A Nomenclature and glossary

A.1 Nomenclature

Symbol	Meaning
\(\alpha\)	Threshold value for statistical significance
\(a\)	Intercept of a linear function
\(b\)	Slope of a linear function
\(C\)	Size of the ceiling zone; A point on the ceiling line \((x_c, y_c)\)
\(ca\)	Model fit metric ceiling accuracy
\(cp\)	Model fit metric complexity
\(d\)	Effect size
\(df\)	Degrees of freedom of a necessity model
\(ex\)	Model fit metric exceptions
\(f\)	General symbol for a mathematical function
\(F\)	Feasible area
\(ft\)	Model fit metric fit
\(h\)	Horizontal segment of a ceiling line
\(H\)	Hypothesis
\(i\)	Index for an observation or of a segment of a ceiling line
\(j\)	Index for a variable
\(J\)	Number of necessary conditions
\(k\)	Number of outliers in a set of outliers
\(lowP\)	Number of cases in the lowP-zone
\(lowS\)	Number of cases in the lowS-zone
\(max\)	Maximum value of a given range
\(medP\)	Number of cases in the medP-zone
\(medS\)	Number of cases in the medS-zone
\(min\)	Minimum value of a given range
\(n\)	Sample size
\(N\)	Necessary condition (in NEST)
\(nc\)	Necessary condition; necessary cause (near arrow in causal graph)
\(ns\)	Model fit metric noise
\(p\)	\(p\)-value for a statistical significance test
\(P\)	Number of peers that define the ceiling line
\(S\)	Scope: the size of the bounding box
\(sd\)	Standard deviation
\(sh\)	Model fit metric sharpness
\(sp\)	Model fit metric spread
\(su\)	Model fit metric support
\(T\)	Time indicator
\(v\)	Vertical segment of a ceiling line
\(X, Y, Z\)	Variable names (capitals)
\(x, y, z\)	Variable values (lower case)

A.2 Glossary

This glossary defines important terms used throughout this book. Defined terms are printed in bold. When a definition contains another defined term, it is printed in italic. When a defined term appears more than once within a single definition, only its first occurrence is highlighted.

# above. An NCA parameter indicating the number of cases above the ceiling line.

Absence/low value of condition/outcome. A value of a condition or outcome that is close to its minimum. Also see Presence/high value of condition/outcome, Direction (of a necessary condition).

Absolute inefficiency. The area of the bounding box where the necessary condition does not constrain the outcome and the outcome is not constrained by the necessary condition. Also see Relative inefficiency, Condition inefficiency, Outcome inefficiency.

Academia. The world of higher education and research, like universities, focusing on theory, discovery, and teaching. Also see Practice.

Accuracy. See Ceiling accuracy, \(p\)-value accuracy.

Adjacent corner. A corner in the bounding box next to the corner of interest. Also see Opposite corner, Expected empty corner.

Alternative hypothesis. A statistical concept describing a competing claim to the null hypothesis. Also see Formal necessity hypothesis.

Analyst. A scholar or practitioner who uses NCA or other methodological approaches.

Binary logic. Two-valued logic where statements can only be true or false. Also see Conditional logic, Causal logic, Necessity logic, Sufficiency logic.

BIPMA. Bottleneck Importance Performance Map Analysis. An NCA tool for giving practical advice based on SEM results and NCA results, based on single bottleneck cases. Also see NERT, IPMA, cIPMA.

Bivariate analysis. An analysis of two variables. Also see Multiple bivariate analyses, \(XY\)-plot, \(XY\)-table, Multivariate analysis.

Boolean logic. See Binary logic.

Bottleneck case. A case without the necessary level(s) of the condition(s), such that it is unable to achieve the target outcome. Also see Non-bottleneck case, Ignored case, Irrelevant case, Single bottleneck case, Multiple bottleneck case.

Bottleneck distance. The gap between a case’s condition value (\(x\)) and target condition value (\(x_c\)). Bottleneck Importance Performance Map Analysis. See BIPMA.

Bottleneck table. A tabular representation of the ceiling line showing which values of the condition(s) is/are necessary for a particular value of the outcome.

Bounding box. The rectangle defined by observed or theoretical limits of the condition and the outcome. Also see Scope, Empirical scope, Theoretical scope, Tight bounding box.

c-accuracy. See Ceiling accuracy.

C-LP. Ceiling–Linear Programming. A linear ceiling line based on minimization of heights of the CE-FDH peers by linear programming. Also see CE-FDH, CR-FDH, CR-VRS, QR.

Case. An instance of a focal unit.

Case selection. The selection of one or a small number of cases from a set of cases for inclusion in a small-n study. Also see Sampling.

Case study. A study design in which one or a small number of cases is selected for a small-n study. Also see Observational study, Longitudinal study, Experimental study.

Causal explanation. A story that connects causes to effects.

Causal interpretation. The causal explanation of a relationship judged as credible based on extra-data considerations such as domain knowledge, simplicity, stability, and the plausibility of underlying assumptions. Often data allow multiple interpretations.

Causal logic. The logic in which statements are causal relationships. Also see Binary logic, Conditional logic, Necessity logic, Sufficiency logic.

Causal narrative. See Causal explanation.

Causal perspective. The perspective selected by the analyst to theorize or infer causality from data. Also see Necessity perspective, Typicality perspective, Sufficiency perspective, Probabilistic sufficiency perspective.

Causal-pluralism study. A multimethod study that uses multiple causal perspectives and corresponding different methods with the same data. Also see Method-triangulation study, Separate studies, Theory-method fit.

Causal relationship. A relationship between two variable characteristics \(X\) and \(Y\) of a focal unit in which a value of \(X\) (or its change) permits, or results in a value of \(Y\) (or in its change).

