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). In an article that develops the notion of "gravity" in the context of meta-analysis, Dr. Travis Gee proposed that the jackknife methods applied to meta-analysis in that article could be extended to examine all possible combinations of studies (where practical) or random subsets of studies (where the combinatorics of the situation made it computationally infeasible). In the original article, k objects (studies) are combined k-1 at a time (jackknife estimation), resulting in k estimates.

Heterogeneity in economics

heterogeneous agentsheterogeneityunobserved heterogeneity
Study heterogeneity.


purple coneflowerConeflowerEchinacea purpurea
Although there are multiple scientific reviews and meta-analyses published on the supposed immunological effects of Echinacea, significant variability of products used among studies has limited conclusions about effects and safety, consequently leading to non-approval by regulatory authorities like the United States Food and Drug Administration of any health benefit or anti-disease activity. While one 2014 systematic review found that Echinacea products are not effective to treat or prevent the common cold, a 2016 meta-analysis found tentative evidence that use of Echinacea extracts reduced the risk of repeated respiratory infections.

Mixture distribution

mixture densitymixturedensity mixture
In meta-analysis of separate studies, study heterogeneity causes distribution of results to be a mixture distribution, and leads to overdispersion of results relative to predicted error. For example, in a statistical survey, the margin of error (determined by sample size) predicts the sampling error and hence dispersion of results on repeated surveys.

Mendelian randomization

epidemiologyMendelian randomisationrandom Mendelian sampling
From a statistical perspective, Mendelian randomization (MR) is an application of the technique of instrumental variables with genotype acting as an instrument for the exposure of interest. The method has also been used in economic research studying the effects of obesity on earnings, and other labor market outcomes. Accuracy of MR depends on a number of assumptions: That there is no direct relationship between the instrumental variable and the dependent variables, and that there are no direct relation between the instrumental variable and any possible confounding variables.

Transgender hormone therapy (male-to-female)

feminizing hormone therapyhormone replacement therapyhormone therapy
There was significant heterogeneity in the rates of VTE across the included studied, and the meta-analysis was unable to perform subgroup analyses between estrogen type, estrogen route, estrogen dosage, concomitant antiandrogen or progestogen use, or patient characteristics (e.g., age, smoking status, weight) corresponding to known risk factors for VTE. Due to the inclusion of some studies using ethinylestradiol, which is more thrombotic and is no longer used in transgender women, the researchers noted that the VTE risk found in their study is likely to be an overestimate.

Evidence-based medicine

evidence-basedmedical evidenceevidence
Although all medicine based on science has some degree of empirical support, EBM goes further, classifying evidence by its epistemologic strength and requiring that only the strongest types (coming from meta-analyses, systematic reviews, and randomized controlled trials) can yield strong recommendations; weaker types (such as from case-control studies) can yield only weak recommendations. The term was originally used to describe an approach to teaching the practice of medicine and improving decisions by individual physicians about individual patients.

Homogeneous and heterogeneous mixtures

homogeneoushomogeneityhomogeneous mixture
A homogeneous mixture is a solid, liquid, or gaseous mixture that has the same proportions of its components throughout any given sample. Conversely, a heterogeneous mixture has components in which proportions vary throughout the sample. "Homogeneous" and "heterogeneous" are not absolute terms, but are dependent on context and the size of the sample. In chemistry, if the volume of a homogeneous suspension is divided in half, the same amount of material is suspended in both halves of the substance. An example of a homogeneous mixture is air. In physical chemistry and materials science this refers to substances and mixtures which are in a single phase.

Frank L. Schmidt

He authored a textbook on meta-analysis with John E. Hunter titled Methods of Meta-Analysis: Correcting Error and Bias in Research Findings. In 1994 he was one of 52 signatories on "Mainstream Science on Intelligence," an editorial written by Linda Gottfredson and published in the Wall Street Journal. He has served on the editorial boards of Students have included Ken Pearlman, Mike A.

