Most frequently asked questions about NCA are answered in more depth in the online NCA book or on the online NCA Forum. If your question is not answered in these sources, or if you want to elaborate on an answer, please raise your question or make your comment on the NCA Forum, or contact a member of the NCA Development team.
NCA Theory
A necessary condition is a (level of a) condition that must be present to have a given (level of the) outcome. Without the condition the outcome will not occur.
See Section 3.3
A necessary condition enables the outcome to exist, while a sufficient condition produces the outcome.
See Chapter 1
A necessary condition is typically expressed in line with necessity logic: The presence of X is necessary for the presence of Y. This statement can, however, also be re-formulated from a sufficiency perspective: the absence of X is sufficient for the absence of Y.
Conventionally, “X is necessary for Y” implies that “the presence or high level of X is necessary for the presence of high level of Y”. It is also possible to formulate necessity relationships with other presence/absence or low/high combinations (e.g., “a high level of X is necessary for a low level of Y”)
See Section 2.5
A dichotomous necessary condition is a necessary condition that can have only two discrete levels (0/1, absent/present, Low/High, etc.). The outcome can have any number of levels (dichotomous, discrete or continuous).
See Section 2.6
A discrete necessary condition is a necessary condition that can have more than two discrete levels, for example trichotomous (0/1/2, absent/neutral/present, Low/Medium/High, etc.). The outcome can have any number of levels (dichotomous, discrete or continuous).
See Section 2.6
A continuous necessary condition is a necessary condition that can have an infinite number of levels between a minimum value and a maximum value. The outcome can have any number of levels (dichotomous, discrete or continuous).
See Section 2.6
A necessary condition “in kind” is a qualitative expression of necessity of the condition for the outcome: “X is necessary for Y”.
See Section 2.6
A necessary condition “in degree” is a quantitative expression of necessity of the condition for the outcome: “X=Xc is necessary for Y=Yc ”, where Xc and Yc are specific levels of the condition and the outcome, respectively.
See Section 2.6
The general mathematical description of necessary conditions is Y ≤ fi(Xi), where Y is the outcome, Xi is the condition, and fi(Xi) is the ceiling line for Xi. NCA assumes that the ceiling line is non-decreasing. This allows making statements like "Xi ≥ Xic is necessary for Y = Yc", where C is a point (Xic ,Yc) on the ceiling line.
With one condition, NCA draws a ceiling line f1(X1), such that X1 ≥ X1c is necessary for Y = Yc. The maximum possible Y = yc for a given value X1 = x1, is yc = f1(x1).
See Section 4.3
With two conditions (X1 and X2), there is a three dimensional space (X1,X2,Y) in which an imaginary blanket is put on the data (ceiling surface). NCA considers only the projection of the ceiling surface on the X1,Y plane to get the ceiling line f1(X1) for X1 , and the projection of the ceiling surface on the X2,Y plane to get the ceiling line f2(X2) for X2. Since both X1 ≥ X1c AND X2 ≥ X2c are necessary for Y = Yc, the maximum possible Y = yc for given values X1 = x1, and X2= x2 is Yc = min {f1(x1), f2(x2)}.
In other words: When considering multiple necessary conditions, each condition individually constrains Y and can be used to estimate a maximum value of Y. The maximum value of Y will always be the lowest maximum value Y estimated across all conditions.
See Section 4.6
A necessity theory has four elements:
- Focal unit: the entity the theory applies to: a person, a firm, a country, a project, etc.
- Concepts: the varying characteristics of the focal unit. In NCA, the cause is called the condition and the effect the outcome.
- A proposition: the causal relationship between condition and outcome, expressed as a necessity relationship: X is necessary for Y
- Theoretical domain: the set of cases defined temporally, geographically, demographically, or conceptually where the theory is claimed to hold.
See Section 3.2
A formal necessity hypothesis is a hypothesis that has been fully developed and is ready for empirical testing. Developing a formal necessity hypothesis consists of three steps: Defining a preliminary hypothesis, conducting thought experiments, and providing a fully developed causal explanation. It has five characteristics:
- Theory-grounded: embedded in a necessity theory (focal unit, concepts, proposition, theoretical domain all defined).
