Data and methods

To examine consolidation effects on friendship segregation across attributes with different segregating power, we use unweighted data from the first wave of the “Children of Immigrants Longitudinal Survey in Four European Countries (CILS4EU)” [35]. While the dataset comprises nationally representative survey responses from students in four different countries, we exclude English schools from the analysis, because instead of classes they organize teaching predominantly in courses, i.e., each student belongs to several subject-specific learning groups. This leaves us with 14,401 students around the age of 14 in 744 school classes at 373 randomly selected secondary schools in Germany, the Netherlands, and Sweden, collected in 2010 and 2011. In all three countries, students were sampled using a stratified, three-stage sampling design: In stage 1, schools were randomly selected with probabilities proportional to their size (oversampling schools with a high proportion of ethnic minority students). In stage 2, two ninth grade classes were randomly selected in each school. In stage 3, all students in the classes were selected. Only students without parental refusal (in Germany, only students with active parental consent) could participate in the study. The CILS4EU data collection received ethical approval from the ethical vetting boards from the Universities of Stockholm, Mannheim, and Oxford. In the Netherlands, ethical approval was not required at the time of data collection, but they followed the same ethical standards as in the other three survey countries. Additional ethical approval for the presented study was not required, as the analysis is based on anonymized secondary data that does not involve direct interaction with human subjects. Access to CILS4EU data can be requested at GESIS Data Archive for the Social Sciences.

We in Study 1 aim to examine how the overall levels of friendship segregation along the outlined seven demographic attributes are affected by consolidation with the remaining other attributes. The seven dependent variables in Study 1 are therefore the share of ingroup friends based on the seven different attributes. They are based on sociometric questions about students’ up to five best friends in their school class (“Who are your best friends in class?”). We define the share of ingroup friends as the proportion of nominated friends reporting the same category in a given demographic attribute as the nominating students. To obtain information on the seven selected attributes, we combine survey responses from the students and their parents. Socio-economic background is defined as low, medium, or high based on the highest value of the parents’ International Socio-economic Index of Occupational Status (ISEI) [36], with categorical cutoffs following the sample terciles in ISEI values across 79 countries in the PISA 2018 database (see Study 2). We define educational background in three categories as primary education or lower, secondary education, or tertiary education based on the highest educational attainment of students’ parents. Country of origin is defined based on the countries of birth of the students and their parents. For students born abroad, we define their own country of birth as their country of origin. For students born in the survey country, we use the mother’s country of birth if she was born abroad and the father’s country of birth otherwise [37]. Students could select their religious affiliation from a list or report another religion in an open-ended question, and we combine both types of information to define students’ religion. The language spoken at home is defined as either the survey country language or students’ second language, based on students’ reports of whether they often or always talk to their family in this second language. In the absence of precise information about where students live, we define their residential area based on dyadic reports about classmates who live within five minutes of each other. Each component in this network of residential proximity is considered a residential area in the respective school class. Students’ gender was collected as a binary variable so we distinguish between students who identify as boys and those who identify as girls.

In additional analyses we further use metric information on students’ self-evaluated math performance (from 1 = “not well at all” to 5 = “very well”), their school satisfaction (from 1 = “very satisfied” to 10 = “very unsatisfied”), and the number of friends in the same class that were nominated by students when asked to list their five best friends in general. We impute missing values in all variables (except students’ friends and place of residence) ten times using multivariate imputation by chained equations, repeat the following steps for each imputed dataset and combine the results using Rubin’s rules [38]. Supplementary analyses using only complete cases yield substantially similar results (see S2 Table in the Appendix).

Attribute consolidation, our covariate of interest, is a contextual feature that does not vary at the individual level but only between demographic categories within classes. Therefore, we follow previous work [18] and aggregate the proportion of in-group friends at the level of groups within classes and use this as our unit of analysis. This means that, for each group in a school class, we calculate the proportion of friendship nominations that group members send to ingroup peers, relative to all nominations that they send to members of their class. A ‘group’ consists of at least three students in the same school class who share the same category for one of the seven specified attributes. For example, in a class with eight students of Turkish origin, ten students of German origin, and one student of Polish origin, we would identify two ethnic groups within the class: Turkish and German.