Gene V. Glass

Gene V GlassGene GlassGlass, Gene V.
Meta-analysis. A video interview of Gene Glass by Audrey Amrein Beardsley. Gene V Glass's Blog on Education. Glass on meta-analysis at 25. Gene V Glass (2008) Fertilizers, Pills & Magnetic Strips: The Fate of Public Education in America. School of Education University of Colorado Boulder. National Education Policy Center. Education Policy Analysis Archives. Education Review/Reseñas Educativas.

Secondary source

secondary sourcessecondarysecondary literature
In general, secondary sources are self-described as review articles or meta-analysis. Primary source materials are typically defined as "original research papers written by the scientists who actually conducted the study." An example of primary source material is the Purpose, Methods, Results, Conclusions sections of a research paper (in IMRAD style) in a scientific journal by the authors who conducted the study. In some fields, a secondary source may include a summary of the literature in the Introduction of a scientific paper, a description of what is known about a disease or treatment in a chapter in a reference book, or a synthesis written to review available literature.

Larry V. Hedges

Larry HedgesHedges, Larry V.
He has authored a number of articles and books on statistical methods for meta-analysis, which is the use of statistical methods for combining results from different studies. He also suggested several estimators for effect sizes and derived their properties. He carried out research on the relation of resources available to schools and student achievement, most notably the relation between class size and achievement. * *

Ingram Olkin

Olkin, IngramI. Olkin
He is known for developing statistical analysis for evaluating policies, particularly in education, and for his contributions to meta-analysis, statistics education, multivariate analysis, and majorization theory. Olkin was born in 1924 in Waterbury, Connecticut. He received a B.S. in mathematics at the City College of New York, an M.A. from Columbia University, and his Ph.D. from the University of North Carolina. Olkin also studied with Harold Hotelling. Olkin's advisor was S. N. Roy and his Ph.D. thesis was "On distribution problems in multivariate analysis" submitted in 1951.

Effective medium approximations

effective mediumeffective medium modeleffective value
Nevertheless, they all assume that the macroscopic system is homogeneous and, typical of all mean field theories, they fail to predict the properties of a multiphase medium close to the percolation threshold due to the absence of long-range correlations or critical fluctuations in the theory. The properties under consideration are usually the conductivity \sigma or the dielectric constant \epsilon of the medium. These parameters are interchangeable in the formulas in a whole range of models due to the wide applicability of the Laplace equation.

Nambury S. Raju

Raju (1937 – October 27, 2005) was an American psychology professor known for his work in psychometrics, meta-analysis, and utility theory. He was a Fellow of the Society of Industrial Organizational Psychology. At the time of his death, Raju was a Distinguished Professor in the Institute of Psychology at Illinois Institute of Technology (IIT) in Chicago, Illinois. Raju worked at Science Research Associates (SRA) from 1961 to 1978, specializing in psychometrics and test validation. His first published article, A new working formula for the split-half reliability model appeared in Educational and Psychological Measurement in 1965 and was published with Isaiah Guttman, a colleague from SRA.

Cochrane (organisation)

Cochrane reviewCochrane CollaborationCochrane
The Cochrane logo represents a meta-analysis of data from seven randomised controlled trials (RCTs), comparing one health care treatment with a placebo in a blobbogram or forest plot. The diagram shows the results of a systematic review and meta-analysis on inexpensive course of corticosteroid given to women about to give birth too early – the evidence on effectiveness that would have been revealed had the available RCTs been reviewed systematically around 1982. This treatment reduces the odds of the babies of such women dying from the complications of immaturity by 30–50%.

Thomas C. Chalmers

December 27, 1995, Lebanon, New Hampshire) was famous for his role in the development of the randomized controlled trial and meta-analysis in medical research. Chalmers began his higher education as an English major at Yale College. He obtained his medical degree from Columbia University College of Physicians and Surgeons in 1943. He spent one year as an intern at the NewYork-Presbyterian Hospital, and completed his residency at the Boston City Hospital. Chalmers' interest in medical research began while working for the United States Army in Japan, where he conducted clinical trials investigating the treatment of hepatitis among Korean War soldiers.