- Testable: X and Y can be operationalized into measurable variables.
- Non-trivial: both the absence of the condition and the presence of the outcome are actually possible (not near-constant).
- Plausible: virtually no cases are reasonably expected to fall in the empty corner.
- Complete: a plausible explanation exists for why X is necessary for Y.
See Section 7.5
A complete causal explanation for a necessity hypothesis answers at least three questions:
- Why does the presence of X enable Y? (Why does X help make Y possible?)
- Why does the absence of X constrain Y? (Why does removing X disrupt the mechanism that produces Y?)
- Why is there no substitute for X? (Why can no other factor or pathway compensate for its absence?)
Additionally, it should be clear why X precedes Y temporally. In some cases, this is self-evident. When it is not, however, the argument and research design need to be adapted accordingly.
See Section 7.5
Necessity models are simple (parsimonious) because even a single factor can explain the absence of the outcome if the necessary condition is absent. This contrasts sufficiency theories and models (e.g., as with structural equation models) where many factors together predict the presence of the outcome.
See Section 3.3
One reason for the complexity of sufficiency theories and models is that for multi-causal phenomena the outcome can only be properly explained when many factors that help to produce the outcome are considered. Furthermore, when population parameters are estimated with regression models, not including relevant variables (confounders) may cause “omitted variable bias” (incorrect estimation of the regression coefficients of the variables that are included in the model). This bias occurs when variables that correlate with other variables in the model and with the outcome are omitted. By adding “control” variables, the explanatory power of the model can be improved, and omitted variable bias can be reduced. As a result sufficiency models can become complex.
See Section 11.3
True necessity relationships are unaffected by omitted variable bias because the necessary condition operates in isolation from the rest of the causal structure. The NCA parameters of the necessary condition are unaffected by adding or deleting other variables from the theory/conceptual model. One reason is that NCA takes the projections of the ceiling surface in XY planes, and is thus bivariate by definition.
If one can come up with an “omitted variable” that better explains the relationship between X and Y, this means that the necessity theory is imperfect and needs to be changed/refined. Issues such as these are strictly theoretical and precede data analysis. With a convincing argument as to why X is necessary for Y (especially why X is non-compensable), omitted variable bias does not apply.
See Section 11.3
Necessity theory and necessity conceptual models do not need control variables because the NCA parameters are the same with and without having control variables in the theory/model. See also the response to the previous question.
See Section 11.3
Unlike QCA, NCA only considers single necessary conditions. In NCA, an OR-combination (X1X1 or X2X2 is necessary for YY) is often an indication that a higher order construct is necessary for the outcome. For example, neither a “green apple” nor a “red apple” are necessary for an apple pie, while “apple” is necessary. In NCA’s procedures for formulating a formal necessary condition hypothesis, a relevant higher order construct (“apple”), rather than the related lower order construct (“green apple” OR “red apple”), should be recognized and become part of the analysis.
See Section 11.5
NCA Research design
In principle, NCA can also be used for an exploratory study. This, however, is generally not recommended.
Three things are required to draw a positive conclusion regarding necessity: 1) statistical significance (e.g., through the p-value), 2) practical significance (e.g., through the d-value or bottleneck table), and 3) a theoretical justification.
When conducting an exploratory study without prior theorizing, only the first two criteria may can be met. The only conclusion that can be validly draw is that the data pattern aligns with a pattern that would be observed under necessity. To actually conclude that X is necessary for Y, a convincing theoretical justification must still be provided. Even if a convincing argument is provided post-hoc, a new hypothesis-testing study would then still have to be conducted to draw a valid conclusion.
At most, an exploratory study may thus inform a necessity hypothesis for future testing. Since necessity theorizing is parsimonious and clear, however, it is almost always most appropriate to evaluate the potential necessity of conditions before conducting any analyses.
See Section 7.2
In an experiment the condition (X) is manipulated and the effect on the outcome (Y) is observed.
In the regular sufficiency-based experiment cases without (or with a low level of) the outcome are selected and the condition is added (or increased) to observe whether the outcome appears (“Gain of function experiment”) by looking at the average effect compared to a control group where the manipulation was not done.
