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When the process of publication favors studies with small p -values, and hence large effect estimates, combined estimates from many studies may be biased. This paper describes a model for estimation of effect size when there is selection based on one-tailed p -values. The model employs the method of maximum likelihood in the context of a mixed (fixed and random) effects general linear model for effect sizes. It offers a test for the presence of publication bias, and corrected estimates of the parameters of the linear model for effect magnitude. The model is illustrated using a well-known data set on the benefits of psychotherapy.
Vevea et al. (Fri,) studied this question.
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