Cross-national differences in the academic impact of socioeconomically integrated schools: The evidence from the PISA data

Cross-national differences in the academic impact of socioeconomically integrated schools: The evidence from the PISA data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Cross-national differences in the academic impact of socioeconomically integrated schools: The evidence from the PISA data Minda Tan, Li Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7172805/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract The link between national income inequality and school socioeconomic diversity complicates the effectiveness of using school integration as a policy tool to promote education equity without harming overall educational outcomes. Using hierarchical linear modelling and propensity score matching, this study investigated PISA 2015 and 2018 data. Three main findings include: (1) a Gatsby-like curve is observed that indicates a positive association between national school diversity and Gini coefficients; (2) school socioeconomic diversity harms the academic performance of students in countries above the estimated curve; (3)the effectiveness of school socioeconomic integration strengthens as the estimated curve evolves. These findings suggest that the effectiveness of integration policy depends on visible income disparities and unequally distributed tangible educational resources in society. The absence of these conditions may render a simple socioeconomic integration inadequate for success. Social science/Development studies Business and commerce/Economics Social science/Economics Social science/Education School socioeconomic diversity National income inequality Integrated schools Education equity Academic performance Figures Figure 1 Introduction Income inequality has become a global concern due to its significant implication of reducing equal educational opportunities and resulting in low intergenerational mobility (Jerrim & Macmillan, 2015 ). Analysing data from Organisation for Economic Co-operation and Development (OECD) economies, Miles Corak ( 2013 ) found a negative relationship between income inequality and intergenerational mobility, illustrated by the Great Gatsby Curve (GGC). The link between income inequality and limited social mobility is primarily attributed to disadvantaged families’ reduced capacity to invest in residences located in high-performing school districts. Further, school segregation contributes to refraining social mobility by impeding socioeconomically disadvantaged students’ access to top-tier universities (Tan, 2022 ). Nevertheless, according to the human capital theory, high income variance within a society can work as a motivating factor, leading parents to invest more to compete for high-quality school education (Mincer, 1984 ). Based on this assumption, countries with significant income disparities tend to show higher school socioeconomic diversity, although its influence on students’ academic attainments remains unsettled (Park & Weng, 2020 ; Parker et al., 2018 ). Despite widespread interest in studying the education role of family socioeconomic composition (SEC), relatively few studies examine the academic influence of socioeconomic diversity and its heterogeneity across countries with differing levels of income inequality. Insufficient knowledge has been gathered regarding the efficacy of employing integrated schools to mitigate educational disparities across schools with varied economic inequalities. Therefore, using the Programme for International Student Assessment (PISA) data, this study aims to contribute threefold to the existing literature. First, similar to the GGC, we plot the Gini coefficient (income inequality) against national school socioeconomic variance (a school diversity measure) to categorise countries into specific education and income inequality groups. Second, we investigate school socioeconomic diversity’s effect on students’ academic performance within different nation groups. Third, we analyse the impact of attending integrated schools based on student and national groups. Theoretical background The Great Gatsby Curve and educational attainment The Great Gatsby Curve depicts a positive association between earnings inequality, measured by the Gini coefficients, and intergenerational persistence, measured by the intergenerational elasticity of income (Durlauf et al., 2022 ). This curve has attracted significant attention from high-ranking policy-makers and scholars as it challenges the widespread belief that equal opportunity for intergenerational mobility through education can counterbalance the social pressures arising from income inequality in the current generation (Durlauf & Seshadri, 2018 ). Education is always regarded as a “social elevator” in intergenerational transmission. Although schooling can be unequal during childhood, educational attainment is essential to the relationship between parental earnings and offspring’s income (Jerrim & Macmillan, 2015 ). The Great Gatsby Curve raises public concerns about whether education provides a