In the necessity experiment cases with (or with a high level of) the outcome are selected and the condition is eliminated (or reduced) to observe whether the outcome disappears (“Loss of function experiment”) by looking at the maximum effect compared to a control group where the manipulation was not done.
See Section 8.2
In an observational study (large N) the condition (X) and the outcome (Y) are observed in real-life context without manipulation of the condition. There is no difference between a sufficiency observational research design, and necessity observational research design. Only the data analysis differs. For causal interpretations, a convincing theoretical explanation is essential.
See Section 8.2
In a (small N) case study the condition (X) and the outcome (Y) are observed in real-life context. The regular sufficiency case study explores conditions (X) that may produce the outcome (Y). The necessity case study identifies the common (hence necessary) conditions (X), in one or more cases with the outcome (Y).
For theory building, there is no difference between a sufficiency-based case study research design, and necessity-based case study research design. Only the data analysis differs. However, whereas the case study can not be used for testing sufficiency theory, it can be used for testing necessity theory. Even one case (and a deterministic view on necessity) can reject a necessity theory, when the assumed necessary condition is not present in a case where the outcome is present.
See Section 8.2
In an archival study, an existing data set (usually from an observational study) is used. In the regular archival study the data are (re)analysed to build or test a theory. In the necessity archival study the data are analysed using NCA. Using NCA with archival data is particularly useful since the data are usually only analysed with a probabilistic sufficiency causal perspective on XY relationships, whereas NCA can add the necessity perspective.
See Section 8.5
Sampling is the selection of cases from a population of cases for subsequent measurement and data analysis. For NCA the common sampling methods are the same as for any other research approach and data analysis technique (e.g., census, probability sampling, convenience sampling). Only purposive sampling (usually done in qualitative research) is performed differently.
A census is a “sample” in which all cases of the population become part of the “sample” (and the data base). With a census statistical inference from sample to population is not relevant and unnecessary because the population information is available in the “sample”. For NCA the census is the same as for any other research approach and data analysis technique.
A probability sample (random sample) is a sample in which all cases of the population had the same probability to become part of the sample (and the data base). This can be achieved by random sampling from a complete list of cases of the population (sampling frame). A probability sample is a requirement for statistical inference from sample to population. For NCA the probability sample is the same as for any other research approaches and data analysis technique.
A convenience sample is a sample in which cases from the population are selected for convenience of the researcher, for example, because cases are easily accessible. When a convenience sample is used as a substitute of a probability sample, statistical inference is flawed. For NCA the convenience sample is the same as for any other research approach and data analysis technique.
A purposive sample is a sample in which cases from the population are specifically selected with a certain purpose. In NCA purposive sampling can be applied for testing necessity theory by sampling only cases with the outcome present With an necessity experiment this sample is used to observe if the outcome disappears when the condition is removed. In an necessity observational study this sample is used to observe if the condition is present in all sampled cases where the outcome is present. If not, necessity is rejected.
With an observational study it is also possible to sample only cases where the condition is absent and to observe if the outcome is present, which results in a rejection.
With a purposive sample, estimations for general parameters of the population (e.g., mean) cannot be obtained because these estimations require information about the entire population.
The short answer is “At least 1, but the larger the better”.
NCA may be performed with a single case. This is possible when the condition and outcome can have only two values (absent/present, low/high, 0/1, etc.) and with a deterministic view on necessity causality. For testing the hypothesis that the presence of X is necessary for the presence of Y, a case with the outcome present should be selected. Then the researcher observes if the condition is present or not. If the condition is not present, the hypothesis is rejected (falsification). This is one test of the hypothesis with a single case. Such test could be replicated with multiple cases, but the test itself is done with a single case.
In most NCA applications X and Y can have several levels, and samples are drawn from a population for the estimation of the NCA parameters, for example the effect size. Like with other methods, the estimation becomes better when sample size increases.
There is no recommended minimum, optimum or maximum sample size. The quality of the estimation depends on many factors.
NCA Data analysis
A bivariate necessary condition analysis is a necessary condition analysis with one condition and one outcome
See Section 4.6
A multiple necessary condition analysis is a necessary condition analysis with more than one conditions and one outcome. It consists of multiple bivariate necessary conditions analyses as the results of the analyses are independent of each other.
