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. 2022 Sep 5;12:363. doi: 10.1038/s41398-022-02128-0

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© The Author(s) 2022

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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — A Plot of the weighted mean of each group. The weighted mean of the empirical cylindrical K-functions minus the theoretical value under CSR in the direction shown at the top. The line type corresponds to the groups: Control (C), Major depressive disorder (MDD), Suicide (SU), and Schizophrenia (SCH) as stated in the legend. B Test the difference between groups in the x, y, and z-axes.95% Global envelope test for testing the hypothesis of no differences in the cylindrical K-functions of the four groups Control (C), Major depressive disorder (MDD), Suicide (SU), and Schizophrenia (SCH). There is a test for the cylindrical K-function in each of the directions of the x-, y-, and z-axes. The 95% global envelopes (gray area) were based on 8000 random permutations. The solid curves are the estimates obtained from data after the theoretical value under CSR was subtracted. The direction is stated at the top of each plot, as well as the p-value of the test.