Information about Meta Analysis
In statistics, a meta-analysis combines the results of several studies that address a set of related research hypotheses. The first meta-analysis was performed by Karl Pearson in 1904, in an attempt to overcome the problem of reduced statistical power in studies with small sample sizes; analyzing the results from a group of studies can allow more accurate data analysis.
Although meta-analysis is widely used in epidemiology and evidence-based medicine today, a meta-analysis of a medical treatment was not published until 1955. In the 1970s, more sophisticated analytical techniques were introduced in educational research, starting with the work of Gene V. Glass, Frank L. Schmidt, and John E. Hunter..
The online Oxford English Dictionary lists the first usage of the term in the statistical sense as 1976 by Glass. The statistical theory surrounding meta-analysis was greatly advanced by the work of Nambury S. Raju, Larry V. Hedges, Ingram Olkin, John E. Hunter, and Frank L. Schmidt.
The method is not restricted to situations in which one or more variables is defined as "dependent." For example, a meta-analysis could be performed on a collection of studies each of which attempts to estimate the incidence of left-handedness in various groups of people.
Researchers should be aware that variations in sampling schemes can introduce heterogeneity to the result, which is the presence of more than one intercept in the solution. For instance, if some studies used 30mg of a drug, and others used 50mg, then we would plausibly expect two clusters to be present in the data, each varying around the mean of one dosage or the other. This can be modelled using a "random effects model."
Results from studies are combined using different approaches. One approach frequently used in meta-analysis in health care research is termed 'inverse variance method'. The average effect size across all studies is computed as a weighted mean, whereby the weights are equal to the inverse variance of each studies' effect estimator. Larger studies and studies with less random variation are given greater weight than smaller studies. Other common approaches include the Mantel Haenszel method and the Peto method. A free Excel-based calculator to perform Mantel Haenszel analysis is available at : [1] They also have a free Excel-based Peto method calculator at : [2]
Cochraine and other sources provide a useful discussion of the differences between these two approaches.
Q : Why not just add up all the results across studies ?
Answer : There is concern about Simpson's paradox. Note, however that Mantel Haenszel analysis and Peto analysis introduce their own biases and distortions of the data results.
A recent approach to studying the influence that weighting schemes can have on results has been proposed through the construct of gravity, which is a special case of combinatorial meta analysis.
Modern meta-analysis does more than just combine the effect sizes of a set of studies. It can test if the studies' outcomes show more variation than the variation that is expected because of sampling different research participants. If that is the case, study characteristics such as measurement instrument used, population sampled, or aspects of the studies' design are coded. These characteristics are then used as predictor variables to analyze the excess variation in the effect sizes. Some methodological weaknesses in studies can be corrected statistically. For example, it is possible to correct effect sizes or correlations for the downward bias due to measurement error or restriction on score ranges.
Meta analysis leads to a shift of emphasis from single studies to multiple studies. It emphasises the practical importance of the effect size instead of the statistical significance of individual studies. This shift in thinking has been termed Metaanalytic thinking.
The results of a meta-analysis are often shown in a forest plot.
John E. "Jack" Hunter (29 March 1939 – June 26 2002) was an American psychology professor known for his work in methodology.
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Although meta-analysis is widely used in epidemiology and evidence-based medicine today, a meta-analysis of a medical treatment was not published until 1955. In the 1970s, more sophisticated analytical techniques were introduced in educational research, starting with the work of Gene V. Glass, Frank L. Schmidt, and John E. Hunter..
The online Oxford English Dictionary lists the first usage of the term in the statistical sense as 1976 by Glass. The statistical theory surrounding meta-analysis was greatly advanced by the work of Nambury S. Raju, Larry V. Hedges, Ingram Olkin, John E. Hunter, and Frank L. Schmidt.
Uses in modern science
Because the results from different studies investigating different independent variables are measured on different scales, the dependent variable in a meta-analysis is some standardized measure of effect size. To describe the results of comparative experiments the usual effect size indicator is the standardized mean difference (d) which is the standard score equivalent to the difference between means, or an odds ratio if the outcome of the experiments is a dichotomous variable (success versus failure). A meta-analysis can be performed on studies that describe their findings in correlation coefficients, as for example, studies of the correlation between familial relationships and intelligence. In these cases, the correlation itself is the indicator of the effect size.The method is not restricted to situations in which one or more variables is defined as "dependent." For example, a meta-analysis could be performed on a collection of studies each of which attempts to estimate the incidence of left-handedness in various groups of people.