placebo rather than a social mobility channel. Three theories explain the role of education in the GGC, shedding light on the underlying mechanisms that link income inequality and intergenerational persistence. First, the classic model of social reproduction theory argues that social inequality perpetuates intergenerational transmission by transferring economic, cultural, and social capital (Bourdieu, 1986 ). As a key component in this process, the educational system unequally assigns academic rewards to students with varied accumulation of different forms of capital (Collins, 2009 ; Lareau, 2011 ). With the income gap growing in a country, affluent parents have a greater capacity to secure educational advantages for their descendants, like school segregation. Such measures utilise education inequalities to enlarge offspring’s socioeconomic variance further. Second, cultural reproduction theory demonstrates that highly educated parents intentionally and unintentionally cultivate their children’s cultural habits, thereby facilitating their adaptation to formal schooling (Bourdieu, 2003 ; Lareau, 2000 ). These cultural experiences enable children to become familiar with the dominant cultural code embedded in the educational system, resulting in favourable treatment by teachers (Jæger & Møllegaard, 2017 ). In unequal countries, advantaged children tend to benefit more from their parents’ educational experiences. Consequently, they are more likely to attain higher incomes due to their privileged position within the educational system (Jerrim & Macmillan, 2015 ). Third, effectively maintained inequality (EMI) theory posits that socioeconomically advantaged parents seek out qualitative educational differences to perpetuate intergenerational persistence when schooling resources are no longer scarce (Lucas, 2001 ). These parents prefer to invest in residences in more affluent communities, facilitating their children’s human capital accumulation. However, this neighbourhood selection mechanism further perpetuates residential and school segregation between wealthy and low-income families, leading to disparate social interactions among children from different family backgrounds and the transmission of socioeconomic privileges across generations (Durlauf et al., 2022 ; Durlauf & Seshadri, 2018 ). This situation is particularly evident in high-inequality countries with less public investment in education (Jerrim & Macmillan, 2015 ). To summarise, privileged parents often take advantage of residential segregation to monopolise high-quality school resources. Therefore, this scenario may reduce the opportunities for low-SES students to succeed within the educational system. In contrast, high-SES students reap the benefits of segregation, thus perpetuating their inherited socioeconomic status. The magnitude of segregation is associated with the Gini coefficient, as high-inequality countries usually have more significant economic and social constraints that hinder students’ access to quality education. Cultural mobility theory and school socioeconomic diversity Existing research focusing on the academic impact of school factors suggests that both educational resources within schools, such as class size and teacher quality, and school climates, including a focus on learning and disciplinary policies, are positively associated with students’ academic achievement (Gustafsson et al., 2018 ; Montt, 2011 ; Rivkin & Schiman, 2015 ; Tan, 2022 ). With governments across countries realising the importance of developing public education, the variance in visible school factors has been narrowed since the 1990s (Baker et al., 2002 ). As a result, scholars have begun investigating the influence of invisible school characteristics, such as socioeconomic diversity. According to cultural mobility theory, diversified socioeconomic composition within schools can simultaneously benefit both advantaged and disadvantaged students’ educational attainment (DiMaggio, 1982 ). Disadvantaged students from low-SES families, who typically have limited cultural capital, benefit more from school resources than their advantaged peers (Andersen & Jæger, 2015 ; Lareau, 2011 ). The presence of significant socioeconomic diversity in schools allows low-SES students, who come from communities with limited exposure to high-status cultural habits, to become more familiar with such school-valued habits and experience academic growth (Jæger & Karlson, 2018 ; Montt, 2016 ). Meanwhile, due to the adequate cultural capital inputs from families, high-SES students’ educational attainments are less vulnerable to the decreasing cultural resources resulting from increased school diversity (Xu & Hampden-Thompson, 2012 ). In light of the cultural mobility theory, promoting socioeconomic integration within schools can be seen as an effective policy measure to mitigate educational inequality, particularly in countries with high Gini coefficients. Empirical studies have yielded inconsistent results regarding the academic consequences of school socioeconomic diversity. The findings of some studies are consistent with the