 The significance filter, the winner's curse and the need to shrinkErik W. van Zwet and Eric A. Cator Statistica Neerlandica, 2021, vol. 75, issue 4, 437-452 Abstract: The “significance filter” refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have been observed, there are no guarantees if we condition on significance. In fact, the significance filter leads to overestimation of the magnitude of the parameter, which has been called the “winner's curse.” It can also lead to undercoverage of the confidence interval. Moreover, these problems become more severe if the power is low. These issues clearly deserve our attention. They have been studied mostly through empirical observation and simulation, while there are relatively few mathematical results. Here we study them both from the frequentist and the Bayesian perspective. We prove that the relative bias of the magnitude is a decreasing function of the power and that the usual confidence interval undercovers when the power is less than 50%. We conclude that it is important to apply the appropriate amount of shrinkage to counter the winner's curse. Date: 2021 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:stanee:v:75:y:2021:i:4:p:437-452 Ordering information: This journal article can be ordered from Access Statistics for this article Statistica Neerlandica is currently edited by Miroslav Ristic, Marijtje van Duijn and Nan van Geloven More articles in Statistica Neerlandica from Netherlands Society for Statistics and Operations Research |
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