Researchers should be aware that variations in sampling schemes can introduce heterogeneity to the result, which is the presence of more than one intercept in the solution. For instance, if some studies used 30mg of a drug, and others used 50mg, then we would plausibly expect two clusters to be present in the data, each varying around the mean of one dosage or the other. This can be modelled using a "random effects model."
Results from studies are combined using different approaches. One approach frequently used in meta-analysis in health care research is termed 'inverse variance method'. The average effect size across all studies is computed as a weighted mean, whereby the weights are equal to the inverse variance of each studies' effect estimator. Larger studies and studies with less random variation are given greater weight than smaller studies. Other common approaches include the Mantel Haenszel method and the Peto method. A free Excel-based calculator to perform Mantel Haenszel analysis is available at : [1] They also have a free Excel-based Peto method calculator at : [2]
Cochraine and other sources provide a useful discussion of the differences between these two approaches.
Q : Why not just add up all the results across studies ?
Answer : There is concern about Simpson's paradox. Note, however that Mantel Haenszel analysis and Peto analysis introduce their own biases and distortions of the data results.
A recent approach to studying the influence that weighting schemes can have on results has been proposed through the construct of gravity, which is a special case of combinatorial meta analysis.
Modern meta-analysis does more than just combine the effect sizes of a set of studies. It can test if the studies' outcomes show more variation than the variation that is expected because of sampling different research participants. If that is the case, study characteristics such as measurement instrument used, population sampled, or aspects of the studies' design are coded. These characteristics are then used as predictor variables to analyze the excess variation in the effect sizes. Some methodological weaknesses in studies can be corrected statistically. For example, it is possible to correct effect sizes or correlations for the downward bias due to measurement error or restriction on score ranges.
Meta analysis leads to a shift of emphasis from single studies to multiple studies. It emphasises the practical importance of the effect size instead of the statistical significance of individual studies. This shift in thinking has been termed Metaanalytic thinking.
The results of a meta-analysis are often shown in a forest plot.
Trial quality
A weakness of the method is that sources of bias are not controlled by the method. A good meta-analysis of badly designed studies will still result in bad statistics. Robert Slavin has argued that only methodologically sound studies should be included in a meta-analysis, a practice he calls 'best evidence meta-analysis'. Other meta-analysts would include weaker studies, and add a study-level predictor variable that reflects the methodological quality of the studies to examine the effect of study quality on the effect size. Another weakness of the method is the heavy reliance on published studies, which may increase the effect as it is very hard to publish studies that show no significant results. This publication bias or "file-drawer effect" (where non-significant studies end up in the desk drawer instead of in the public domain) should be seriously considered when interpreting the outcomes of a meta-analysis. Because of the risk of publication bias, many meta-analyses now include a "failsafe N" statistic that calculates the number of studies with null results that would need to be added to the meta-analysis in order for an effect to no longer be reliable.See also
- Epidemiologic methods
- Educational psychology
- Fisher's method for combining independent tests of significance
- Galbraith plot
- Selection bias
- Simpson's paradox
- Study heterogeneity
- Systematic review
- Metaanalytic thinking
- Meta, the word or prefix
External links
- Effect Size and Meta-Analysis
- Effect Size and Meta-Analysis Software
- Introduction to meta-analysis for systematic reviewers
- Meta-Analysis: Methods of Accumulating Results Across Research Domains
- Meta-analysis blog
- Meta-Analysis in Educational Research
- Meta-Analysis Research on Science Instruction
- The Cochrane Library
- What is meta-analysis? (Hayward Medical Communications)
- MIX: Free Software for Meta-analysis of Causal Research Data
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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Karl Pearson
Karl Pearson
Born March 27 1857
London, England
Died March 27 1936 (aged 79)
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Karl Pearson
Born March 27 1857
London, England
Died March 27 1936 (aged 79)
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The power of a statistical test is the probability that the test will reject a false null hypothesis (that it will not make a Type II error). As power increases, the chances of a Type II error decrease, and vice versa. The probability of a Type II error is referred to as β.