See Section 4.6
A ceiling line is a ceiling in the two-dimensional space, where the ceiling function f(X) is a line. The line can be estimated using various different techniques:
| Common ceiling Techniques in NCA | Name in NCA software | Name |
| CE-FDH | ce_fdh | Ceiling Envelopment with Free Disposal Hull |
| CR-FDH | cr_fdh | Ceiling Regression with Free Disposal Hull |
| C-LP | c_lp | Ceiling - Linear Programming |
| CE-VRS | ce_vrs | Ceiling Envelopment with Varying Return to Scale |
| CR-VRS | cr_vrs | Ceiling Regression with Varying Return to Scale |
See Section 4.3
The Ceiling Envelopment – Free Disposal Hull (CE-FDH ) ceiling technique is a ceiling approximation obtained from the Free Disposal Hull (FDH) data envelopment technique that assumes that the ceiling is non-decreasing, resulting in a non-decreasing step function. In the NCA software package for R, the CE-FDH ceiling technique is the default ceiling technique for dichotomous and discrete (with few values) necessary conditions or when the border is 'jumpy'.
See Section 4.3
The Ceiling Regression - Free Disposal Hull (CR-FDH) ceiling technique is a ceiling approximation that smooths the step function obtained by the CE-FDH technique by using OLS regression through the upper-left corners of the step function. In the NCA software package for R, the CR-FDH ceiling technique is the default ceiling technique for discrete (with many values) and continuous necessary conditions.
See Section 4.3
The Ceiling - Linear Programming (C-LP) ceiling technique is a ceiling approximation that selects two upper left points from the step function obtained by the CE-FDH such that the empty space is maximum. The ceiling accuracy of this line is 100%. It can be used for simulations when there is no measurement error in the data.
See Section 4.3
The Ceiling Envelopment - Varying Return to Scale (CE-VRS ) ceiling technique is a ceiling approximation obtained from Data Envelopment Analysis (DEA) that assumes that the ceiling is convex, resulting in a piecewise linear convex ceiling function.
See Section 4.3
The Ceiling Regression - Varying Return to Scale (CE-VRS ) ceiling technique is a ceiling approximation that smooths the piecewise linear function obtained by the CE-VRS technique by using OLS regression through the corners of the piecewise linear function.
See Section 4.3
The bounding box is the rectangle defined by the observed or theoretical limits of the condition and outcome.
See Section 4.3
The scope is the surface area of the bounding box.
See Section 4.4
The ceiling zone (C) is the area in a corner of the bounding box where points cannot exist (except for exceptions and noise in certain cases).
See Section 4.4
The necessary condition effect size (d) is the proportion of the scope above the ceiling: d = C/S. It ranges from 0 to 1 (0 ≤ d ≤ 1). The effect size indicates to what extent the condition is necessary for the outcome. In other words: to what extent the condition constrains the outcome, and the outcome is constrained by the condition.
See Section 4.4
There is no fixed, universal benchmark. NCA's typically suggested threshold is d = 0.10, originally proposed in Dul (2016):
“An effect size can be valued as important or not, depending on the context. A given effect size can be small in one context and large in another. General qualifications for the size of an effect as ‘small,’ ‘medium,’ or ‘large’ are therefore disputable. If, nevertheless, a researcher wishes to have a general benchmark for necessary condition effect size, I would offer 0 < d < 0.1 as a ‘small effect,’ 0.1 ≤ d < 0.3 as a ‘medium effect,’ 0.3 ≤ d < 0.5 as a ‘large effect,’ and d ≥ 0.5 as a ‘very large effect’.”(Dul, 2016, p.30).
However, an effect size threshold should always be consciously chosen. In situations where a weak constraint can have significant consequences, a lower threshold level may be selected; when consequences are costly or critical, a higher threshold may be needed.
See Section 9.4
Condition inefficiency is the percentage of the range of the condition where the condition is not necessary for the outcome. In other words: where the condition does not constrain the outcome.
See Section 4.4
Outcome inefficiency is the percentage of the range of the outcome where the condition is not necessary for the outcome. In other words: where the outcome is not constrained by the condition.