Causal underdetermination. The idea that data are compatible with multiple distinct causal perspectives and explanations, so the causal structure cannot be uniquely identified from the data alone.

Cause. A variable characteristic \(X\) of a focal unit of which the value (or its change) permits, or results in a value (or its change) of another variable characteristic \(Y\). Also see Necessity cause, Sufficiency cause.

CB-SEM. Covariance-Based SEM. A SEM approach that estimates model parameters based on the covariance matrix. Also see PLS-SEM.

CE-FDH. Ceiling Envelopment–Free Disposal Hull. A stepwise linear ceiling line based on the free disposal hull. Also see Ceiling line, CR-FDH, CE-VRS.

CE-VRS. Ceiling Envelopment–Variable Returns to Scale. A piecewise linear ceiling line consisting of oblique line segments such that envelope is concave when the ceiling zone is in corner 1. Also see Ceiling line, CE-FDH, CR-FDH, CR-VRS.

Ceiling accuracy. A model fit metric expressing the extent to which cases are on or below the ceiling line.

Ceiling Envelopment–Free Disposal Hull. See CE-FDH.

Ceiling Envelopment–Variable Returns to Scale. See CE-VRS.

Ceiling line. The borderline within the bounding box between the area where cases are impossible (ceiling zone) and the area where cases are possible (feasible area), such that a point \((x, y)\) is on the ceiling if and only if, for any other point \((x', y')\) in the bounding box, it holds that if \(x' < x\) and \(y' > y\), then \((x', y')\) is in the ceiling zone and if \(x' \ge x\) and \(y' \le y\), then \((x', y')\) is in the feasible area. Also see CE-FDH, CR-FDH, C-LP, CE-VRS, CR-VRS, QR.

Ceiling outlier. An outlier in the ceiling zone. Also see Scope outlier.

Ceiling Regression–Free Disposal Hull. See CR-FDH.

Ceiling zone. The area in a corner of the bounding box where points cannot exist, except for exceptions and noise. Also see Feasible area.

Chain (of) necessity. See Necessity chain.

Chain necessity effect. The necessity effect of the first element in a necessity chain on the final outcome (the extent to which the initial condition constrains the maximum attainable level of the chain’s endpoint through the intermediate necessary links).

Chained necessity. See Chain necessity effect.

cIPMA. Combined Importance Performance Map Analysis. An extended version of IPMA that includes NCA results by considering a condition’s number of bottleneck cases. Also see BIPMA.

Combined Importance Performance Map Analysis. See cIPMA.

Complete hypothesis. A necessity hypothesis with a plausible causal explanation about why the condition is necessary for the outcome. Also see Formal necessity hypothesis, Trivial hypothesis, Testable hypothesis, Plausible hypothesis.

Completeness. See Complete hypothesis.

Complexity. A model fit metric expressing the number of parameters that are needed for describing the necessity model (degrees of freedom − 4). Also see Model specification.

Concept. The varying characteristic of a focal unit of a theory. Also see Condition, Outcome.

Conceptual model. A visual representation of a hypothesis of a necessity theory in which the condition and outcome are presented by rectangles and the relationship between them by an arrow. The arrow originates in the condition and points to the outcome and represents the causal direction with the letters nc near it to express the direction of the necessary condition. Also see Formal necessity hypothesis.

Condition. A varying characteristic \(X\) of a focal unit of which the value (or its change) permits, or results in a value (or its change) of another varying characteristic \(Y\) (which is called the outcome). Also see Necessary condition, Sufficient condition, Outcome, Predictor (variable).

Condition inefficiency. The area of the bounding box where the condition does not constrain the outcome. Also see Absolute inefficiency, Relative inefficiency, Outcome inefficiency.

Conditional logic. If-then statements that can only be true or false. Also see Binary logic, Causal logic, Necessity logic, Sufficiency logic.

Confounder. A term used in regression-based analysis indicating the theoretical role of a concept as a common cause of two other concepts and that may account for part of the observed relationship between them. Also see Mediator, Moderator.

Contingency table. See \(XY\)-table.

Continuous necessity. A necessity relationship in which the condition and the outcome can have infinite numbers of levels (values). Also see Dichotomous necessity, Discrete necessity.

Contrast test. A permutation test in NCA in which for each case the labels \(X_1\) and \(X_2\) are switched with 50/50 probability. Also see Null test, Independent test, Paired test.

Control variable. A variable that is added in a regression-based data analyses for improving the prediction of the outcome and avoiding biased estimation of regression coefficients. Also see Predictor (variable), Predicted variable.

Convenience sample. A sample in which the instances are selected for convenience of the analyst. Also see Random sample, Purposive case selection.

Corner 1. Upper-left corner of the \(XY\)-plot or bounding box.

Corner 2. Upper-right corner of the \(XY\)-plot or bounding box.

Corner 3. Lower-left corner of the \(XY\)-plot or bounding box.

Corner 4. Lower-right corner of the \(XY\)-plot or bounding box.

Corner of interest. The corner of the bounding box implied by the necessity hypothesis. Also see Formal necessity hypothesis, Corner 1, Corner 2, Corner 3, Corner 4.

Counterexample. A case that is inconsistent with the necessity hypothesis. Also see Exception, Outlier, Noise.

Covariance-Based SEM. See CB-SEM

CR-FDH. Ceiling Regression Free Disposal Hull. A linear ceiling line based on a trend line through the CE-FDH peers. Also see C-LP, QR, CR-VRS.

Credibility. The trustworthiness of conclusions about necessity identified from data. Also see Statistical credibility, Empirical credibility.

Crisp-set Qualitative Comparative Analysis (csQCA). See csQCA.

