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. 2023 May 2;8:11. doi: 10.1038/s41539-023-00162-1

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© The Author(s) 2023

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 Scatter plots between alpha-band student-top coupling (left, top students’ number = 4) and alpha-band student-class coupling (right) and the final exam score of Chinese. b Correlation r values as a function of the number of top students included in the calculation of student-top couplings. c Scatter plots between alpha-band student-top couplings (left, top students’ number = 4) and alpha-band student-class couplings (right) and the final exam scores of Math. d Correlation r values as a function of the number of top students included in the calculation of student-top couplings. The violin plots showed the distribution of correlation r values generated by the 5000 shuffled versions, the black line indicated the 95th percentile of the distribution, and the blue line indicated the mean value of the distribution. The star indicates a significant correlation when both Pearson’s p and permutation p were smaller than 0.05. The cross indicates a marginal significance. The colored lines in (b) and (d) represent the trend of how correlation values changed with the number of top students. The color was chosen according to the corresponding discipline (pink for Chinese and blue for Math). Note that the top students themselves were not included in the correlation analysis.