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Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.
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Evidence-based medicine (EBM) or scientific medicine is an attempt to apply more uniformly the standards of evidence gained from the scientific method to certain aspects of medical practice.
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Educational research is research conducted to investigate behavioral patterns in pupils, students, teachers and other participants in schools and other educational institutions.
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Gene V Glass (June 19 1940 - ), a statistician and researcher working in educational psychology and the social sciences, coined the term "meta-analysis" and illustrated its use in 1976 while a faculty member at the University of Colorado at Boulder.
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Frank L. Schmidt is an American psychology professor known for his work in personnel selection and employment testing. Schmidt is a researcher in the area of industrial and organizational psychology with the most number of publications in the two major journals in the 1980s.
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For other persons of the same name, see John Hunter.
John E. "Jack" Hunter (29 March 1939 – June 26 2002) was an American psychology professor known for his work in methodology.
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The Oxford English Dictionary (OED) is a dictionary published by the Oxford University Press (OUP), and is the most comprehensive dictionary of the English language.
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In mathematics, an independent variable is any of the arguments, i.e. "inputs", to a function. These are contrasted with the dependent variable, which is the value, i.e. the "output", of the function.
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In mathematics, an independent variable is any of the arguments, i.e. "inputs", to a function. These are contrasted with the dependent variable, which is the value, i.e. the "output", of the function.
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In statistics, effect size is a measure of the strength of the relationship between two variables. In scientific experiments, it is often useful to know not only whether an experiment has a statistically significant effect, but also the size of any observed effects.
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standard score, also called the z-score or normal score, is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
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The odds ratio is a measure of effect size particularly important in Bayesian statistics and logistic regression.
It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that
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It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that
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correlation, also called correlation coefficient, indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence.
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Intelligence is a property of mind that encompasses many related abilities, such as the capacities to reason, to plan, to solve problems, to think abstractly, to comprehend ideas, to use language, and to learn. There are several ways to define intelligence.
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Heterogeneous (American English)) means that something (an object or system) consists of a diverse range of different items. It is the antonym of , which means that an object or system consists of many identical items.
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In statistics, a random effect(s) model, also called a variance components model is a kind of hierarchical linear model. It assumes that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy.
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Simpson's paradox (or the Yule-Simpson effect) is a statistical paradox wherein the successes of groups seem reversed when the groups are combined. This result is often encountered in social and medical science statistics,[1]
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Social science results are often subjected to meta analysis, which is a statistical procedure that combines the results of studies to produce an overall estimate of the effect size.
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since March 2007.
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Please [improve the article] or discuss this issue on the talk page. This article has been tagged since March 2007.
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Thompson (2002, p.28) defines meta analytic thinking as: “a) the prospective formulation of study expectations and design by explicitly invoking prior effect size measures and b) the retrospective interpretation of new results, once they are in hand, via explicit, direct comparison
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A forest plot is a graph displaying the results of multiple studies in a meta-analysis. Typically, there is a set of horizontal lines representing each study, its effect size and confidence intervals, with a summary overall result and confidence interval shown as a diamond.
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Robert Slavin is a noted psychologist who studies educational and academic issues. He founded the Success for All reform program for primary and middle schools.
He will lead the Institute for Effective Education at the University of York - this is an international,
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He will lead the Institute for Effective Education at the University of York - this is an international,
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Publication bias arises from the tendency for researchers and editors to handle experimental results that are positive (they found something) differently from results that are negative (found that something did not happen) or inconclusive.
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Texts and literature in epidemiology often make use of jargon related to epidemiological methods without reference to their actual definition.
A number of basic concepts recur with particular frequency:
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A number of basic concepts recur with particular frequency:
- Hazard ratio, also known as the Incidence Rate Ratio
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Educational psychology is the study of how humans learn in educational settings, the effectiveness of educational interventions, the psychology of teaching, and the social psychology of schools as organizations.
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In statistics, Fisher's method, developed by and named for Ronald Fisher, is a data fusion or "meta-analysis" (analysis after analysis) technique for combining the results from a variety of independent tests bearing upon the same overall hypothesis (H0
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In probability theory, to say that two events are independent, intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs.
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