CR-VRS. Ceiling Regression Variable Returns to Scale. A linear ceiling line based on a trend line through the CE-VRS peers. Also see CR-FDH, C-LP, QR.

csQCA. Crisp-set Qualitative Comparative Analysis. A variant of QCA in which all conditions and outcomes are expressed as binary (0/1) set membership scores, indicating full non-membership (0) or full membership (1) in a set. Also see fsQCA.

\(\mathbf{d}\). See Effect size.

Data. Recordings of evidence generated in the process of data collection. Also see Measurement, Qualitative data, Quantitative data, Longitudinal data.

Data analysis. The interpretation of scores obtained in a study in order to generate the result of the study. Also see Qualitative data analysis, Quantitative data analysis.

Data collection. The process of identifying and selecting one or more objects of measurement, extracting evidence of the value of the relevant variable properties or characteristics from these objects, and recording this evidence. Also see Data, Measurement, Score, Dataset.

Data Generation Process. See DGP.

Dataset. A collection of scores obtained from data collection.

Degrees of freedom. The minimum number of parameters that are needed for describing a necessity model. See also Model specification, Complexity.

Deterministic necessity. Necessity from the deterministic perspective. Also see Typicality necessity.

Deterministic perspective. A causal perspective taken by the analyst that a cause always influences an effect without exceptions. Also see Probabilistic perspective, Typicality perspective.

DGP. Data Generation Process. The hypothetical mechanism that produces the data that are observed.

Dichotomous necessity. A necessity relationship in which the condition or the outcome has only two levels (values). Also see Discrete necessity, Continuous necessity.

Direct effect. A term used in regression-based analyses indicating the effect of \(X\) on \(Y\) without going through an intermediate variable (mediator). Also see Indirect effect, Total effect, Moderator.

Direction (of a necessary condition). An indication whether the condition and outcome in the necessity hypothesis are absent or present. Also see nc, Formal necessity hypothesis.

Discrete necessity. A necessity relationship in which the condition or the outcome has a finite number of levels (values). Also see Dichotomous necessity, Continuous necessity.

Domain. See Theoretical domain.

Effect size. The magnitude of the constraint that a necessary condition poses on the outcome expressed as the size of the ceiling zone relative to the size of the bounding box (scope). Also see \(p\)-value.

Effect size threshold. The value of the effect size selected by the analyst for evaluating the necessity hypothesis. Also see Formal necessity hypothesis, Statistical significance threshold.

Effective case. An intervention case that is in the bottleneck area (bottleneck case) before the intervention and removed from it after the intervention. Also see Ineffective case, Irrelevant case, Ignored case.

Embedded necessity theory. A necessity theory with one or more necessity relationships and one or more other relationships. Also see Pure necessity theory.

Emerging theory. A theory that is not (yet) broadly accepted in academia or practice. Also see Established theory.

Empirical credibility. The trustworthiness of the necessity hypothesis, the study design, the data, and the data analysis used to draw conclusions about necessity. Also see Formal necessity hypothesis, Statistical credibility, Effect size, \(p\)-value, Robustness, Model fit.

Empirical data. Data from the real world. Also see Simulation data

Empirical scope. The bounding box (or its area) defined by empirically observed minimum and maximum values of the condition and the outcome. Also see Theoretical scope, Scope.

Empty area. See Ceiling zone.

Empty corner. See Ceiling zone.

Empty space. See Ceiling zone.

Established theory. A theory that is broadly accepted in academia or practice. Also see Emerging theory.

Evidence-based intervention. An intervention that is based on a hypothesis tested with empirical data.

Exception. A case in the lowP-zone of the ceiling zone that is not the result of error and is accepted by the analyst as a rare counterexample of necessity. Also see Outlier, Noise, Typicality perspective.

Exceptions. A model fit metric expressing the number of cases in the lowP-zone of the ceiling zone that the analyst considers an exception.

Expected empty corner. The area in the bounding box that is predicted to be empty according to the necessity hypothesis. Also see Formal necessity hypothesis, Ceiling zone.

Experimental study. A study design in which the condition is manipulated and the outcome is observed. Also see Observational study, Longitudinal study, Case study.

Expert knowledge. Tacit knowledge of a scholar or practitioner. Also see Explicit knowledge.

Explicit knowledge. Documented knowledge in the literature from academia and practice to be used for formulating a formal necessity hypothesis. Also see Tacit knowledge, Expert knowledge.

Extension. A horizontal or vertical line segment added to the ceiling line that connects peers to envelop the feasible area.

Falsification. The view that theories and hypotheses cannot be proven true, but can only be proven false.

Feasible area. The area within the bounding box below the ceiling line for corner 1 or corner 2, or above the ceiling line (“floor line”) for corner 3 or corner 4. Also see Ceiling zone.

Fiss chart. A solution table of QCA with specific notation for presence or absence of a condition, and for core or peripheral conditions. Also see Solution table, NEST.

Fit. A model fit metric expressing the effect size of a selected ceiling line as percentage of the effect size of the CE-FDH ceiling line.

Floor line. A ceiling line in corner 3 or 4.

Focal unit. The unit of a theory or hypothesis. Examples are ‘employee’, ‘team’, ‘company’, ‘country’. Also see Theory, Theoretical domain.

Formal necessity hypothesis. A necessity relationship that is theory-grounded, testable, non-trivial, plausible and complete. Also see Preliminary necessity hypothesis.

Formal necessity theory. A necessity theory in which the necessity hypotheses are formal necessity hypotheses. Also see Preliminary necessity theory.

Fragility. The absence of robustness.

fsQCA. Fuzzy-set Qualitative Comparative Analysis. A variant of QCA in which conditions and outcomes are expressed as fuzzy set membership scores ranging from 0 to 1. Also see csQCA.

Fuzzy-set Qualitative Comparative Analysis. See fsQCA.