Mixtures can be either homogeneous or heterogeneous. A mixture in which its constituents are distributed uniformly is called homogeneous mixture, such as salt in water. A mixture in which its constituents are not distributed uniformly is called heterogeneous mixture, such as sand in water. One example of a mixture is air. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances. Salt, sugar, and many other substances dissolve in water to form homogeneous mixtures. A homogeneous mixture in which there is both a solute and solvent present is also a solution. Mixtures can have any amounts of ingredients.

Effect size

Cohen's deffect sizesmagnitude
Practical meta-analysis. Sage: Thousand Oaks, CA. Imdadullah, M. (2014). Effect Size for dependent Sample t test. document on Effect Size for dependent Sample t test. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage: Thousand Oaks, CA. Imdadullah, M. (2014). Effect Size for dependent Sample t test. document on Effect Size for dependent Sample t test. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage: Thousand Oaks, CA. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage: Thousand Oaks, CA. Effect Size (ES). Measuring Effect Size.

Ordinary least squares

OLSleast squaresOrdinary least squares regression
In such case the method of instrumental variables may be used to carry out inference. Then the matrix Q xx = E[X T X / n] is finite and positive semi-definite. :When this assumption is violated the regressors are called linearly dependent or perfectly multicollinear. In such case the value of the regression coefficient β cannot be learned, although prediction of y values is still possible for new values of the regressors that lie in the same linearly dependent subspace.  X ] = σ 2, which means that the error term has the same variance σ 2 in each observation.

Joshua Angrist

AngristJoshua D. Angrist
Instrumental variables estimation. Quasi-natural experiments. Faculty profile of Joshua Angrist on the website of MIT. Profile of Joshua Angrist on the website of the NBER. Profile of Joshua Angrist as research fellow on the website of IZA.

Research synthesis

Meta-analysis is the preferred technique of quantitative research synthesis in many fields, such as medical science. This technique can sometimes accurately estimate an overall effect, but it may suffer from limitations when there is variation in the included studies with regard to study design, the type of evidence, or other key characteristics. Methods of qualitative research synthesis include narrative synthesis and meta-ethnography. Narrative synthesis allows researchers to address a wide range of questions in their review, while meta-ethnography aims to preserve the cultural context in which the original findings of the included studies were generated.

Preferred Reporting Items for Systematic Reviews and Meta-Analyses

PRISMAThe PRISMA statement
PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) is an evidence-based minimum set of items aimed at helping authors to report a wide array of systematic reviews and meta-analyses that assess the benefits and harms of a health care intervention. PRISMA focuses on ways in which authors can ensure a transparent and complete reporting of this type of research. The PRISMA standard supersedes the QUOROM standard. The aim of the PRISMA statement is to help authors improve the reporting of systematic reviews and meta-analyses.

Sewall Wright

WrightSewall G. WrightS. Wright
Sewall Green Wright (December 21, 1889 – March 3, 1988) was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. He was a founder of population genetics alongside Ronald Fisher and J. B. S. Haldane, which was a major step in the development of the modern synthesis combining genetics with evolution. He discovered the inbreeding coefficient and methods of computing it in pedigree animals.

Jacob Cohen (statistician)

Jacob CohenCohen, JacobCohen
Jacob Cohen (April 20, 1923 – January 20, 1998) was an American psychologist and statistician best known for his work on statistical power and effect size, which helped to lay foundations for current statistical meta-analysis and the methods of estimation statistics. He gave his name to such measures as Cohen's kappa, Cohen's d, and Cohen's h. In addition to being an advocate of power analysis and effect size, Cohen was a critic of reliance on, and lack of understanding of, significance testing procedures used in statistics, especially misunderstandings of null hypothesis significance testing.