cultural mobility theory. Jæger and Møllegaard ( 2017 ) argued that teachers’ bias generated by socioeconomic variance is not permanent and has a minor impact on students’ educational success. Thus, low-SES students tend to receive more educational returns from studying in high-SES and high socioeconomic diversity schools (Zhang & Hu, 2019 ). Other studies aligning with this argument claimed that the education equity problem is attributed to school socioeconomic segregation, whose negative impact can be mitigated by increasing the diversity of school socioeconomic composition (Langenkamp & Carbonaro, 2018 ; Palardy, 2013 ; Wu & Huang, 2017 ). However, seemingly contradictory findings have been presented, indicating that school socioeconomic diversity consistently predicts negative student performance in Chinese secondary schools (Hu & Wang, 2019 ). Tan ( 2022 ), analysing the data from the China Education Panel Survey, explained this contradiction by highlighting that the positive effect of increasing school socioeconomic diversity is conditional. Specifically, low-SES students who are “overmatched” to top-tier secondary schools may encounter serious adjustment issues, which potentially hinder their educational trajectories. In conclusion, an effective policy aimed at promoting educational equity should narrow the achievement gap without deterring the overall attainment level in an educational system by diminishing the educational achievements of advantaged students (Montt, 2016 ). The precise effect of socioeconomic integration within schools on students from diverse family backgrounds remains indeterminate. The consistency of these impacts across nations with varied income disparities remains unanswered. Current study and hypotheses Using PISA 2015 and 2018 data, the present study explores the impact of within-school socioeconomic diversity on students’ academic performance in countries notable for their income disparities. Our initial hypotheses stem from the premise of the Great Gatsby Curve, which posits that countries with higher economic inequality have lower socioeconomic mobility. Housing policies in numerous market economies facilitate sorting based on the ability to pay, rendering residential preferences vulnerable to family income levels and national income inequalities (Reardon & Bischoff, 2018 ). As a result, in countries with substantial income disparities, high- and low-SES families often remain segregated from the rest, which impedes the diversification of schools’ socioeconomic composition (Dignum et al., 2022 ). Given this, we hypothesise: Hypothesis 1 National school socioeconomic diversity is negatively associated with income inequalities (represented by the Gini index). Our second hypothesis addresses the heterogeneous effects of school socioeconomic diversity on students’ academic performance among countries clustered by a curvilinear relationship indicated between national school diversity and Gini coefficients. The inherent inequality in academic achievement across all educational systems stems from the unequal distribution of educational resources. A large socioeconomic variance within schools implies a broader spectrum of disadvantaged students accessing relatively high-quality educational environments. This situation should improve the overall academic performance in a country (Berkowitz et al., 2017 ). Drawing upon the insights from the Great Gatsby Curve, we can deduce that promoting socioeconomic diversity within schools would be inversely associated with the Gini coefficient. This is because high-quality educational resources become particularly valuable in countries where significant financial and social barriers exist (Mincer, 1984 ; Montt, 2011 ). Integrating both theories, we assume that, due to its scarcity, a diverse student socioeconomic composition may yield larger positive effects in countries with relatively more educational and economic inequality. This leads us to propose our second hypothesis: Hypothesis 2 School socioeconomic diversity is positively associated with students’ performance in reading and mathematics. This effect is more pronounced in countries with greater educational and economic inequality. Finally, we focus on the potential of utilising school socioeconomic integration as a policy tool to narrow the achievement gap. Two competing theories regarding heterogeneity in return to attend integrated schools in different countries exist. According to cultural mobility theory, disadvantaged students should benefit from schooling with more advantaged cohorts (Andersen & Jæger, 2015 ; Jæger & Karlson, 2018 ). Therefore, learning in an integrated school should positively impact students from disadvantaged family backgrounds (Montt, 2016 ), especially in countries characterised by high levels of income inequality. Conversely, the cultural reproduction theory suggests that the educational system is designed to perpetuate social inequality and marginalise disadvantaged students by delivering negative signals in academic competitions (Mckown, 2013 ; Tan, 2022 ). In that case, disadvantaged students hardly