High-high necessity. A necessity relationship where the presence/high value of the condition is necessary for the presence/high value of the outcome (‘+ nc +’). Also see nc, Low-high necessity, High-low necessity, Low-low necessity, direction.

High-low necessity. A necessity relationship where the presence/high value of the condition is necessary for the absence/low value of the outcome (‘+ nc -’). Also see nc, High-high necessity, Low-high necessity, Low-low necessity, direction.

Hypothesis. A statement about the relationship between concepts or variables. Also see Hypothesis testing, Necessity hypothesis, Formal necessity hypothesis.

Hypothesis testing. The procedure of making a decision about the credibility of a hypothesis. Also see Statistical credibility, Empirical credibility, Null hypothesis test, Thought experiment.

Ignored case. A non-intervention case that is in the bottleneck area (bottleneck case) before and after the intervention. Also see Irrelevant case, Effective case, Ineffective case.

Importance Performance Map Analysis. See IPMA.

Independent test. A permutation test in which from a pool of two groups of cases are randomly reassigned to two groups of the same sizes. Also see Null test, Contrast test, Paired test.

Indirect effect. A term used in regression-based analyses indicating the effect of \(X\) on \(Y\) through a mediator. Also see Direct effect, Total effect, Moderator.

Ineffective case. An intervention case that is in the bottleneck area (bottleneck case) before and after the intervention. Also see Effective case, Irrelevant case, Ignored case.

Inefficiency. A set of NCA parameters related to the extent to which the necessary condition covers the range of the condition and the outcome. Also see Absolute inefficiency, Relative inefficiency, Condition inefficiency, Outcome inefficiency.

Infeasible area. See Ceiling zone.

Influential case. A case that has a large influence on the necessity effect size when removed. Also see Outlier.

Informant. A person who is the object of measurement for a variable and who is knowledgeable about that variable and informs the analyst about it. Also see Subject.

Instance of a focal unit. A single case.

Intervention. An external action applied to a case in order to increase or decrease the condition value with the intention to remove the case from the bottleneck area (for a desired target outcome) or move it into the bottleneck area (for an undesired target outcome).

Intervention case. A case to which an intervention is applied. Also see Non-intervention case, Effective case, Ineffective case, Irrelevant case.

Intervention design. The approach to collect and analyze data and displaying crucial results using the bottleneck area.

Intervention effectiveness. The number of treated bottleneck cases that have left the bottleneck area (effective cases) as a percentage of intervention cases.

Intervention efficiency. The amount of intervention effort on intervention cases that was effective in removing cases from the bottleneck area. It is the complement of intervention waste and is expressed in percentages.

Intervention effort. The magnitude of change in the condition value produced by the intervention.

Intervention goal. The intended result of an intervention specified as desired or undesired outcome and possibly by a specific target outcome.

Intervention group. A group consisting of intervention cases.

Intervention strategy. The approach to establish the team for the intervention, set the goals and the target groups, evaluate drivers and barriers, and formulate hypotheses. See also Intervention design.

Intervention waste. The amount of intervention effort that does not contribute to moving cases out of or into the bottleneck area. Also see Undershoot waste, Overshoot waste.

Irrelevant case. An intervention case that is not in the bottleneck area (non-bottleneck case) before (and after) the intervention. Also see Ignored case, Effective case, Ineffective case.

IPMA Importance Performance Map Analysis. A tool for giving practical advice based on SEM results. Also see cIPMA, BIPMA.

Iso-purity line. See Iso-P line.

Iso-P line. A line representing points with the same purity value. Also see Iso-S line, Model fit, NCA ribbon.

Iso-solidity line. See Iso-S line.

Iso-S line. A line representing points with the same solidity value. Also see Iso-P line, Model fit, NCA ribbon.

Large-n study. A study with a large number of cases. n stands for the number of cases. Also see Small-n study.

Likert scale. A rating scale in the format of a limited number of points (e.g., 5 or 7) that can represent a person’s response. Also see Informant, Subject.

Logic. See Binary logic, Causal logic, Conditional logic, Necessity logic, Sufficiency logic.

Longitudinal data. Scores of condition and outcome that are measured at multiple time points. Also see Quantitative data, Qualitative data, Set membership data.

Longitudinal study. A study design with data collection at multiple time points. Also see Observational study, Case study, Experimental study.

Low-high necessity. A necessity relationship where the absence/low value of the condition is necessary for the presence/high value of the outcome (‘- nc +’). Also see nc, High-high necessity, High-low necessity, Low-low necessity, direction.

Low-low necessity. A necessity relationship where the absence/low value of the condition is necessary for the absence/low value of the outcome (‘- nc -’). Also see nc, High-high necessity, Low-high necessity, High-low necessity, direction.

Low-purity zone. See lowP-zone.

Low-solidity zone. See lowS-zone.

lowP-zone. The area of the ceiling zone far from the ceiling line. Also see lowS-zone, medP-zone.

lowS-zone. The part of the feasible area far from the ceiling line. Also see lowP-zone, medS-zone.

Measurement. The process in which scores are generated for data analysis. Also see Data, Measurement validity, Measurement reliability.

Measurement reliability. The degree of precision of a score when the measurement is repeated. Also see Measurement, Measurement validity.

Measurement validity. The extent to which procedures of data collection and of scoring can be considered to meaningfully capture the ideas contained in the concept of which the value is measured. Also see Measurement, Measurement reliability.

Mediator. A term used in regression-based analyses indicating the theoretical intermediate role of a concept between two other concepts. Also see Moderator, Confounder, Necessity chain.

Medium-purity zone. See medP-zone.

Medium-solidity zone. See medS-zone.

medP-zone. The area of the ceiling zone close to the ceiling line. Also see lowP-zone, Iso-P line.

medS-zone. The part of the feasible area close to the ceiling line. Also see lowS-zone, Iso-S line.

Membership score. See Set membership data.

