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. 2018 Mar 27;18:32. doi: 10.1186/s12874-018-0473-2

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© The Author(s). 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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.

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Fig. 3 — Type I error rates of Sobel’s (black line), distribution of the product (red line), and bootstrap (blue line) methods under various sample sizes with 3 repeated measures and ICC of 0.3