We introduce a new meta-analysis estimator, the weighted and iterated least squares (WILS), that greatly reduces publication selection bias (PSB) when selective reporting for statistical significance (SSS) is present. WILS is the simple weighted average that has smaller bias and rates of false positives than conventional meta-analysis estimators, the unrestricted weighted least squares (UWLS), and the weighted average of the adequately powered (WAAP) when there is SSS. As a simple weighted average, it is not vulnerable to violations in publication bias corrections models’ assumptions too often seen in application. WILS is based on the novel idea of allowing excess statistical significance (ESS), which is a necessary condition of SSS, to identify when and how to reduce PSB. We show in comparisons with large-scale preregistered replications and in evidence-based simulations that the remaining bias is small. The routine application of WILS in the place of random effects would do much to reduce conventional meta-analysis’s notable biases and high rates of false positives.

中文翻译：

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利用超额统计显着性的力量：加权和迭代最小二乘法。

我们引入了一种新的荟萃分析估计器，即加权迭代最小二乘法 (WILS)，当存在选择性报告统计显着性 (SSS) 时，它可以大大减少出版物选择偏差 (PSB)。WILS 是简单加权平均值，与传统荟萃分析估计器、无限制加权最小二乘法 (UWLS) 以及存在 SSS 时的充分功效加权平均值 (WAAP) 相比，偏差和误报率更小。作为一个简单的加权平均值，它不易受到应用中常见的发表偏差校正模型假设的违反。WILS 基于允许超额统计显着性 (ESS)（这是 SSS 的必要条件）的新颖想法，以确定何时以及如何减少 PSB。我们通过与大规模预先注册的复制和基于证据的模拟的比较表明，剩余的偏差很小。WILS 的常规应用代替随机效应将大大减少传统荟萃分析的显着偏差和高误报率。