Method-triangulation study. A multimethod study that uses a single causal perspective and corresponding different methods with the same or different data. Also see Causal-pluralism study, Separate-studies, Theory-method fit.

Min-max normalization. A linear transformation that maps values from an original range [min,max] to a chosen range (e.g., 0–1, or 0–100). Also see Standardization.

Model fit. The extent to which a model captures the pattern in the data. Also see Complexity, Fit, Ceiling accuracy, Noise, Exceptions, Support, Spread, Sharpness, Purity, Solidity.

Model specification. The process of selecting the functional form of the ceiling line and the bounding box for chosen condition(s) and outcome.

Moderator. A term used in regression-based analyses indicating the theoretical role of a concept as qualifier of the relationship between two other concepts. Also see Mediator, Confounder, Subgroup ceiling line.

Monte Carlo simulation. A computational method that uses repeated random sampling to approximate the behavior of a system or the value of a quantity. Also see Power.

Multimethod study. A hypothesis-testing study that uses different methods for testing one or more hypotheses with the same or a different causal perspective and with the same or different data. Also see Method-triangulation study, Causal-pluralism study, Separate studies, Theory-method fit.

Multiple bivariate analyses. A series of bivariate analyses. Also see \(XY\)-plot, \(XY\)-table, Multivariate analysis.

Multiple bottleneck case. A case that is a bottleneck case for multiple conditions.

Multiple NCA. The application of NCA with the same outcome and different conditions, where each condition-outcome pair is analyzed with NCA.

Multivariate analysis. An analysis that involves multiple variables simultaneously. Also see bivariate analysis, Multiple bivariate analyses.

Natural distribution. The distribution describing how a system behaves under its unaltered, observable conditions, without forced manipulation.

nc. An abbreviation of ‘necessary condition’ or ‘necessity cause’ placed near the arrow in a conceptual model and preceded and followed by ‘+’ or ‘-’ to indicate the direction of the necessary condition. Also see high-high necessity, low-high necessity, high-low necessity, low-low necessity.

NCA. Necessary Condition Analysis. A methodological approach developed by Jan Dul that uses a necessity causal logic (methodology) for identifying necessary conditions from data (method). Also see NESS, QCA, SCC.

NCA approach. See NCA.

NCA method. The part of NCA concerned with data analysis and empirical testing. Also see NCA methodology.

NCA methodology. The part of NCA concerned with causal logic and theory. Also see NCA method.

NCA parameter. A quantity to evaluate a necessary condition. Also see Ceiling zone, Effect size, # above, Model fit, Inefficiency.

NCA Ribbon. The zone in the bounding box consisting of the medP-zone and medS-zone. Also see Purity, Solidity.

NCA statistical test. One of NCA’s permutation tests to estimate the \(p\)-value. Also see Null test, Contrast test, Independent test, Paired test.

NCA-Extended Solution Table. See NEST.

Necessary condition. A cause that must exist in order for the outcome to exist. Also see Sufficient condition.

Necessary Condition Analysis. See NCA.

Necessary condition hypothesis. See Necessity hypothesis, Formal necessity hypothesis.

Necessary condition in degree. See NiD.

Necessary condition in kind. See NiK.

Necessary Element of a Sufficient Set. See NESS.

Necessity cause. See Necessary condition.

Necessity chain. A sequence of linked necessary conditions where each condition is required for the next outcome in the sequence to be possible. Also see Chain necessity effect.

Necessity corner. See Expected empty corner.

Necessity hypothesis. A hypothesis about a necessity relationship. Also see Preliminary necessity hypothesis, Formal necessity hypothesis.

Necessity-in-degree. See NiD.

Necessity-in-kind. See NiK.

Necessity logic. A causal logic describing a necessity relationship. Also see Binary logic, Conditional logic, Sufficiency logic.

Necessity model. The ceiling line and the bounding box representing necessity-in-degree. Also see Model specification.

Necessity perspective. The causal perspective on necessity selected by the analyst. In NCA the Deterministic perspective or the Typicality perspective can be selected. Also see Sufficiency perspective, Probabilistic sufficiency perspective.

Necessity relationship. A causal relationship in which the cause always, probably or typically enables or constrains the outcome. Also see Necessity hypothesis, Formal necessity hypothesis, Deterministic necessity, Typicality necessity.

Necessity theory. A theory consisting of at least one necessity hypothesis, with specified focal unit, condition(s) and outcome(s), and a defined theoretical domain. Also see Preliminary necessity theory, Formal necessity theory.

NESS. Necessary Element of a Sufficient Set. A tool developed by Richard W. Wright that argues that an event is a legal cause of an outcome if and only if the event was a necessary element of a set of conditions that together were sufficient for the outcome to occur. Also see NCA, QCA, SCC.

NEST. NCA-Extended Solution Table. A solution table to with an extra column representing the condition’s minimum required necessity level according to NCA. Also see Fiss chart.

NHST. Null Hypothesis Statistical Test. A procedure for deciding whether sample data provide enough evidence to reject a null hypothesis. Also see Null test, Contrast test, Independent test, Paired test, Alternative hypothesis, Formal necessity hypothesis.

NiD. Necessity-in-degree. A necessary condition that is quantitatively formulated as level \(x\) of \(X\) is necessary for level \(y\) of \(Y\). Also see NiK.

NiK. Necessity-in-kind. A necessary condition that is qualitatively formulated as \(X\) is necessary for \(Y\). Also see NiD.

Noise. A model fit metric expressing the number of cases in the medP-zone of the ceiling zone as a percentage of all cases in the bounding box. Also see, Counterexample, Exception, Outlier.

Non-bottleneck case. A case with satisfied target condition level. Also see Bottleneck case, Necessity-in-degree, Bottleneck table.