See Section 4.4
The bottleneck table is a tabular representation of the ceiling. It indicates the required necessary level of the condition(s) for a given level of the outcome ("necessity in degree". The bottleneck table is particularly useful for interpreting multiple necessary conditions.
See Section 9.11
NCA’s statistical test relies on permutation tests to estimate the p-value, with the necessity effect size itself as the test statistic. The core version, the "Null" test, evaluates whether the observed effect size differs from 0. Other tests ("Contrast," "Independent," "Paired") compare effect sizes between conditions, groups, or time points.
A simulation of the power of the test for estimating a desirable sample size for a new NCA study can be activated in the NCA software using the nca_power function.
See Section 5.3
NCA’s significance test (p-value) displaying a value below a specified threshold is only one of three criteria used in the decision process. The other criteria are the availability of theoretical support (e.g., through a formal necessity hypothesis) which focuses the analysis on the right expected empty corner of the XY plot, and a large enough effect size that is considered practically relevant (e.g., > 0.10). If one of these requirements is not satisfied, NCA rejects necessity. NCA considers necessity being supported (not rejected) only if all three requirements are met.
Simulations show that with this approach NCA has a high True Positive Rate (sensitivity) and a high True Negative Rate (specificity), which help to minimize the risk of false positive and false negative conclusions about necessity.
BIPMA refers to the Bottleneck Importance Performance Map Analysis. It is a visualization tool that can assist practitioners to prioritize their actions and resources based on the results of (PLS-)SEM and NCA.
See Section 11.4 and Appendix H
NERT extends a conventional regression table by adding two columns: the necessity effect size and its significance. It facilitates side-by-side reporting and interpretation of regression/SEM results (average effects) and NCA results (necessity).
See Section 11.3
NEST (NCA-Extended Solution Table) combines NCA's necessity-in-degree results with QCA's sufficiency (solution table) results, giving a joint view of necessary and sufficient conditions for the same outcome.
See Section 11.6
NCA limitations
No. NCA only can predict the absence of an outcome, not the presence of the outcome. NCA focuses on single conditions that each will prevent the outcome to occur when the conditions is absent or has a low level. Traditional sufficiency methods such as Multiple Regression, Structural Equation Modeling, Partial Least Squares, as well as methods like QCA consider the complex causal structures that produce the outcome. These methods must be used to predict the presence of the outcome from a set of conditions.
See Section 2.4
No. Just like other data analysis approaches NCA presumes that the data to be analysed are valid, reliable and meaningful. If this assumption is not correct the results of the NCA analysis can be flawed. NCA is not sensitive for measurement error of observations (far) below the ceiling line, but sensitive for measurement error of observations around the ceiling line.
See Section 5.8
No. Just like other data analysis approaches, NCA may be sensitive for outliers. NCA has a specific outlier analysis approach. In NCA an outlier is defined as case that -if removed from the dataset- has a large influence on the effect size. Two types of outliers exist: ceiling outlliers are cases that define the ceiling and scope outliers that define the scope. If the outlier is caused by measurement error that cannot be corrected or by sampling error because the case does not belong to the theoretical domain, the outliers is removed from the data set. If there is a outlier without known reason the outlier is usually kept in the data set.
See Section 9.8
No. Just like any other method, causality cannot be inferred exclusively from data. Strong research design and, most importantly, a convincing causal argument are required to draw causal conclusions.
See Section 2.7
No. Just like other quantitative data analysis approaches NCA presumes that the sample is a probability sample (e.g., random sample) from the population. If this assumption is not true and the sample is not representative for the population, the results of the NCA analysis (and any other data analysis approach for statistical inference) can be flawed.
See Section 8.3
NCA and other data analysis methods
For a comprehensive discussion of NCA, QCA, and regression-based methods, see Chapter 11 and the downloads below.
A more comprehensive comparison between NCA and QCA is available in the downloads below.
