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**Publication** The article was published in the *International Journal of Psychophysiology* under the DOI [10.1016/j.ijpsycho.2018.03.019][1]. **Corresponding author** Florian Scharf (florian.scharf@uni-leipzig.de). **The following material is available:** 1. The post-peer-review [author's version][2] of the article. 2. Original Figures 3. Scripts for simulations, analyses and figure generation 4. Sample results necessary to produce the results (i.e., loading, effect size and factor correlation estimates as well as SRMR) 5. Supplementary Simulation with Kayser and Tenke's (2003) approach. 6. The slides of a talk presented at EAM 2018 in Jena reporting selected results of the study. If you have any questions, please do not hesitate to contact Florian Scharf. **Original Samples** Although our simulation scripts should be able to reproduce the same random samples due to the seed and although the results should not be fundamentally different for any other set of random samples, we saved every single random sample used in our analyses. Due to space limitations (file size ~ 11GB), we decided not to upload the single samples. These are only available on request to the corresponding author. **Sample sizes** We originally simulated another sample size condition (N = 60) which was left out of the paper in order to preserve comprehensibility because it did not add any new information (From the article, you can see, that none of the central results depended on sample size). [1]: https://www.sciencedirect.com/science/article/pii/S016787601830028X [2]: https://www.biphaps.uni-leipzig.de/fileadmin/user_upload/ag-psymeth/Pre-Prints/ScharfNestler2018.pdf