We use Cramer’s V to measure attribute consolidation, following prior research that applies this statistic to assess the association between student attributes in school classes [17,18]. Cramer’s V is based on the chi-squared statistic and well-suited to measure the association between nominal variables with multiple response categories. It ranges from 0 (no overlap) to 1 (perfect overlap) and is defined as

,

for each group g (defined by attribute A, e.g., low, medium, and high when A = SES) in class c in survey country s, where is the chi-squared statistic, the total number of students in class, and the number of categories in attribute B. As we measure consolidation as the overlap between group membership (defined by attribute A) and attribute B, it varies not only across classes but also groups within classes, as indicated by the subscript g,c,s. For example, in a class with 10 low-SES boys, 5 medium-SES girls, and 10 high-SES girls, group membership is more strongly consolidated with gender from the perspective of the low-SES students (Cramer’s V = 1) than medium-SES students (Cramer’s V = 0.4).

For each of the seven attributes, we create separate datasets, containing information on each group’s share of ingroup friends (see above), the consolidation of group membership with each of the other six attributes (see above), the class size, the group size, the ingroup-outgroup diversity (measured as the inverse Herfindahl index of the proportions of in- and outgroup members in class), the diversity of the other six attributes (again, inverse Herfindahl index), the absolute difference in the two diversity measures, and the number of categories in class of all other non-binary attributes (see below for details). We exclude groups without any nominated friend and groups without outgroup members in the respective class. To check whether excluding groups without any nominated friend biases our results, we included these groups in supplementary analyses (with their ingroup share artificially assigned to either 0 or 1). However, as this sample restriction affects only six groups out of over 6,000, it does not meaningfully change the results (see S3 and S4 Tables in the Appendix). To ensure sufficient coverage of the classes’ network structure, we drop all groups from classes with less than 10 respondents, a participation rate below 60 percent, or 25 percent or more without any sociometric nominations. Moreover, to ensure comparability across the different attributes, we drop all groups from classes that are included only in some but not all seven groups-in-classes datasets. Across the seven resulting datasets (i.e., demographic attributes of interest), the final sample size varies between 800 and 1,348 groups in 524 school classes. See S5 and S6 Tables in the Appendix for descriptive information on the analytical samples.

Building on the approach of Kroneberg et al. [18], we examine the effects of attribute consolidation on overall levels of friendship segregation rather than focusing on individual preferences for similar others, as explored by Zhao [17]. Given our focus, network approaches such as exponential random graphs [39], which are designed to estimate segregation tendencies while accounting for other tie formation mechanisms, are not suited to our analysis. Instead, we regress the proportion of ingroup friends on the consolidation of the group-defining attribute with the other six attributes in 42 separate models using OLS regressions with cluster-robust standard errors. The 42 models are used to examine heterogeneity in consolidation effects across different combinations of attributes. Because Hypothesis 1 examines the significance of consolidation effects across multiple attribute combinations, we apply corrections for multiple testing [40]. In contrast, such corrections are unnecessary for Hypothesis 2, as it focuses on differences between estimates rather than the significance of a universally applying consolidation effect. The following equation presents our regression model, with attribute A and B defined by all possible combinations of the seven selected attributes in 42 separate models:

To address different sources of confounding, we include groups-in-survey-countries fixed effects (i.e., dummy variables for the combination of group characteristics and survey countries, e.g., high-SES groups in Sweden or students of Turkish ethnic origin in Germany). Supplementary analyses using school fixed effects instead of groups-in-survey-country fixed effects yield similar results (see S7 Table in the Appendix). Further, we control for structural determinants of consolidation. We supplemented a set of determinants identified in prior research [18] with additional structural variables associated with consolidation in our sample, as revealed by exploratory analyses (see S8 Table in the Appendix). Specifically, we control for class size (25 in the example above), group size (10 for low-SES students in the example above), ingroup-outgroup diversity (measured as the inverse Herfindahl index of the proportions of in- and outgroup members, which equals 0.48 for the low-SES group in the example above), diversity in attribute B (also measured as the inverse Herfindahl index, which equals 0.5 for attribute B defined as gender in the example above), the absolute difference between the two diversity measures (0.02 in the example above), and the number of categories in attribute B (2 in the example above).

All analyses of Study 1 and 2 are conducted in R version 4.2.1 [41], using the packages tidyverse, data.table, parallel, haven, labelled, mice, miceadds, rcompanion, igraph, netseg, caret, patchwork, writexl, MASS, scales, segregation, gridExtra, and randomForest.