Qualitative Comparative Analysis (QCA; Ragin 1987, 2000, 2008, see also http://www.compasss.org/) is a method for identifying necessary and sufficient conditions using fuzzy sets. Condition X and outcome Y are expressed in terms of set membership scores, rather than conventional variable scores. With respect to a certain characteristic a case can be fully out of the set (set membership score = 0) or fully in the set (set membership score = 1). For example, the Netherlands is a case (of all countries) that can be considered as “fully in the set” of rich countries (based on the economic variable Gross Domestic Product, GDP), and Ethiopia can be considered as a case that is “fully out of the set” of rich countries. In crisp-set QCA (csQCA) the set membership scores can only be 0 and 1. In fuzzy-set QCA the membership scores can also have values between 0 and 1. For example, Croatia could be allocated a set membership score of 0.7 indicating that it is “more in the set” than “out of the set” of rich countries.
Set membership scores are obtained by transforming variable data and other information into set membership scores. This transformation process is called “calibration”. Calibration can be based on the distribution of the data, the measurement scale, or expert knowledge. Users of QCA can evaluate the (potentially large) effect of calibration on necessity using calibration evaluation tool.
QCA performs two separate analyses: a necessity analysis for identifying necessary conditions, and a truth table analysis for identifying sufficient configurations.
Although in most NCA applications conventional variable scores are used for quantifying condition X and outcome Y, NCA can also employ set membership scores for the conditions and the outcome, allowing a comparison between NCA and QCA. CsQCA and fsQCA have different procedures for identifying necessary conditions.
Necessity analysis of csQCA compared to NCA
The necessity analysis of csQCA is basically the same as NCA’s necessity analysis for dichotomous scores of X and Y. A necessary condition is assumed to exist if the condition is present (X=1) in virtually all cases where the outcome is present (Y=1), hence virtually no cases exist in which the outcome is present (Y=1) and the condition is absent (X=0). This is illustrated with the contingency table (see figure).
When cases are present in the “empty” zone above the diagonal (open circles) fsQCA considers these cases as “deviant cases”. FsQCA accepts some deviant cases as long as the necessity consistency level, which is computed from the total vertical distances of the deviant cases to the diagonal, is not smaller than a certain threshold, usually 0.9. FsQCA makes a qualitative (“in kind”) statement about the necessity of X for Y: “X is necessary for Y” (e.g., the presence of X is necessary for the presence of Y).
In contrast, NCA uses the ceiling line (see above) as the reference line (see right figure) for evaluating the necessity of X for Y (with possibly some cases above the ceiling line; accuracy below 100%). In situations where fsQCA observes “deviant cases”, NCA includes these cases in the analysis by moving the reference line from the diagonal position to the boundary between the zone with cases and the zone without cases. NCA considers cases around the ceiling line (and usually above the diagonal) as “best practice” cases rather than “deviant” cases. These cases are able to reach a high level of outcome (e.g., an output that is desired) for a relatively low level of condition (e.g., an input that requires effort).
In NCA the size of the “empty” zone as a fraction of the total zone (empty plus full zone) is called the necessity effect size (see above). If the effect size is greater than zero (an empty zone is present) NCA has identified a necessary condition “in kind” that can be formulated as: “X is necessary for Y”, indicating that for at least a part of the range of X and the range of Y a certain level of X is necessary for a certain level of Y.
Additionally, NCA can quantitatively formulate necessary condition “in degree” by using the ceiling line: “level Xc of X is necessary for level Yc of Y”. The ceiling line represents all combinations X and Y where X is necessary for Y. (Although also fsQCA’s diagonal reference line allows for making quantitative necessary conditions statements, e.g. X>0.3 is necessary for Y=0.3, fsQCA does not make such statements).
When the ceiling line coincides with the diagonal (corresponding to the situation that fsQCA considers) the statement “X is necessary for Y” applies to all X-levels [0,1] and all Y-levels [0,1] and the results of the qualitative necessity analysis of fsQCA and NCA are the same. When the ceiling line is positioned above the diagonal “X is necessary for Y” only applies to a specific range of X and a specific range of Y. Outside these ranges X is not necessary for Y (“inefficiency”, see above). Then the results of the qualitative necessity analysis of fsQCA and NCA can be different.
Normally, NCA identifies more necessary conditions than fsQCA (see Comparing NCA and QCA in the downloads below). In the example NCA identifies that X is necessary for Y because there is an empty zone above the ceiling line. For example, for reaching an outcome level of Yc = 0.8 the necessary level of the condition is Xc = 0.6. Thus, when the condition level is below 0.6, it is not possible to reach an outcome level of 0.8. However, fsQCA would conclude that X is not necessary for Y, because the necessity consistency level is too small in this example (<0.9).
