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14-September-2008 10:43:23 - Meta-analysis This article may require cleanup to meet 's quality standards. Please improve this article if you can. August 2007 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, Harris Cooper, Ingram Olkin, John E. Hunter, Jacob Cohen, and Frank L. Schmidt. Contents 1 Uses in modern science 2 Weaknesses 3 Books 4 See also 5 References 6 External links 6.1 Software 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 : http://www.pitt.edu/~super1/lecture/lec1171/014.htm. They also have a free Excel-based Peto method calculator at : http://www.pitt.edu/~super1/lecture/lec1171/015.htm 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. Weaknesses 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. Books Sutton, A.J., Jones, D.R., Abrams, K.R., Sheldon, T.A., Song, F. Methods for Meta-analysis in Medical Research. London: John Wiley 2000. ISBN 0-471-49066-0 See also Statistics portal Wikiversity At Wikiversity, you can learn about: Meta-analysis Epidemiologic methods Educational psychology Fisher's method for combining independent tests of significance Galbraith plot Selection bias Simpson's paradox Study heterogeneity Systematic review Newcastle-Ottawa scale Meta-analytic thinking Meta, the word or prefix References Meta-Analysis of Controlled Clinical Trials by Anne Whitehead. Publisher-London: John Wiley Sons LTD External links Cochrane Handbook for Systematic Reviews of Interventions Effect Size and Meta-Analysis ERIC Digest Meta-Analysis in Educational Research ERIC Digest Meta-Analysis: Methods of Accumulating Results Across Research Domains article by Larry Lyons Meta-analysis Psychwiki.com article Software ClinTools commercial Comprehensive Meta-Analysis commercial MIX Excel-based tool for meta-analysis free What meta-analysis features are available in Stata? free add-ons to commercial package The Meta-Analysis Calculator free on-line tool for conducting a meta-analysis Metastat Free v d e Statistics Experimental design Design of experiments - Sampling - Stratified sampling - Replication - Blocking - Statistical power - Sample size Descriptive statistics Continuous data Mean Arithmetic, Geometric, Harmonic - Median - Mode - Range - Variance - Standard deviation - Skewness - Kurtosis - Effect size Categorical data Frequency - Contingency table Inferential statistics Bayesian inference - Hypothesis testing - Significance - Power - Null hypothesis/Alternative hypothesis/Error - Z-test - Student's t-test - Chi-square test - F-test - P-value - Interval estimation - Maximum likelihood - Analysis of variance - Meta-analysis - Confidence interval Survival analysis Survival function - Kaplan-Meier - Logrank test - Failure rate - Proportional hazards models Correlation Confounding variable - Pearson product-moment correlation coefficient - Rank correlation Spearman's rank correlation coefficient, Kendall tau rank correlation coefficient Regression analysis Linear regression - Nonlinear regression - Logistic regression - Maximum Likelihood Estimation Statistical graphics Bar chart - Biplot - Box plot - Control chart - Histogram - Q-Q plot - Run chart - Scatterplot - Stemplot Category · Project · Portal · List of topics Retrieved from http://en..org/wiki/Meta-analysis Categories: Research methods | Meta-analysis | Social sciences methodology | Educational psychology | Evaluation methods | Evidence-based medicine | Systematic reviewHidden categories: Cleanup from August 2007 | All pages needing cleanup Views Article Discussion this page History Personal tools Log in / create account Navigation Main page Contents Featured content Current events Random article Search Go Search Interaction Community portal Recent changes Contact Donate to Help Toolbox What links here Related changes Upload file Special pages Printable version Permanent link Cite this page Languages Dansk Deutsch Español Français Italiano Nederlands 日本語 Norsk bokmål Polski Svenska 中文 This page was last modified on 4 September 2008, at 01:50
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