prior
regression analyses. The same goes for Cronqvist and Berg-Schlosser’s
(2006) aforementioned MVQCA analysis of explanatory factors of AIDS
prevalence in Sub-Saharan Africa. We should also mention the confronta-
tion between fuzzy sets and regression analyses by Katz et al. (2005) on
socioeconomic development in Spanish American countries during the
18th and 19th centuries. From a methodological viewpoint, they are able
to demonstrate that OLS regression yields less robust and more unstable
results, especially as the N becomes low. QCA has in fact already been
confronted with quite a few different statistical techniques: discriminant
analysis (Berg-Schlosser and De Meur, 1997), factor analysis (Berg-
Schlosser and Cronqvist, 2005), various types of multiple regression (e.g.
Amenta and Poulsen, 1996; Ebbinghaus and Visser, 1998; Kittel et al., 2000;
Nelson, 2004), logistic regression (Amoroso and Ragin, 1999; Ragin and
Bradshaw, 1991) and logit regression (Heikkila, 2003; Dumont and Bäck,
forthcoming).
In another vein, an original attempt is made by Yamasaki and Spreitzer
(2006), who combine QCA with social network analysis (SNA). First, they
identify some key problems of applied research: representing and deci-
phering complexity, formalizing social phenomena, allowing generaliza-
tion and providing pragmatic results. It is argued that both QCA and SNA
provide useful answers to these problems: they assume complexity as a
pre-existing context, they assume multiple and combinatorial causality,
they offer some formal data processing, as well as some visualization
tools. The authors follow by envisaging two ways of combining those
methods: a QCA can be followed by a SNA, e.g. for purposes of visual-
ization and interpretation of the QCA minimal formulae; conversely, a
QCA can complement a SNA, e.g. by entering some network data into a

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QCA matrix. This is applied on two empirical examples. Stevenson and

Greenberg (2000) have also, in other ways, explored this connection.
At this stage of combination/confrontation with other methods, the
most contested topic is probably the respective pros and cons of QCA and
connected techniques vs statistical techniques. Answering recent critiques
(e.g. Lieberson, 2004; Seawright, 2004), Ragin and Rihoux (2004b) raise
some counterarguments and, in essence, conclude that the intention of
QCA is certainly not to supplant regression and related analyses, especi-
ally since the underlying logic and goals of the respective methods display
stark differences. One of the key differences is that regression-based
methods focus primarily on the problem of estimating the net, indepen-
dent effect of each variable included in an analysis on the outcome. By
contrast, it would be a serious mistake to apply QCA to this task, as the
latter focuses on combinations of conditions. From the perspective of
QCA, the idea of isolating the net, independent, context-free effect of each
independent variable makes no sense.

Tentative Conclusions: A Broad Potential to be Exploited

In the field of systematic comparative case analysis methods, the tech-
nique that so far has been most widely applied , QCA, has met some fierce
criticisms, especially from researchers with a quantitative – i.e. main-
stream statistical – worldview. A detailed discussion of these critiques,
and answers to these critiques, goes beyond the scope of this contri-
bution.7 The bottom line is that many of these critiques are technically
incorrect, for they are based on assumptions that are simply not valid for
Boolean-type data treatment. This is not to say, of course, that QCA is
devoid of limitations (Rihoux, 2003). In this contribution, I have shown
that a more advanced exploitation of dichotomous QCA, on the one hand,
and the development of three connected methods, MVQCA, fuzzy sets
and MSDO/MDSO, on the other hand, have begun to bring some solu-
tions to these limitations.
With respect to dichotomous QCA, out of the more than 300 published
applications8 surveyed at the time of writing, in terms of disciplinary
orientation, more than two-thirds are found in political science (compara-
tive politics, welfare state studies, policy analysis and so on) and sociol-
ogy (historical sociology, organizational sociology and so on). There is
also a growing number of applications in other disciplines such as politi-
cal economy, management studies and criminology. Finally, a few appli-
cations can be found in history, geography, psychology and education
studies.
Although QCA is mainly designed for small- and intermediate-N
research, there is substantial variation across studies in the number of

