Publication bias and p-hacking are two well-known phenomena that strongly affect the scientific literature and cause severe problems in meta-analyses. Due to these phenomena, the assumptions of meta-analyses are seriously violated and the results of the studies cannot be trusted. While publication bias is very often captured well by the weighting function selection model, p-hacking is much harder to model and no definitive solution has been found yet. In this paper, we advocate the selection model approach to model publication bias and propose a mixture model for p-hacking. We derive some properties for these models, and we compare them formally and through simulations. Finally, two real data examples are used to show how the models work in practice.

中文翻译：

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建模出版偏见和 p-hacking

发表偏倚和p -hacking 是两种众所周知的现象，它们强烈影响科学文献并在荟萃分析中造成严重问题。由于这些现象，严重违反了荟萃分析的假设，研究结果不可信。虽然权重函数选择模型通常可以很好地捕获发表偏差，但p -hacking 更难建模，并且尚未找到确定的解决方案。在本文中，我们提倡使用选择模型方法来模拟发布偏差，并提出了一种用于p -hacking 的混合模型。我们推导出这些模型的一些属性，并通过模拟对它们进行正式比较。最后，使用两个真实数据示例来展示模型在实践中的工作原理。