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. 2020 Jul 1;20:175. doi: 10.1186/s12874-020-01055-2

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© The Author(s) 2020

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. 6 — Performance of the RQRs in detecting over-dispersion of a sample dataset of size n=1000. The panels in the first row present the RQRs for the true fitted model: NB model. The panels in the second row present the RQRs for the fitted wrong model: Poisson model with the same mean structure as the true model. The first two columns display the scatter plots and QQ plots of the RQRs, respectively. The red dashed lines in the QQ plots represent the simulated envelopes. The third column presents the histograms of the SW p-values for the RQRs over 5000 randomly generated datasets from the true model