Non-intervention case. A case to which an intervention is not applied. Also see Intervention case, Ignored case.

Non-trivial hypothesis. A hypothesis where both the absence of the condition and the presence of the outcome are possible; otherwise it is trivial. Also see Formal necessity hypothesis.

Normal distribution. A continuous probability distribution in which values cluster around a mean in a symmetric, bell-shaped pattern, defined by its mean and standard deviation. Also see Uniform distribution, Truncated normal distribution, Skewed distribution.

Normalization. See Min-max normalization.

Null hypothesis. The statistical concept describing the claim of no (nil) effect or relationship in the population. Also see Null test, Contrast test, Independent test, Paired test, Alternative hypothesis.

Null hypothesis test. See NHST.

Null test. A permutation test in which \(Y\) is randomly shuffled across cases while keeping \(X\) fixed. Also see Contrast test, Independent test, Paired test.

Observational study. A study design in which variables are observed in the real life context without manipulation by the analyst. Also see Longitudinal study, Case study, Experimental study.

Omitted variable bias. The estimation error that is made in a regression-based analysis when a variable is omitted from the regression model specification.

Opposite corner. A corner in the bounding box diagonally across the corner of interest. Also see Adjacent corner.

Outcome. The varying characteristic \(Y\) of a focal unit of which the value (or its change) is the result of, or is permitted by a value (or its change) of another varying characteristic \(X\) (which is called the condition). Also see Predicted variable.

Outcome inefficiency. The area of the bounding box where the outcome is not constrained by the condition. Also see Absolute inefficiency, Relative inefficiency, Condition inefficiency.

Outlier. A point (case) in the bounding box that is considered to be ‘far away’ from the other points (cases) and has a large influence on the effect size if removed. Also see Ceiling outlier, Scope outlier, Counterexample, Exception, Noise, LowP-zone, MedP-zone.

Overall ceiling line. A ceiling line that applies to the total group of cases. Also see Subgroup ceiling line.

Overshoot waste. Intervention waste caused by too much intervention effort beyond what is required for reaching the target condition. Also see Undershoot waste.

\(\mathbf{p}\)-value. The probability of obtaining a result that is greater than or equal to the observed result when the null hypothesis is true. Also see Permutation test, NCA statistical test.

\(\mathbf{p}\)-value accuracy. The estimated difference between the exact \(p\)-value and the estimated \(p\)-value Also see Permutation test, NCA statistical test

\(\mathbf{p}\)-value threshold. See Statistical significance threshold.

Paired test. A permutation test in which for each case it is randomly decided whether to switch the labels. Also see Null test, Contrast test, Independent test.

Partial Least Squares SEM. See PLS-SEM.

Peer. A point in the \(XY\)-plane that is used to define a ceiling line. Also see CE-FDH, CE-VRS, CR-FDH, CR-VRS, C-LP.

Permutation test. A statistical test that builds an empirical null distribution by repeatedly randomly permuting the observed \(X\)-\(Y\) data to break any systematic relationship, recomputing NCA’s effect size each time, and then comparing the original effect size to this distribution to obtain the \(p\)-value. Also see Null test, Contrast test, Independent test, Paired test.

Plausible hypothesis. A hypothesis for which virtually no cases are reasonably expected in the ceiling zone. Also see Formal necessity hypothesis, Trivial hypothesis, Testable hypothesis, Complete hypothesis.

Plausibility. See Plausible hypothesis.

PLS-SEM. Partial Least Squares SEM. A component-based SEM approach that estimates model parameters to maximize explained variance in the predicted variables. Also see CB-SEM.

Population. The set of instances of a focal unit defined by one or a small number of criteria and that is defined in the theoretical domain. Also see Sample.

Potential necessary condition. A condition that is suggested to be necessary based existing knowledge and is a candidate for formulating a necessity hypothesis. Also see Preliminary necessity hypothesis, Formal necessity hypothesis, Expert knowledge, Tacit knowledge, Explicit knowledge.

Potential outlier. A case that has a large influence on the effect size if removed. Also see Outlier.

Power. The probability that a statistical test correctly rejects the null hypothesis when a specific alternative hypothesis is true. Also see \(p\)-value, Statistical credibility.

Practice. The real-world application of knowledge, like business, policy, or services, focusing on action, outcomes, and impact. Also see Academia, Practitioner.

Practitioner. An investigator, a data analyst, a data scientist, etc. active in practice. Also see Analyst, Scholar.

Predicted variable. Name used for outcome in the context of a regression-based analysis. Also see Predictor (variable).

Predictor (variable). Name used for a condition in the context of a regression analysis. Also see Predicted variable.

Preliminary necessity hypothesis. A “best guess” necessity hypothesis based on existing sources of knowledge about potential necessary conditions and to be developed toward a formal necessity hypothesis.

Preliminary necessity theory. A necessity theory in which the necessity hypotheses are not yet formal necessity hypotheses. Also see Formal necessity theory.

Presence/high value of condition/outcome. A value of a condition or outcome that is close to its maximum. Also see Absence/low value of condition/outcome, Direction (of a necessary condition).

Probabilistic sufficiency perspective. The probabilistic perspective selected by the analyst that a cause probably produces an effect. Also see Necessity perspective Deterministic perspective, Typicality perspective, Sufficiency perspective.

Proposition. A statement about the relationship between concepts of a theory. Also see Hypothesis.

Pure necessity theory. A necessity theory with only necessity relationships. Also see Embedded necessity theory.

Purity. A measure of closeness of a point in the ceiling zone to the ceiling. Also see Solidity, Model fit, NCA ribbon.

Purposive case selection. A selection of cases from the theoretical domain in which instances are selected purposefully (e.g., instances with a certain value of the outcome). Also see Convenience sample, Random sample.

Qualitative Comparative Analysis. See QCA.