Results

The degree of consolidation potentially experienced by groups of demographically similar students varies across learning environments and attributes. Fig 2 illustrates how group membership, defined by the seven demographic attributes, aligns with six other attributes across the 524 school classes in the analytical sample. The distributions of these alignments vary considerably across various attribute combinations. Gender consolidation, which reflects the alignment between group membership and gender similarity, is right-skewed across all group-defining attributes. Most groups are placed in classes where the alignment between group membership and gender is small, but a few are situated in environments with strong gender consolidation. Conversely, the consolidation of language groups with countries of origin is strongly left-skewed, indicating that students who speak the same language at home typically share a similar country of origin. This contrast highlights the impact of cohort compositions in the production of attribute consolidation in school classes (see Study 2). While languages and countries of origin are often consolidated at broader levels (e.g., school cohorts or national populations), leaving little room for variation between classes, strong gender consolidation appears only in certain classes, likely as a random consequence of schools not prioritizing gender consolidation in student placements [18].

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Fig 2. Attribute consolidation in 524 school classes in Germany, the Netherlands, and Sweden.

The seven panels show the consolidation (Cramer’s V) of group membership as defined by seven demographic attributes (see panel headings) with the six other demographic attributes across all 524 classes in the analytical sample of Study 1.

https://doi.org/10.1371/journal.pone.0339581.g002

Fig 3 illustrates the results of 42 regression models that estimate the relationship between the share of ingroup friends and attribute consolidation. The units of analysis are groups in classes (defined as at least three similar students). The seven rows in Fig 3 represent seven group-defining attributes. The seven columns represent the different consolidating attributes. The x-axis in each model quantifies the consolidation of group membership with the consolidating attribute, measured as Cramer’s V. Values of zero correspond to completely unconsolidated contexts and values of one correspond to perfectly consolidated contexts. The y-axis in each model shows the group’s share of ingroup friends. For each of the regression models, the figure shows conditional expected values plots and unstandardized regression coefficients with their significance levels. See S9 Table in the Appendix for full regression results.

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Fig 3. The association between attribute consolidation and friendship segregation across 42 attribute combinations.

Conditional expected values plots and unstandardized regression coefficients of OLS regressions modelling the association between consolidation and the share of ingroup friends with cluster robust standard errors, groups-in-survey-countries fixed-effects, and controlled for class size, group size, ingroup-outgroup diversity, diversity of the consolidating attribute, the absolute difference in diversity, and the number of categories of the consolidating attribute. Pooled results over 10 imputed datasets using Rubin’s rules [38]. Background color of panels visualizes coefficient significance and size. ***p < 0.001 **p < 0.01 *p < 0.05.

https://doi.org/10.1371/journal.pone.0339581.g003

Across models, positive relationships between attribute consolidation and friendship segregation are observed. Almost all coefficients are positive (40 of the 42 coefficients) and more than half of them are statistically significant and positive (25 coefficients). Even after applying a Bonferroni correction that divides the significance threshold by 42 – a highly conservative adjustment given the large number of tests – 14 coefficients remain statistically significant (see S10 Table in the Appendix). This indicates that the observed consolidation effects are unlikely to be mere artifacts of multiple testing. Consistent with theoretical expectations, consolidation is positively related to friendship segregation across a wide range of demographic attributes.

Moreover, there is considerable variation in the strength of this relationship across the seven consolidating attributes. Gender consolidation stands out with particularly strong associations with friendship segregation (see last column in Fig 3). Here, the coefficients vary between 0.227 and 0.416, are all statistically significant (t-values between 7 and 14.48, see S9 Table in the Appendix), and are almost all significantly higher than the other attributes’ consolidation coefficients (see S11 Table in the Appendix). As expected, among all demographic attributes under investigation, gender consolidation is particularly important for friendship segregation.

Further, friendship segregation by gender is unrelated to most types of attribute consolidation (see last row in Fig 3). The coefficient sizes for the relationship between friendship segregation by gender and the consolidation with socio-economic background (0.025, t = 0.72), educational background (0.011, t = 0.32), religion (0.05, t = 1.54), and language (−0.003, t = −0.06) are close to zero and insignificant, the consolidation with country of origin even negative (−0.092, t = −2.1), and only the consolidation with residential area significantly positive related to gender segregation (0.09, t = 2.27). Gender segregation in adolescents’ friendships is prevalent across contexts, largely independent of the extent of consolidation with other demographic attributes.