obtain extra support from learning in more diversified schools. This relationship should be consistent across countries with varying levels of income inequality. To test both theories, we put forward the fourth hypothesis: Hypothesis 3 Attending an integrated school contributes to narrowing the income-achievement gap in countries with relatively high economic inequality but fails to work effectively as a policy tool to promote education equity among countries with limited income gaps. Data and methods Data The study analysed datasets from the PISA (Programme for International Student Assessment) 2015 and 2018 databases, as well as data from the World Bank. The PISA assessment, which covers 72 countries and regions, gauges the proficiency of 15-year-old students in reading, mathematics, and science literacy. Apart from standardised test results, PISA data provides insights into students’ demographic characteristics, study habits, and the conditions of their school environments. Regarding educational resources and environments, the PISA data also includes school-level variables. Additionally, weights were applied to the data to ensure the sample accurately represents each country’s target population. Moreover, two country-level indices, GDP per capita and the Gini coefficients were retrieved from World Bank datasets and integrated with the PISA data. It is worth noting that the sizes of the analytical samples varied between PISA 2015 and 2018 due to some countries missing one or more of the PISA tests or standardised exams. To deal with the missing values in individual- and school-level variables, we applied the strategy of multiple imputations, then deletion (MID) to minimise potential bias (Von Hippel, 2007 ). We imputed 100 times and then excluded the imputed outcome variables from analytic procedures to promise reliability. The final samples for analysis included 61 countries with a total sample size of 282,289 for PISA 2015. For PISA 2018, the sample included 355,027 students across 69 countries for mathematics achievement analysis and 329,483 students for reading achievement analysis. Measurement Dependent variables We used participants’ mathematics and reading test results to represent academic performance. Science scores were not included because students’ mathematics performance is likely to affect their achievement in science tests (Rivkin & Schiman, 2015 ). PISA designed specific tests each round to enable cross-national comparisons in students’ academic achievement. Instead of examining students’ mastery of the curriculum, PISA tried to test the extent to which students emerging from school are adequately prepared to apply mathematics and reading tools to deal with issues and challenges in modern society. To achieve this purpose, PISA formed tests to measure students’ proficiencies in three subject domains, respectively. Then, item-response theory (IRT) was used to estimate average mathematics and reading literacy scores for each education system. Ten plausible values were generated for each student, representing their true proficiency in mathematics and reading. Independent variables School socioeconomic diversity This study generates a variable indicating school socioeconomic composition by calculating the mean of students’ economic, social, and cultural status (ESCS) per school. The coefficients of students’ ESCS are measured and provided by PISA data. Then, this study calculated the standard deviation of students’ ESCS in each school as the socioeconomic diversity at the school level. Integrated schools Integrated schools refer to schools with an average socioeconomic composition and high diversity of socioeconomic status. Control variables Economic, social, and cultural status (ESCS) PISA 2015 and 2018 provide an index of students’ economic, social, and cultural status, which is a composite measure representing the financial, social, cultural, and human-capital resources available to students (OECD, 2016 ; PISA, 2019 ). Similar to the Trinity Model used to generate family socioeconomic status, the ESCS derived from several variables related to students’ family backgrounds, including parental education levels, occupations, and home possessions, which can be taken as proxies for a family’s material wealth or cultural capital. The top and bottom 25% of the ESCS index are defined as high- and low-SES in this study, respectively. Gini coefficients (World Bank) The Gini index, supplied by the World Bank, evaluates income distribution disparities among individuals or households within an economy. It measures the deviation from perfect equality. An index of 0 symbolises ideal equality, while a score of 100 suggests total inequality. Typically, a Gini index surpassing 50 signifies a high income disparity. GDP per capita (World Bank) GDP per capita is the most commonly used indicator of living standards across countries. It is calculated by dividing the sum of gross value produced within an economy in a given year by midyear population. GDP per capita provides an essential measure of the value of output per person, which is an indirect