QCA. A comparative method developed by Charles Ragin that analyzes combinations of conditions (configurations) that are sufficient for the outcome using set theory. Also see fsQCA, csQCA, NCA, NESS, SCC.

QR. Quantile Regression. A linear (pseudo) ceiling line obtained through a regression method that estimates the relationship between \(X\) and a chosen conditional high quantile of \(Y\). Also see Ceiling line, CR-FDH, CR-VRS, C-LP.

Qualitative data. Scores expressing in words or letters the extent to which a case has a property or characteristic. Also see Quantitative data, Longitudinal data, Set membership data.

Qualitative data analysis. Identifying and evaluating a pattern in qualitative data.

Quantitative data. Scores expressing in numbers the extent to which a case has a property or characteristic. Also see Qualitative data, Longitudinal data, Set membership data.

Quantitative data analysis. Generating and evaluating a pattern in quantitative data. Also see Qualitative data analysis.

R. A programming language and environment for statistical computing and graphics, used to import, manage, analyze, and visualize data.

Random sample. A sample in which instances have the same probability of being selected from the population into the sample. Also see Convenience sample, Purposive case selection.

Rating scale. A method in which a person assigns a value to an object. Also see Informant, Subject.

Relative inefficiency. The total area of the bounding box where the necessary condition does not constrain the outcome and the outcome is not constrained by the necessary condition, expressed as percentage of the scope. Also see Absolute inefficiency, Condition inefficiency, Outcome inefficiency.

Replication. Conducting a test of a hypothesis in another instance, or in another group or population of instances of the focal unit.

Ribbon. See NCA ribbon.

Robustness. The extent to which the conclusions of a study remain essentially unchanged when the analyst makes other plausible choices (e.g., model specification, evaluation criteria). Also see Fragility.

Robustness check. An analysis where the original analysis is re-run using other plausible choices by the analyst to conclude if the results are robust or fragile.

Sample. A set of instances selected from a population of the theoretical domain. Also see Convenience sample, Random sample, Purposive case selection.

Sampling. The process of drawing a sample. Also see Sampling frame.

Sampling frame. A list of all instances of a population. Also see Random sample.

SatP. Saturated purity zone. The feasible area including the ceiling line where Purity = 1.

SatS. Saturated solidity zone. The feasible area including the ceiling line where Solidity = 1.

Saturated purity zone. See SatP.

Saturated solidity zone. See SatS.

Scatter plot. See \(XY\)-plot

SCC. Sufficient-Component Cause model. A conceptual framework in epidemiology (also called causal pie) developed by Kenneth J. Rothman, that explains how an outcome occurs when a complete set of component causes collectively forms a sufficient cause. Also see NCA, NESS, QCA.

Scholar. A researcher active in academia. Also see Practitioner, Analyst.

Scope. The area of the bounding box. Also see Empirical scope, Theoretical scope.

Scope outlier. An outlier on the bounds of the bounding box.

Score. A value assigned to a condition or outcome based on data or expert knowledge. Also see Quantitative data, Longitudinal data. Set membership data.

SCoRe checklist. The Strengthening (theoretical rigor), Conducting (data & analysis quality), and Reporting (transparency) checklist. A tool for authors, editors and reviewers to evaluate the quality of an NCA study and its reporting.

SEM. Structural Equation Modeling. A model consisting of a measurement model specifying how indicators relate to the underlying constructs (“latent variables”) and a structural model specifying the (average) relationships among the constructs. (latent variables). Also see PLS-SEM, CB-SEM.

Sensitivity. See TPR.

Separate studies. Studies that use multiple causal perspectives and corresponding different methods with different data. Also see Method-triangulation study, Causal-pluralism study, Theory-method fit.

Set membership data. Scores expressing the extent to which a case belongs to a set. Also see Qualitative data, Quantitative data, Longitudinal data

Sharpness. A model fit metric expressing the difference in density of cases in the lowS-zone and cases in the lowP-zone.

Significance. See Statistical significance, Substantive significance.

Simulated data. Data that are fabricated, for example, for a Monte Carlo simulation. Also see Empirical data.

Single bottleneck case. A bottleneck case for only one condition. Also see BIPMA.

Skewed distribution. A distribution with a longer tail on one side (right-skewed or left-skewed). Also see Truncated normal distribution, Uniform distribution, Normal distribution.

Small-n study. A study with one or a small number of cases. The letter n stands for the number of cases. Also see Large-n study.

Solidity. A measure of closeness of a point in the feasible area to the ceiling. Also see Purity, Model fit, NCA ribbon.

Solution table. A table presenting the results of a QCA sufficiency analysis as the configurations (combinations of conditions) that consistently led to the outcome (pass the frequency and consistency thresholds set by the analyst) together with their consistency and coverage information. Also see QCA, Fiss chart.

Specificity. See TNR.

Spread. A model fit metric expressing the evenness of the \(X\) positions of the cases in the medS-zone and on the ceiling line.

Spurious relationship. An observed relationship that seems causal but is more plausibly explained by another model.

Standardization. A linear transformation that centers and scales values using the sample mean \(\mu\) and standard deviation \(\sigma\), producing values in standard deviation units. Also see Normalization.

Statistic. A number computed from a sample that summarizes the evidence against the null hypothesis. Also see Effect size.

Statistical credibility. The trustworthiness of conclusions about necessity identified from data when necessity is absent or present in the population. Also see Empirical credibility, TPR, TNR.

Statistical generalization. The statement that the study results that are obtained in a sample of a population also apply to the population from which the sample is drawn.

Statistical significance. The meaningfulness of the effect size from a statistical perspective. Also see \(p\)-value, Substantive significance.

Statistical significance threshold. The \(p\)-value (\(\alpha\)) selected by the analyst for evaluating the formal necessity hypothesis. Also see Effect size threshold.