Finally, Fig 3 reveals remarkably high coefficient sizes for the combination of the three ethno-religious attributes (country of origin, religion, and language) and the combination of residential area with religion. For example, while language consolidation is not or only weakly related to segregation along the lines of socio-economic background (0.072, t = 1.95), educational background (0.046, t = 1.62), residential area (0.087, t = 2.28), and gender (−0.003, t = −0.06), its relation to country-of-origin segregation is surprisingly high (0.164, t = 4.48). This suggests the presence of salience effects that increase friendship segregation beyond the mechanical effects of attribute consolidation. Preferences to form outgroup friendships may increase in distinctive ways when certain attributes are consolidated due to unique experiences or identities that lie at the intersections of attributes. However, despite the potential presence of other segregation-enhancing mechanisms for certain attribute combinations, none of these coefficients reach the overarching strong consolidation effects imposed by gender.

Data and methods

We aim to determine how much friendship segregation in schools could be reduced by considering attribute consolidation in class placement. Based on the findings of Study 1, we test the proposed sorting heuristic (see Fig 4) with a focus on gender, as minimizing gender consolidation appears to have the strongest impact on reducing segregation (see Study 1). Our analysis consists of two sets of simulations. First, we compare the heuristic’s outcomes to actual class placements in schools in Germany, the Netherlands, and Sweden. Second, we move beyond real-world placements to explore whether the heuristic’s effectiveness depends on the demographic composition of the student body. By applying the heuristic to a range of empirically plausible cohort compositions, we assess how consistently it reduces friendship segregation across different student populations.

For the first set of simulations, we again use data from the first wave of the “Children of Immigrants Longitudinal Survey in Four European Countries (CILS4EU)” [35]. We restrict the sample used in Study 1 to 188 schools for which we have data on two randomly selected classes. We use the same selection and measurement of attributes as in Study 1. Only residential areas are excluded from Study 2, because information on students’ residential proximity is only available within classes and not across them. For each of the attributes socio-economic background, educational background, country of origin, religion, and language, we simulate class placements that minimize the consolidation of the selected attribute and gender: We create subgroups based on the combination of the respective attribute and gender, and then assign the subgroup members evenly to two classes (see Fig 4). This sorting heuristic minimizes the consolidation of the selected attribute with gender while maximizing the diversity of gender and the selected attribute across classes. We simulate this sorting heuristic 200 times for each of the five selected attributes and 188 schools in the sample. As a benchmark for comparison, we use the observed class placements. In supplementary analyses (S1 Fig in the Appendix), we replace this benchmark with 200 simulations of random class placements.

For each of the observed and simulated classes we predict friendship segregation based on the models of Study 1. First, we transform the data analogously to Study 1 into a groups-in-classes structure and generate a separate dataset for each demographic attribute. Second, we generate the same variables as in Study 1: The consolidation of group membership with gender, class size, group size, ingroup-outgroup diversity, gender diversity, and the absolute difference in the two diversity measures. Third, we use the models estimated in Study 1 (M37 to M41 in S9 Table in the Appendix) to predict the share of ingroup friends for the groups in the observed and simulated classes. As the outcome measure of each class placement, we report the maximum predicted ingroup share across all groups in the two classes. That is, we evaluate the performance of a class placement based on the predicted segregation for the most segregated group. Rather than minimizing segregation in one group or class, possibly at the expense of increasing segregation in a less advantaged group or class, this outcome focuses on the potential payoff for the ‘least advantaged’ group in a school (though possibly at the expense of a more advantaged group [43]). In S1 Text in the Appendix, we describe the rationale and implications of the selected outcome measure in more detail. Finally, we compute the difference in this outcome measure between the observed class placements and the averages over 200 simulations of our hypothetical sorting heuristic that minimizes gender consolidation.

