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[14],where we preserve the network topology and randomly reshuffle the assignment of the GPAsto the node. We repeat this procedure 10,000 times to obtain a distribution of the measures Hand IX. We can then test the null hypothesis that GPAs are independent of network topology,and to compute corresponding p-values.Supporting informationS1 Text.(PDF)S1 Fig. The average number of interaction (”likes“) per day between university students ispresented for each cohort. The maximum observed value is 200 or 0.13 “likes” per day perstudent.
The steep increase in September marks the beginning of studies. Some students kneweach other before the matriculation.(TIF)S2 Fig. Average GPA for high school and university students (inset) over time. Results areshown as mean values ± standard deviations. Females have better grades on average. GPAsand their variance do practically not change with time.(TIF)S3 Fig. In the high school data the network is getting more connected over time. It is therefore possible to re-define new time intervals in such a way that for each time interval the average degree in the network is approximately the same.
Clearly the homophily index H increasesas before, indicating that the degree is not an explanatory variable. The same argument holdsfor the clustering coefficient.(TIF)S4 Fig. There are no consistent differences in gender. While both genders show about thesame increase over time, it is larger for females in the sophomore and senior groups, and largerfor males for the high school students and juniors.(TIF)S5 Fig. Homophily increase varies from subject to subject. Since there are only 4 possiblevalues of grades (scores) possible for the individual subjects, we expect to observe less stableresults than for the GPA.
However, the general pattern of homophily increase over time holds,for mathematics it is not much pronounced.(TIF)S6 Fig. Time schedule of data collection for university (a) and high school (b) students.Network data is in the form of adjacency matrices Aij(t), where Aij(t) = 1 means that student igave at least one “like” to student j from time t − 1 to time t. The time period from t − 1 to t isPLOS ONE | https://doi.org/10.1371/journal.pone.0183473 August 30, 201712 / 16Formation of homophily in academic performanceequal to 3 months. (a) For the university students (seniors, juniors, sophomores) the aggre U , from the beginning of their studies on the 1st of Septembergated average GPA, Gi(2012/2013/2014) until the 1st of March, 2016 is collected.
This period is equal to 3.5 years forseniors, 2.5 years for juniors and 1.5 years for sophomores respectively. The temporal GPAdata, GUi ðtÞ, was also collected for the last 3 semesters for all 3 cohorts (arrows). (b) For thehigh school students the temporal GPA data, GHSi ðtÞ, is collected at the end of each trimesterfor the last 5 trimesters (arrows). As students do not study in summer, we assume the same HSperformance at that period as at the last available time point i.e. spring, GHS ð3Þ ¼ GHS ð4Þ. Giiiis computed as the average over the 5 trimesters.(TIF)S1 Table.
Descriptive statistics of students’ GPA scores across the whole period of theirstudies. h.ii means average over all students in the group. Mean values and standard deviations(in brackets) are presented. Females have better grades than males on average.(PDF)S2 Table. Coefficients from the regression model. The GPA at the current time point isalmost fully explained by the GPA at the previous time point. The influence of gender is alsosignificant, males have lower grades also after controlling for their previous GPA. The averageGPA of friends at the previous time point is not significant.(PDF)S3 Table.
Re-organization of the students’ network over time. The GPA distance for newfriends is consistently and significantly smaller (tested with two-sample Students’ test) thanthe GPA distance for discontinued friends in the observed data. Comparable results areobtained with the model.(PDF)AcknowledgmentsWe thank Dr. Alexander Sidorkin from the Institute of Education, Higher School of Economics, Moscow, for providing us with the dataset.Author ContributionsConceptualization: Ivan Smirnov, Stefan Thurner.Data curation: Ivan Smirnov.Formal analysis: Ivan Smirnov, Stefan Thurner.Investigation: Ivan Smirnov, Stefan Thurner.Methodology: Ivan Smirnov, Stefan Thurner.Writing – original draft: Ivan Smirnov, Stefan Thurner.Writing – review & editing: Ivan Smirnov, Stefan Thurner.References1.Shrum W, Cheek NH, Saundra MH. Friendship in School: Gender and Racial Homophily.
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