indicator of per capita income. Although no officially defined standard cut-off values exist, some economists use 25,000 USD as the threshold for developed economies. This study also controlled students’ demographic variables, such as gender and age, in the estimation models. Additionally, extensive covariates are included in the investigation process. Specifically, we isolated the effects of variables related to students’ repetition records in lower secondary schools, the experience of attending a kindergarten, language spoken at home, and parental support at the school level. Moreover, we controlled for school-level variables such as the proportion of certified teachers, school challenges, and availability of teacher support. A detailed description and summary of the variables utilised in the estimation process can be found in Table 1 . Table 1 Definition of Variables and Summary Statistics Variable Definition 2015 2018 School-level variables Mean SD Mean SD School socioeconomic diversity The standard deviation of school ESCS. 0.782 0.181 0.802 0.188 School socioeconomic composition The school-level mean of students’ ESCS. -0.312 0.811 -0.337 0.776 Fully certified teachers Index proportion of all teachers fully certified. 0.807 0.323 0.803 0.333 Challenges in school education Representing problems in school resources and climate. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables. 0.027 1.431 0.031 1.429 Education material shortage It measures the extent to which a school principal believed the lack of educational resources might influence school functioning. 121.3 102.8 232.1 183 Staff shortage It measures the extent to which a school principal believed the lack of stuff influenced might influence school functioning. 100.7 106.3 222 220 Student improper behaviour It measures a school principal’s perception of student behaviours that hindered learning at school. 227.5 171.7 1473 993 Teacher improper behaviour It measures a school principal’s perception of teacher behaviours that hindered learning at school. 229.2 198.9 562 442 Availability of teacher support Representing the availability of teacher support to children. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables. 0.008 1.711 -0.001 1.735 Interest in students’ learning The teacher shows an interest in every student’s learning. 3.096 0.878 3.169 0.944 Extra help The teacher gives extra help when students need it. 3.135 0.855 3.188 0.920 Extra assistance to learning The teacher helps students with their learning. 3.149 0.881 3.278 0.900 Patience of teachers The teacher continues teaching until the students understands. 3.093 0.899 3.156 0.946 Nation-level variables Gini index Collected from the World Bank database. 36.33 7.073 35.130 7.054 GDP per capita Collected from the World Bank database. 26994 23425 25517 21959 Student-level variables ESCS An index of students’ economic, social and cultural status -0.312 1.131 -0.337 1.121 Grade repetition Indicating students’ repetition records in lower secondary schools. 0.124 0.329 0.129 0.335 Parental support at the school level Representing parental supports concerning schooling process. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables. 0.044 1.519 0.006 1.573 Academic support Indicating whether parents are supportive when their children make efforts at school. 3.657 0.25 3.593 0.264 Dealing with difficulties Indicating whether parents provide supports to children when they are facing difficulties at school. 3.665 0.251 3.630 0.266 Parental encouragement Indicating whether parents encourage children to be confident. 3.736 0.23 3.717 0.234 Speak native language at home Indicating whether children speak native language at home. 0.883 0.321 0.850 0.357 Never attend kindergarten Indicating whether children have attended kindergarten before. 0.052 0.222 0.074 0.261 Age Indicating surveyed students’ age. 8.438 3.481 9.454 3.483 Gender Indicating surveyed students’ sex. 0.504 0.5 0.500 0.500 Note: The World Bank does not provide national economic data for each country every year. Thus, we use the index of the adjacent year to substitute the missing values in Gini and GDP per capita. [Table 1 about here] Analytic procedure We mainly conducted three analytic approaches to test the research hypothesis. Hypothesis 1 examined the relationship between national income inequality and school diversity. We calculated each country’s average school socioeconomic variance to obtain an estimated national school diversity. Subsequently, we plotted a curve representing the correlation between the Gini coefficients and national school diversity. This generated curve, intersected by a vertical line at Gini = 50, categorises countries into four districts. Each district represents a distinct combination of school segregation and income inequality degrees. Hypothesis 2 focused on the heterogeneous impact of school socioeconomic diversity on student academic performance across differing districts. The PISA data, being nested within schools and countries, required the estimation of multilevel regressions. We used student and family characteristics, school