For the second set of simulations, we rely on unweighted data from the “OECD Programme for International Student Assessment (PISA)” in 2018. The PISA 2018 database comprises survey responses of 612,004 students in 21,903 schools in 80 countries. In each country, students were sampled in a two-stage stratified sampling design: In stage 1, 150 schools were randomly selected within each country with probabilities proportional to the number of 15-year-old students. In stage 2, 42 students at the age of 15 were randomly selected within each school. In 809 schools in 20 countries, the number of respondents exceeds 42 due to these countries’ participation in an optional module [44]. We draw a random sample of 42 students from these schools to avoid biases in the school comparisons. In supplementary analyses with the full cohorts of these 809 schools, we test how this affects the results of Study 2 (see S12 Table in the Appendix). All procedures for data collection and consent were managed by national project teams in accordance with OECD guidelines and respective national regulations. PISA data is publicly available through the OECD database and is de-identified to ensure participant confidentiality. Ethical approval for the presented study was not required, as the analysis is based on anonymized secondary data that does not involve direct interaction with human subjects.

Students’ demographic attributes are defined similarly to the analyses relying on CILS4EU data (see S2 Text in the Appendix for a detailed comparison of coding schemes). However, given the lack of information on students’ religion and residential area, we limit our analysis to the remaining five demographic attributes. We drop all schools in Singapore due to missing language information and all schools with less than 20 respondents (i.e., the minimal class size is 10 students, as in Study 1), resulting in a final sample size of 521,210 students in 16,117 schools in 79 countries. We impute missing values in all five variables ten times using multivariate imputation by chained equations, repeat the following steps for each imputed dataset and combine the results using Rubin’s rules [38].

For each of the 16,117 schools, we simulate 200 class placements that minimize gender consolidation (for each of the attributes socio-economic background, educational background, country of origin, and language spoken at home) and 200 random class placements. Analogously to the first simulation study, we then transform the data into a groups-in-class structure, predict for each group the share of ingroup friends using the models estimated in Study 1, and summarize the predictions by selecting the maximum predicted ingroup share across all groups and classes within each simulated class placement. Finally, we compute the difference in this outcome measure between the averages over 200 simulations of our suggested sorting heuristic that minimizes gender consolidation and 200 random class placements. See S1 Text and S2 Fig in the Appendix for a more detailed description and visualization of the simulation. In supplementary analyses, we use gender balanced class placements (i.e., assigning boys and girls evenly to the two classes) instead of random class placements as the benchmark of comparison (see S13 Table and S4 Fig in the Appendix).

In a second step, we then analyze how the estimated potential impact of the sorting heuristic that minimizes gender consolidation is related to distributional characteristics at school and country level. Using random forests with 5-fold cross-validation, we explore how well the simulated reductions in friendship segregation are predicted by five compositional characteristics of schools: The diversity in the group-defining attribute (measured as the inverse Herfindahl index), the consolidation of the selected attribute and gender (measured as Cramer’s V), the number of students, the gender diversity (measured as the inverse Herfindahl index), and the number of categories in the group-defining attribute (see S13 Table in the Appendix for the summary statistics of all included variables). To assess the importance of these five school characteristics, we measure each variable’s contribution to the model’s prediction accuracy. We do this by comparing how much the models’ accuracy in predicting the outcome decreases after randomly permuting the values of each variable one at a time. Finally, we explore the functional shape of each variable’s marginal effects on the outcome variable with partial dependence plots.

Results

In the first set of simulations, we examine how friendship segregation, as predicted by the models estimated in Study 1, differs between empirically observed class placements in 188 German, Dutch, and Swedish schools and simulations of counterfactual class placements that minimize gender consolidation. Fig 5 visualizes the results. The green points in each panel show the highest predicted share of ingroup friends for groups in the observed classes. The blue points show for the same schools the highest predicted share of ingroup friends averaged over 200 simulations of gender consolidation minimizing class placements (interquartile ranges are visualized by the blue lines around each point). The average predicted share of ingroup friends across the 188 schools decreases from 57.5 to 50.7 percent for socio-economic background groups, from 70.3 to 65.7 percent for educational background groups, from 69.7 to 64.3 percent for country of origin groups, from 72.6 to 66.8 percent for religion groups, and from 77.4 to 73 percent for language groups. This corresponds to an average estimated decrease of 4–7 percentage points.

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Fig 5. Difference in predicted friendship segregation between observed and simulated class placements.