FsQCA’s necessity analysis can be considered as a special case of NCA (an NCA analysis with discrete or continuous fuzzy set membership scores for X and Y, a ceiling line that is diagonal, an allowance of a specific number of cases in the empty zone given by the necessity consistency threshold, and the formulation of a qualitative “in kind” necessity statement).
Although QCA can perform a necessity analysis as shown above, most QCA researchers focus on the sufficiency analysis. Whereas single necessary conditions are not uncommon (and very relevant because when the necessary levels of the condition are not in place the outcome will not occur), single sufficient conditions are extremely rare (in multicausal phenomena no single condition can produce the outcome). Therefore QCA focuses on combinations of conditions that are sufficient for the outcome (sufficient configurations). For identifying sufficient configurations QCA uses binary logic (using a truth table where the condition and outcome can have only two values: true of false). With k conditions of two values, a total of 2k possible combinations can be formulated. QCA identifies which of these combinations are observed in cases. Usually several configurations that can produce the outcome are observed(“equifinality”). When identified configurations are parsimonious (non-rerdundant) causal interpretations may be possible (Baumgartner, 2015).
QCA’s logical statements are expressed for example as follows (adapted from Goertz, 2003):
Y = X1*X2*X3 + X4*X5 (1)
In this example five conditions (X1, X2, X3, X4, X5) and one outcome Y are present. The symbol “+” means the logical “OR” and the symbol “*” means the logical “AND.” Equation (1) indicates that the presence of Y can be achieved via only two paths. The first paths is configuration X1*X2*X3 (the presence of X1 AND X2 AND X3) and the second possible path is configuration X4*X5 (the presence of X4 AND X5).
Each configuration has certain conditions (e.g., X1, X2,... ) that must be part of the configuration such that the configuration can produce the outcome. For example, X3 is part of the first configuration that can produce the outcome. The necessary parts of an outcome producing configuration are called INUS conditions (Mackie,1965): “Insufficient but Non-redundant (i.e., Necessary) part of an Unnecessary but Sufficient condition.” Non-redundant means that the conditions that are part of the configuration that produces (is sufficient for) the outcome, are essential (necessary).
Mackie (1965) repeatedly makes a distinction between an INUS condition and a necessary condition. For example he states on page 253: "Again, some causal statements pick out something that is not only an INUS condition but also a necessary condition". An INUS condition is only necessary for a specific configuration (non-redundant part of it), whereas a necessary condition is necessary for the outcome (hence must be present in all configurations that can produce the outcome). In equation (1) X3 is an INUS condition that is necessary for the configuration to produce the outcome, but it is not necessary for the outcome because configuration X4*X5 can also produce the outcome and does not contain X3. In contrast, in equation (2) below, where Y can be produced by only two configurations (X1*X2*X3 or X4*X3), X3 is part of both configurations that can produce the outcome.
Y = X1*X2*X3 + X4*X3 (2)
In equation (2) X3 is not only an INUS conditions for the two configurations, but also a necessary condition for the outcome. A condition is necessary if it is present in all configurations that produce the outcome. Normally, an INUS condition is not a necessary condition, but a necessary condition is always an INUS condition. Or as Mackie (1965, p. 253) puts it: "... some causal statements pick out something that is not only an INUS condition, but also a necessary condition."
It is possible that no necessary condition exist in the causal structure, but that only INUS conditions exist. For example in equation (1) there is no necessary condition and five INUS conditions. However, when a necessary condition is identified its practical relevance is clear-cut: if the condition is not in place in any possible configurations, the configuration will not produce the outcome. When the outcome is desired (e.g., performance in business applications) a practitioner must ensure that the necessary condition is always present. When the outcome is undesired (e.g., disease in medical applications) the practitioner must ensure that the necessary condition is never present (see NOTE below).
NCA is a method for identifying necessary conditions (hence its name). It is not designed for identifying sufficient configurations, nor for identifying INUS conditions of sufficient configurations. NCA only identifies necessary conditions for the outcome. These necessary conditions must be part of all sufficient configurations (and therefore become also INUS conditions for the configurations: insufficient but necessary parts of all unnecessary sufficient configurations).