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cases. Quite a few applications have a very small N, as low as five (e.g.
Kitchener et al., 2002), six (e.g. Vanderborght and Yamasaki, 2004) or seven
cases (e.g. Brueggemann and Boswell, 1998; Hellström, 2001). In the inter-
mediate-N range, most applications are to be found in the broad range
from 10 to 50 cases. However, several applications address between 50
and 80 cases (e.g. Williams and Farrell, 1990; Rudel and Roper, 1996;
Nomiya, 2001). Still further, some applications are to be found in the large-
N domain, up to more than 100 (Drass and Spencer, 1987; Yonetani et al.,
2003) or even more than 1000 cases (Ragin and Bradshaw, 1991; Amoroso
and Ragin, 1999; Miethe and Drass, 1999). Hence the method has been
applied fruitfully in a very broad range of research designs.
The nature of the cases studied is also diverse. In most applications,
cases and outcomes are macro- or meso-level phenomena, such as policy
fields, collective actors, organizations, country or regional characteristics,
and so on. Only very few scholars have applied QCA to micro-level data,
though there is arguably a potential to do so – indeed some PhD projects
are currently under way in this direction, especially in the field of
education research and psychology.
This quick and selective mapping of QCA applications, as well as the
recent developments discussed in this contribution, shows the quite large
potential of QCA, in terms of discipline, number of cases, research design
and types of uses. However, probably it is a bit overstated to argue that
QCA is a middle path between case-oriented and variable-oriented
research, as Ragin (1987) initially argued. All things considered, QCA is
more related to case study methods. Hence, as with any case-oriented
methods, a researcher using QCA meets a trade-off between the goals of
reaching a certain level of theoretical parsimony, establishing explanatory
richness, and keeping the number of cases at a manageable level (George
and Bennett, 2005). What is specific about QCA, as compared with George
and Bennett’s ‘focused, structured comparison’, is that it enables one to
consider a larger number of cases, provided one is willing to accept a
certain level of simplification and synthesis necessitated for Boolean treat-
ment. Still, in that process, one does not sacrifice explanatory richness,
and the possible generalizations that are produced will always be contin-
gent, in the sense that they only apply to some specific types or clusters
of well-delineated cases that operate in specific contexts (George and
Bennett, 2005).
Naturally, QCA and connected techniques should not be viewed in
isolation. They are clearly compatible with other overarching efforts,
especially around comparative historical analysis (Mahoney and
Rueschemeyer, 2003) and theory-led case-oriented research (George and
Bennett, 2005). In addition, much progress can be expected within the next
few years, when QCA and connected techniques will hopefully be

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combined/confronted more systematically with other techniques, be they

more qualitative or more quantitative. At the same time, we can also
expect some significant further development in terms of software to
perform QCA, MSDO/MDSO, MVQCA and fuzzy sets analyses, e.g. in
terms of visualization, connections with other software packages, user
interface, etc. In addition, dissemination of these techniques is now being
amplified through training programmes and specialized courses in
various institutions. Among other dissemination efforts, an English-
language textbook (Rihoux and Ragin, forthcoming) is also in the making.
Though of course neither QCA, nor MVQCA nor fuzzy sets constitute
miracle techniques – no technique should be expected to perform miracles
or solve all research questions – these techniques still display a broad
potential to be exploited, in many fields across the social sciences broadly
defined.

Notes
The author wishes to thank Andrea Herrmann and Lasse Cronqvist for their
authorization to use a draft figure from their work-in-progress, as well as the three
anonymous reviewers for their useful suggestions.

1. For an accessible presentation of key elements of Boolean logic and operations,

see Ragin (1987). For details on using the software for analysis, see De Meur
and Rihoux (2002) and Rihoux and Ragin (forthcoming), as well as the
COMPASSS resource site: at: www.compasss.org
2. Two main free-access software are being developed. Fs/QCA is available
through www.compasss.org and at www.u.arizona.edu/~cragin/QCA.htm,
and performs dichotomous crisp set as well as fuzzy set analysis. TOSMANA
performs dichotomous crisp set analysis as well as MVQCA, with some
additional features. It is available through www.compasss.org and at www.
tosmana.net/. Some other efforts are under way, such as the development of
a QCA module in the ‘R’ package.
3. See, however, De Meur and Rihoux’s (2002) defence of the analytical strength
of dichotomous QCA.
4. No public version is yet available at the time of writing. Some ‘beta’ versions
are being elaborated.
5. However QCA has also been applied in large-N settings as well (see later).
6. Adapted from Herrmann and Cronqvist (2005).
7. For an overview of the critiques, see De Meur and Rihoux (2002), Rihoux (2003),
Rihoux et al. (2004) and De Meur et al. (forthcoming).
8. Among other resources, an exhaustive list of applications can be found on the
COMPASSS resource site: www.compasss.org

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Biographical Note: Benoît Rihoux is Professor of Political Science at the Univer-

sité catholique de Louvain (Belgium). His substantive research interests include
political parties, new social movements and organizational studies. He is coor-
dinator of the COMPASSS research group (www.compasss.org) around system-
atic comparative methods, and joint convenor of international initiatives around
methods more generally, such as the ECPR Standing Group on Political Method-
ology and the ECPR Summer School in Methods and Techniques.
Address: Centre de Politique Comparée (CPC) and COMPASSS, Université
catholique de Louvain (UCL), 1/7 Place Montesquieu, B-1348 Louvain-la-Neuve,
Belgium. [email: rihoux@spri.ucl.ac.be]

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