Share of ingroup friends predicted with the models of Study 1 for 188 empirically observed (green) and simulated counterfactual (blue) class placements in Germany, the Netherlands, and Sweden.

https://doi.org/10.1371/journal.pone.0339581.g005

Fig 5 reveals a considerable between-school variation in the estimated reductions of friendship segregation (Std. Dev. = 5.5, 4.6, 4.8, 5.6, and 5.1 percentage points). While the predicted reduction in students’ share of ingroup friends is close to zero for some schools, it ranges up to 26 percentage points in the most extreme case.

This variation could stem from two sources: differences in current sorting approaches (e.g., whether school administrators balance ethnicity across classes) and differences in cohort compositions (e.g., the level of ethnic diversity within a school). To disentangle the roles of these factors, we conduct supplementary analyses that use random class placements – rather than the empirically observed class placements – as the benchmark of comparison (see S1 Fig in the Appendix). In this analysis, school differences in the potential impact of the sorting heuristic can only be attributed to compositional differences, not to observed sorting approaches. Compared to random class placements, the suggested sorting heuristic could reduce friendship segregation on average by 3–6 percentage points, with standard deviations between 1 and 2 percentage points and a maximum predicted reduction of 10 percentage points. Even when differences in sorting approaches are held constant, the heuristic’s potential effectiveness still varies between schools. This indicates that the cohort’s composition plays an important role in determining how effective the proposed sorting heuristic can be.

To examine how compositional features of the cohort to be sorted shape the potential effects of the proposed sorting heuristic, we run another set of simulations using a much larger dataset. To address the complete, plausible value space of cohort compositions, we simulate the proposed sorting heuristic for 16,117 empirically observed schools in 79 countries. To focus on the role of cohort compositions in shaping the potential effects of the hypothetical sorting heuristic, we use random class placements as the benchmark of comparison. A comparison with gender balanced class placements yields similar results (see S13 Table and S4 Fig in the Appendix). We do this separately for the available attributes of socio-economic background, educational background, country of origin, and language. The extent to which the hypothetical sorting heuristic could reduce friendship segregation varies considerably across schools and attributes. In 94% of the simulated cases, the reductions are positive, up to a maximum reduction of 11 percentage points. On average, the simulated reductions in ingroup shares with respect to students’ socio-economic backgrounds, educational backgrounds, countries of origin, and languages spoken at home are 4.8, 4.6, 2.4, and 2.3 percentage points (Std. Dev. = 1.6, 1.9, 1.9, and 2.1 percentage points).

Fig 6 summarizes the results of exploratory analyses using random forests. School diversity is the most important of the compositional variables in predicting the potential effectiveness of the hypothetical sorting heuristic. Panel B in Fig 6 shows the marginal effects of school diversity on the reductions in predicted ingroup shares. The relationship is positive with decreasing steepness, meaning that the proposed sorting heuristic can be more effective in more diverse schools. S5 Fig in the Appendix shows the marginal effects of the other compositional variables. The sorting heuristic’s potential effectiveness is larger when the cohort to be sorted is characterized by a low consolidation of the selected attribute and gender, higher number of students, and a stronger gender diversity.

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Fig 6. Random forest analysis of factors predicting simulated reductions in friendship segregation.

Results of random forests that predict simulated reductions in friendship segregation with gender consolidation minimizing class placements (compared to random class placements) for 16,117 schools in 79 countries with 5-fold cross-validation. (A) Relative importance of each predictor variable based on a comparison of prediction errors after permuting each of the variables in the out-of-bag data. (B) Partial dependence plots with the marginal effects of school diversity on reductions in predicted ingroup shares.

https://doi.org/10.1371/journal.pone.0339581.g006

In supplementary analyses, we explore the potential implications of the observed positive relationship between school diversity and the sorting heuristic’s effectiveness for schools in national contexts with different compositional features. S6 Fig and S14 Table in the Appendix indicate that the proposed sorting heuristic could theoretically be more effective in countries with high levels of diversity and low levels of between-school segregation. It is important to note, however, that this analysis does not account for country-specific differences in sorting practices or in the effects of gender consolidation. Instead, it relies solely on differences in school compositions and should therefore be interpreted with caution.

Overall, schools vary considerably in the extent to which the sorting heuristic that minimizes gender consolidation can reduce friendship segregation. While much of this variation stems from differences in observed class placements, the composition of the student cohort also plays a role. In particular, diverse schools – which are more common in countries with high levels of diversity and low levels of between-school segregation – may provide more favorable structural conditions for diverse friendships by trying to reduce gender consolidation in their class placement.