NOTE: In his influential work on causes in epidemiological research, Rothman (1976) introduces the notion component causes of disease, which corresponds to Mackie’s INUS logic. “If there exists a component cause which is a member of every sufficient cause, such a component is termed a necessary cause. Necessary causes are often identifiable as part of the definition of effect” (p. 588, emphasis added). For example, certain bacteria and viruses are dichotomous necessary causes of infectious diseases: the tubercle bacillus is a necessary cause of tuberculosis, the Human Immunodeficiency Virus (HIV) is a necessary cause of AIDS, and the Human Papilloma Virus (HPV) is a necessary cause of cervical cancer (Dul, 2016b). Rothman et al. (2008) refer to a necessary cause (i.e., component cause of all sufficient causes) as a “universally necessary cause”. Prevention then can focus on the necessary cause (e.g., HPV screening and vaccination of women for prevention of cervical cancer).
Conditional statements are not the same as causal statements. According to the logic of conditional statements “A is necessary for B”, is equivalent to the conditional statements: “not A is sufficient for not B”, “B is sufficient for A”, and “not B is necessary for not A”. For example, when A is HIV and B is AIDS the following logical conditional statements apply if HIV is necessary for AIDS:
- HIV is necessary for AIDS
- No HIV is sufficient for no AIDS
- AIDS is sufficient for HIV
- No AIDS is necessary for no HIV
Conditional logic makes no assumption about the causal direction of the relationship between the concepts A and B. A fundamental difference between conditional statements and causal statements is that the latter presumes a temporal order between the concepts: first the cause (antecedent), then the effect (consequent). An infection of HIV precedes the disease AIDS (A causes B). Then it is not possible that AIDS precedes HIV (B causes A). Therefore conditional statements 3 and 4 are no correct causal statements. Only conditional statements 1 and 2 reflect that HIV is a necessary cause of AIDS. Statement 1 is the necessity of presence formulation of the necessary cause and statement 2 is the sufficiency of absence formulation of the necessary cause (Dul 2016b).
When researchers use NCA and other data analysis techniques for building and testing theory they presume a causal relationship between concepts. A fundamental characteristic of any scientific theory is that causal relationships exist between the concepts of the theory. These causal relationships are represented by arrows in a conceptual model, and allow for making predictions, which is one main goal of theory in applied sciences (“there is nothing as practical as a good theory”). In the context of theory causal statements are named “propositions”, and in the context of theory building or testing empirical research they are called “hypotheses”. In a necessary condition theory it is known or presumed that the condition precedes the outcome. This is emphasized by using the convention “X” for the condition (the cause), and “Y” for the outcome (the effect). Hence, in the context of theory and theory building or testing research “X is a necessary condition for Y” means “the presence of X is a necessary cause for the presence of Y”.
Empirical data can provide support or not for a causal necessary condition relationship. If the data suggest that A is a necessary condition for B, with the researcher’s information that A precedes B it is plausible that A is a necessary cause of B. Then the alternative reverse causality that B is a sufficient cause of A is not plausible, as B does not precede A. In other words, although the data may also support that B is a sufficient condition for A, the researcher’s information on the causal direction excludes the possibility that B is a sufficient cause of A. Information about the causal direction can be obtained, for example, by using a (quasi) experimental research design (where the condition X changes before the outcome Y), by providing theoretical arguments for the causal direction X --> Y, or by process tracing of cases to evaluate whether condition X changes before outcome Y. This additional information for making causal interpretations is similar to the additional information that is needed for making causal interpretations of correlations and associations in regression analyses.
A researcher in the applied sciences who uses a tool for analysing empirical data for building or testing theory assumes causal directions between the concepts of interest (reflected in propositions), based on additional information. Researchers who use NCA's (or QCA's) necessity analyses, usually assume that the condition causes the outcome, hence that A or B is the antecedent condition (X) and the other one is the outcome Y that follows. If it is assumed that B (assigned Y) follows A (assigned X), the data suggest that A (X) is necessary cause of B (Y). However, if it were assumed that A (assigned Y) follows B (assigned X) then the data suggest that B (X) is a sufficient cause of A (Y).
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