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. 2024 Sep 9;24:197. doi: 10.1186/s12874-024-02306-2

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 2 — Family wise error rate testing simultaneously superiority tests ( $S_{1}$ ) and ( $S_{2}$ ) for different scenarios of the Fill-it-up-design depending on the choice of the significance level of the equivalence pre-test. A medium effect size $δ = 0.5$ with $n_{H} = 500$ historical controls and an equivalence margin of $Δ = 0.44$ is examined