Combinatorial Meta-Analysis¶

Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research).

Version: v1 · 2026-09-28 · History
Domain-specific #: 8559
Domain group: Formal Sciences
Origin domain: Experimental Design & Statistics
Subdomain: Meta Analysis → Experimental Design & Statistics

Core Idea¶

Combinatorial Meta-Analysis is treated here as the recurring formal models and representations identity summarized by this source-grounded definition: Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research). Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research). In an article that develops the notion of "gravity" in the context of meta-analysis, Travis Gee proposed that the jackknife methods applied to meta-analysis in that article.

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Trying Every Study Group

Scientists sometimes gather lots of studies that asked the same question. Combinatorial Meta-Analysis means picking different groups of those studies, one at a time, two at a time and so on, and checking the answer for each group. Then they see how often the answer comes out the same way, to tell whether it depends on which studies you pick.

Trying Every Group of Studies

A meta-analysis combines the results of many studies on the same question to get an overall answer. Combinatorial Meta-Analysis goes further: it looks at the results for many different combinations of those studies, taking them one at a time, two at a time, and so on up to all of them. If there are too many combinations, it uses random groups instead. One handy picture is the PPES plot, which shows, for each group size, what fraction of the combinations point to a positive effect. This helps show how much the overall conclusion depends on which studies happen to be included.

Subset-Combination Meta-Analysis

Combinatorial Meta-Analysis (CMA) studies how the statistical results of a meta-analysis behave across different combinations of the studies in its dataset, typically in social science research. Travis Gee proposed extending jackknife methods—where each study is left out in turn—to examine all possible combinations of studies, or random subsets when there are too many combinations to compute. For each subset size j, from 1 up to all k studies, CMA finds the proportion of combinations showing a positive effect size. Gee's PPES ('Probability of Positive Effect Size') plot graphs this proportion against j, assuming effects are scaled so that positive is the desired direction. The jackknife, which combines k studies k − 1 at a time, is a special case of this broader approach.

Combinatorial Meta-Analysis (CMA) is the study of how statistical properties of a meta-analytic result behave across combinations of the constituent studies, typically in social science research. Travis Gee, in work developing a notion of 'gravity' in meta-analysis, proposed generalizing jackknife methods to all possible combinations of studies where computationally practical, or to random subsets where the combinatorics make exhaustive enumeration infeasible. For each subset size j = 1, …, k, the proportion of combinations yielding a positive effect size (using either weighted mean difference or standardized mean difference) is computed and plotted against j in a PPES ('Probability of Positive Effect Size') plot, with effects signed so the positive direction is desired. The classical jackknife, combining k studies k − 1 at a time to produce k estimates, is thus a special case of CMA. The defining feature is systematic evaluation of meta-analytic statistics over combinations of studies.

Scope of Application¶

Implications. Software support for this method is maintained in the widely used R package metafor, whose function fits equal-effects models to all (or a large random sample of) subsets of a fitted.
Concept. This differs from the standard approach in meta-analysis of adopting a single method and computing a single result, and allows significant triangulation to occur, by computing different indices for each combination.
Implications. CMA can thus be used as a data mining method to identify the number of intercepts that may be present in the dataset by looking at which studies are included in.
Implications. Recent applications of combinatorial and bootstrap methods in meta-analysis.
Bootstrap methods. A study proposing a bootstrap resampling method for meta-analysis of magnetic resonance imaging (MRI) data collected across multiple scanners used individual participant data within each scanner and estimated the variance of.

Clarity¶

A clear use of Combinatorial Meta-Analysis names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research).

Manages Complexity¶

Combinatorial Meta-Analysis compresses multiple formal models and representations details into a stable diagnostic relation. The source shows both the central mechanism—cMA can thus be used as a data mining method to identify the number of intercepts that may be present in the dataset by looking at which studies are included in the local minima that may be obtained through recombination.—and the practical consequence—more recent work by a.

Abstract Reasoning¶

Type the carrier. Identify the formal models and representations entities to which the claim applies.
State the relation. Use the source-grounded identity: Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research).
Check operation and conditions. A useful tool developed by Gee was the "PPES" plot (standing for "Probability of Positive Effect Size", assuming differences are scaled such that larger in a positive direction is desired).
Demand recognition evidence.

Knowledge Transfer¶

Within the home domain. Knowledge about Combinatorial Meta-Analysis transfers literally when a new case preserves the same carrier type, relation, and recognition test. Software support for this method is maintained in the widely used R package metafor, whose function fits equal-effects models to all (or a large random sample of) subsets of a fitted meta-analytic model, and companion packages such as dmetar extend the technique with unsupervised clustering algorithms (k-means, DBSCAN, and Gaussian mixture models) to automatically flag.

Neighborhood in Abstraction Space¶

Combinatorial Meta-Analysis sits in a sparse region of the domain-specific corpus (75^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Clinical Trial & Research Methodology (20 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08