In vielen Bereichen werden Teststatistiken dadurch erhalten, da Schatzer aus verschiedenen Experimenten oder Studien kombiniert werden. Der ublicherweise verwendete Schatzer des Gesamteffektes aus unabhangigen Studien fuhrt zu systematischen Uberschatzungen des Signifikanzniveaus, vgl. Li et al. (1994), und daher zu vielen ungerechtfertigten Signifikanzen. Mit Hilfe der Konvexitat zusammengesetzter Funktionen und Anwendung hoherer sowie inverser Momente der x 2-Verteilung stellen wir Korrekturen fur die geschatzte Standardabweichung des Gesamteffektschatzers vor. Analytische Ergebnisse und Simulationen zeigen, dass das nominelle Niveau durch diese Korrekturen besser eingehalten wird.

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Some Corrections of the Significance Level in Meta - Analysis

Generalized Cochran-Wald statistics in combining of experiments

In many meta-analysis cases the estimator of the overall effect in independent trials or experiments leads to unjustified significant results. This paper considers trials with two arms where the summary statistic of interest is either the mean difference or the risk difference. By using convexity principles of the relevant composed functions and the moments of the chi-square distribution, corrections are made on the estimated standard deviation of the estimator of the overall treatment difference. It is shown, analytically and by simulations, that by making such corrections on the estimated standard deviation, significance levels are attained which are relatively closer to the nominal level.

https://www.econstor.eu/bitstream/10419/77301/2/2000-10.pdf

On the Meta-Analysis of Treatment Differences in Heteroscedastic Samples

Non-iterative t-distribution Based Tests for Meta-Analysis and figures

The variance function of the optimal estimator of the overall mean in a heteroscedastic one-way ANOVA model is dominated by positive semi-definite quadratic functions. This makes it possible to develop closely related tests on the nullity of the overall mean parameter in one-way fixed and random effects ANOVA models, which make use of the quantiles of the t-distribution. These tests are founded on the convexity arguments similar to Hartung (1976). Simulation results indicate that the proposed tests attain type I error rates which are far more acceptable than those of the commonly used tests.

https://www.econstor.eu/bitstream/10419/77316/2/1999-38.pdf

Joachim G. Hartung

Papers

Some Inequalities for a Random Function