Among scientists who study scientific production, the relationship between the quantity of a scientist’s production and the quality of their work has long been a topic of empirical research and theoretical debate. One principal theoretical perspective on the quantity–quality relationship has been the equal odds baseline, which posits that a scientist’s number of high-quality products increases linearly with their total number of products, and that there is a zero correlation between a scientist’s total number of products and the average quality of those products. While these central tenets of the equal odds baseline are well known, it also posits a number of more specific and less discussed aspects of the quality–quantity relation, including the expected residual variance and heteroscedastic errors when quality is regressed on quantity. After a careful examination of the expected variance by means of a non-parametric bootstrap approach, we forward a further prediction based on the heteroscedasticity implied by the equal-odds baseline that we term the tilted funnel hypothesis, that describes the shape of a bivariate scatterplot when quality is regressed on quantity, as well as the change in the strength of slope coefficients at different conditional quantiles of the quality distribution. In this study, we empirically test the expected residual variance and the tilted funnel hypothesis across three large datasets (including approximately 1.5 million inventors, 1800 psychologists, and 20,000 multidisciplinary scientists). Across all of the data sets, the results empirically supported the tilted funnel hypothesis, and therefore the results provided further evidence of the utility of the equal odds baseline.

中文翻译：

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研究科学创造力中的数量-质量关系：对预期残差和倾斜漏斗假设的实证检验

在研究科学生产的科学家中，科学家的生产数量与其工作质量之间的关系长期以来一直是实证研究和理论争论的话题。关于数量-质量关系的一个主要理论观点是等赔率基线，它假定科学家的高质量产品数量与他们的产品总数呈线性增长，并且科学家的总数量之间存在零相关性。产品和这些产品的平均质量。虽然等赔率基线的这些中心原则是众所周知的，但它也提出了质量-数量关系的一些更具体和较少讨论的方面，包括当质量对数量进行回归时的预期残差和异方差误差。在通过非参数自举方法仔细检查预期方差后，我们根据等赔率基线隐含的异方差性进行进一步预测，我们将其称为倾斜漏斗假设，它描述了二元散点图的形状当质量对数量进行回归时，以及质量分布的不同条件分位数的斜率系数强度的变化。在这项研究中，我们对三个大型数据集（包括大约 150 万名发明家、1800 名心理学家和 20,000 名多学科科学家）的预期残差和倾斜漏斗假设进行了实证检验。在所有数据集中，结果从经验上支持倾斜漏斗假设，