Structural Equation Modeling. See SEM.

Study. An academic research activity or a project in practice.

Study design. A category of procedures for selecting or generating one or more instances of a focal unit as well as for analyzing the data that are observed or generated in the selected or generated instance or instances. Also see Observational study, Longitudinal study, Experimental study, Case study.

Subgroup ceiling line. A ceiling line that applies to a subgroup of the total group of cases. Also see Overall ceiling line.

Subject. A person who is the object of measurement and an instance of the focal unit of the theory. Also see Informant.

Substantive significance. The meaningfulness of the effect size from a practical perspective. Also see Statistical significance.

Sufficiency cause. See Sufficient condition.

Sufficiency logic. A causal logic describing a sufficiency relationship. Also see Sufficiency relationship, Necessity logic.

Sufficiency perspective. The causal perspective on sufficiency selected by the analyst. Also see Necessity perspective, Probabilistic sufficiency perspective.

Sufficient condition. A cause that always results in an outcome. Also see Necessary condition.

Sufficient-Component Cause model. See SCC.

Support. A model fit metric expressing the number of cases in the medS-zone of the feasible area including the cases on the ceiling line as a percentage of all cases in the bounding box.

Tacit knowledge. Undocumented knowledge in academia and practice to be used for formulating a formal necessity hypothesis. Also see Explicit knowledge, Expert knowledge.

Target condition. The level of a condition that is necessary for the target outcome. Also see Necessity-in-degree.

Target group. The group of cases for which an intervention goal is set.

Target outcome. A desired or undesired level of the outcome set by the analyst that is to be achieved or to be avoided. Also see Target condition, Necessity-in-degree.

Test. Determining whether a hypothesis is rejected or not rejected (supported) in an instance or in a group or population of instances selected from the theoretical domain.

Test statistic. See Statistic.

Testable hypothesis. A hypothesis with measurable variables (variables that can have scores). Also see Formal necessity hypothesis, Trivial hypothesis, Plausible hypothesis, Complete hypothesis.

Testability. See Testable hypothesis.

Theoretical domain. The universe of instances of a focal unit of a theory or hypothesis where the theory or hypothesis is supposed to hold. Also see Necessity theory, Formal necessity hypothesis.

Theoretical justification. The availability of a formal necessity hypothesis when evaluating a necessity relationship.

Theoretical scope. The bounding box (or its area) defined by specified minimum and maximum values of the condition and the outcome. Also see Empirical scope, Scope.

Theorizing. Development of a formal (necessity) hypothesis.

Theory. A (set of) hypotheses (propositions) regarding the relationships between the varying characteristics (concepts) of a focal unit, and the description why the relations exist (causal explanation) in a theoretical domain. Also see Formal necessity hypothesis.

Theory-grounded hypothesis: A hypothesis that is embedded in a necessity theory. Also see Formal necessity hypothesis.

Theory-in-use. A more or less consistent set of beliefs in practice about the world. Also see Theory, Formal necessity hypothesis.

Theory-method fit. The situation that the causal perspective is aligned with the data analysis method.

Thought experiment. The mental evaluation to check the validity of the necessity theory and its hypothesis. Also see Hypothesis testing, Formal necessity hypothesis.

Tight bounding box. The pair of bounding box and ceiling line when the ceiling zone holds the single corner of interest.

TNR. True Negative Rate (specificity). The ability of an approach to correctly identify that necessity does not exist in the population. Also see TPR, Credibility, Statistical credibility, Empirical credibility, Formal hypothesis. Effect size, \(p\)-value, Robustness, Model fit.

Total effect. A term used in regression-based analyses indicating the combined effect of the direct effect and the indirect effect of \(X\) on \(Y\). Also see Direct effect, Indirect effect.

Total intervention effort. The sum of intervention efforts applied to the intervention cases.

TPR. True Positive Rate (sensitivity). The ability of an approach to correctly identify that necessity exists in the population. Also see TNR, Credibility, Statistical credibility, Empirical credibility, Formal hypothesis. Effect size, \(p\)-value, Robustness, Model fit.

Treated bottleneck cases. Bottleneck cases that received the intervention.

Trivial hypothesis. A hypothesis in which the absence of the condition or the presence of the outcome are not possible. Also see Formal necessity hypothesis, Testable hypothesis, Plausible hypothesis, Complete hypothesis.

Triviality. See Trivial hypothesis.

True Negative Rate. See TNR.

True Positive Rate. See TPR.

Truncated normal distribution. A normal distribution that is restricted to a range. Also see Uniform distribution, Skewed distribution

Typicality necessity. Necessity from the typicality perspective. Also see Deterministic necessity.

Typicality perspective. A lens taken by the analyst that a cause always influences an effect, but that there can be rare exceptions. Also see Necessity perspective, Sufficiency perspective, Probabilistic sufficiency perspective.

Undershoot waste. Intervention waste caused by insufficient intervention effort such that cases do not move from or into the bottleneck area. Also see Overshoot waste.

Uniform distribution. A distribution in which all values within a specified range are equally likely. Also see Truncated normal distribution, Normal distribution, Skewed distribution.

Unit box. A special case of a bounding box in which the condition and the outcome are both limited to the interval [0,1]. Also see Min-max normalization.

Variable. The operationalized concept (varying characteristic of a focal unit of a hypothesis).

Visual inspection. The procedure by which patterns are discovered or compared by looking at the scores or a graphical representation of the scores.

\(\mathbf{XY}\)-plot. A graphical representation of the relationship between condition and outcome in a coordinate system with cases shown as points. Also see \(XY\)-table.

\(\mathbf{XY}\)-table. A matrix representation of the relationship between condition and outcome with the number of cases shown in the cells. Also see \(XY\)-plot.