factors, as well as national economic variables to predict students’ achievement in mathematics and reading. This facilitated the construction of three-level random coefficient models, considering both sampling and replicate weights provided by PISA. Hierarchical Linear Modeling (HLM) proved highly suitable for this context, as the intercept and slope coefficients of students’ ESCS and school socioeconomic variance may vary across countries. To ensure the robustness of our results, we adjusted the model specification, for instance, by integrating additional control variables and modifying weight variables. Our findings remained consistent across these modified models. Hypothesis 3 explores the impact of attending integrated schools on students from high- and low-SES families across country districts. Given that school choice is not randomly assigned among students, it becomes difficult to gauge the unbiased effects of implementing integrated schools to promote educational equity. To tackle this complexity, we adopted the Propensity Score Matching (PSM) technique to formulate counterfactual models, thereby mitigating the selection bias in our estimation process. Our first step involved estimating a logit model using the set of observable variables mentioned above. This enabled us to obtain propensity scores, which are defined as the probability of students being educated at integrated schools. We then applied kernel matching to calculate the average treatment effect of attending integrated schools. To check the covariate balance, we ran t-tests to compare the means of covariates between the treatment and control groups performed pre- and post-matching. Moreover, we used the test for Standardised Bias (SB) to measure the extent of bias reduction. Finally, we conducted a test of Rosenbaum Bounding (RB) to investigate the potential vulnerability of our estimated effect to unobserved covariates, thereby determining the existence of any hidden bias (Li, 2013 ). Results The Gatsby-like relationship between national school diversity and the Gini index Figure 1 plots national school socioeconomic diversity against income inequality. The left-hand panel illustrates a relationship determined by the data collected from PISA 2015. A correlation coefficient of 0.50 (Spearman’s rank is also 0.50) suggests a moderate positive correlation between these two national attributes (Schober et al., 2018 ). The right-hand panel delineates a curvilinear liaison based on PISA 2018 data. In this instance, the correlation coefficient stands at 0.67 (and Spearman’s rank at 0.64), which implies a moderate and positive correlation between school diversity in a nation and its corresponding Gini coefficients. Notably, the results are consistent across the two datasets. [ Fig. 1 about here] The graph features a sloping curve intersecting a vertical line at a Gini of 50, signifying an imbalance in the distribution of national income. This divides the participating countries into four discernible districts. District 1 includes countries experiencing non-severe income disparities, yet displaying a higher-than-expected level of school socioeconomic segregation. District 2 accommodates nations with relative economic equality alongside elevated national school diversity. District 3 encompasses countries with substantial income inequality and high national school diversity. District 4 comprises countries suffering from pronounced income inequalities while demonstrating higher levels of school segregation. The academic impact of school socioeconomic diversity by nation districts Table 2 outlines the disparate impacts of school socioeconomic diversity on mathematics and reading performance according to the PISA 2015 data. The findings reveal that greater school socioeconomic diversity resulted in lower mathematics and reading performance scores among students in Districts 1, 2, and 4. Despite the tenuous correlation with school diversity, the Gini index, indicative of income inequality, displayed a significant and positive association with the academic achievement of students from District 3. Notably, the impact of school socioeconomic diversity was more pronounced in countries with comparatively low levels of school segregation and income inequality. Considering other variables, school socioeconomic composition and family economic, social, and cultural status (ESCS) positively predict students’ academic performance. Table 2 The effects of school socioeconomic diversity and national income inequality on academic performance in PISA 2015 District 1 District 2 District 3 District 4 (1) Mathematics (2) Reading (3) Mathematics (4) Reading (5) Mathematics (6) Reading (7) Mathematics (8) Reading School-level: School socioeconomic diversity -35.73 *** -35.83 *** -24.92 *** -17.51 ** -10.64 -10.06 -21.70 ** -21.03 ** (4.410) (4.711) (5.567) (5.637) (5.433) (5.345) (6.886) (6.861) School socioeconomic composition 46.40 *** 54.27 *** 24.83 *** 31.03 *** 31.77 *** 37.34 *** 33.16 *** 35.43 *** (1.628) (1.747) (1.514) (1.564) (1.439) (1.495) (1.637) (1.707) National level: Gini index -2.125 *** -1.729 *** 5.692 *** 6.171 *** -3.003 *** -1.770 *** -1.708 *** 0.167 (0.174) (0.195) (0.276) (0.266) (0.259) (0.260) (0.331) (0.353) GDP per capita (Thousand dollars) -0.357 *** -0.234 *** 0.618 *** 0.595 *** -0.108 0.088 -1.33 ** -0.697 (0.044) (0.046) (0.047) (0.048) (0.095) (0.098) (0.412) (0.417) Student-level: ESCS 17.12 *** 16.58 *** 12.25 *** 11.84 *** 8.873 *** 8.150 *** 9.001 *** 9.322 *** (0.555) (0.486) (0.422) (0.433) (0.476) (0.626) (0.711) (0.648) Controls √ √ √ √ √ √ √ √ Note: Standard errors are reported in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 [ Table 2 about here] Table 3 presents findings from the PISA 2018 data. While most results align with the 2015 dataset, a striking difference emerges in the context of school socioeconomic diversity. Increased diversity in schools was not associated with a decline in mathematics performance for students from District 2. Additionally, there was a weak but positive relationship between school socioeconomic diversity and academic achievement for students in District 3. Table 3 The effects of school socioeconomic diversity on academic performance in PISA 2018 District 1 District 2 District 3 District 4 (1) Mathematics (2) Reading (3) Mathematics (4) Reading (5) Mathematics (6) Reading (7) Mathematics (8) Reading School-level: School socioeconomic diversity -31.43 *** -35.15 *** -0.015 -15.65 *** 6.751 8.434 -16.20 ** -17.37 ** (4.485) (4.341) (3.804) (4.601) (4.897) (5.264) (5.219) (5.373) School socioeconomic composition 52.43 *** 61.80 *** 52.75 *** 61.70 *** 38.29 *** 45.83 *** 36.11 *** 44.57 *** (1.432) (1.369) (1.161) (1.232) (1.268) (1.302) (1.483) (1.478) National level: Gini index 2.676 *** 2.295 *** 0.788 *** 1.900 *** 0.630 1.191 *** -0.241 3.340 *** (0.157) (0.154) (0.169) (0.190) (0.327) (0.330) (0.250) (0.247) GDP per capita (Thousand dollars) -0.217 *** -0.154 *** 0.141 *** 0.022 1.44 *** 0.986 *** -0.613 1.28 *** (0.041) (0.041 (0.034) (0.035) (0.044) (0.045) (0.338) (0.347) Student-level: ESCS 13.10 *** 12.04 *** 13.90 *** 12.01 *** 8.453 *** 9.412 *** 7.188 *** 6.425 *** (0.507) (0.307) (0.566) (0.381) (0.409) (0.377) (0.670) (0.513) Controls √ √ √ √ √ √ √ √ Note: Standard errors are reported in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 [ Table 3 about here] The effectiveness of using integrated schools to promote education equity Before estimating the treatment effects, we compare the covariate balance before and after matching. A summary of the covariate balance is provided in Appendix 1 and 2. Researchers typically consider a standard bias below 5 or 10% acceptable (Chiteng Kot, 2014 ). In this study, we observed a significant improvement in covariate balance, as none of the estimated models had a standard bias greater than 10%. In fact, 15 out of 16 estimated models had a standard bias of less than 5%. Table 4 presents the estimated average treatment effect on the treated of learning at integrated schools on high- and low-SES students’ mathematics and reading performance across country districts. Additionally, we conducted a sensitivity analysis to test for potential bias resulting from unobservable variables. The sensitivity analysis results are displayed in the last column of each subject panel. Based on our analysis of PISA 2015 data, attending a school with a middle-level socioeconomic composition and high-level socioeconomic diversity was consistently associated with a decrease in mathematics and reading performance for students from high-SES families. However, the sensitivity check results indicate that the treatment effect estimated in District 1 and 2 were relatively robust, which respectively ceased to be significant at \(\:\varGamma\:=1.65\) and \(\:\varGamma\:=1.30\) at the .05 significance level. In contrast, the findings from District 3 and 4 countries were highly vulnerable to hidden bias. Table 4 PSM results of attending integrated schools in different districts Mathematics performance Reading performance District Difference (Treated – Control) S.E. t \(\:\varGamma\:\) bc Difference (Treated – Control) S.E. t \(\:\varGamma\:\) bc PISA 2015 High-SES students 1 -42.594 *** 2.514 -16.945 1.65 -46.646 *** 2.730 -17.086 1.65 2 -26.132 *** 1.837 -14.224 1.30 -28.493 *** 1.934 -14.733 1.30 3 -19.889 *** 3.050 -6.522 1.05 -20.766 *** 3.366 -6.169 1.05 4 -36.615 *** 6.126 -5.977 1.00 -42.438 *** 5.483 -7.740 1.00 Low-SES students 1 -17.651 *** 2.760 -6.395 1.30 -15.194 *** 2.854 -5.323 1.15 2 10.107 *** 1.702 5.939 1.35 14.441 *** 1.718 8.403 1.40 3 34.817 *** 1.911 18.218 1.70 41.997 *** 2.054 20.449 1.80 4 41.230 *** 4.349 9.481 1.65 43.776 *** 4.515 9.695 1.80 PISA 2018 High-SES students 1 -44.754 *** 2.102 -21.288 1.70 -50.403 *** 2.050 -24.590 1.80 2 -32.523 *** 1.679 -19.367 1.35 -47.557 *** 2.011 -23.642 1.60 3 4.585 3.016 1.520 N/A d -0.181 2.918 -0.062 N/A d 4 -54.654 *** 5.547 -9.853 1.65 -66.649 *** 5.824 -11.444 1.85 Low-SES students 1 -1.323 2.287 -0.579 N/A d 2.121 2.029 1.045 N/A d 2 37.162 *** 1.545 24.055 1.75 35.156 *** 1.779 19.758 1.75 3 54.669 *** 2.027 26.964 2.25 63.767 *** 2.114 30.170 2.45 4 37.137 *** 4.176 8.894 1.50 36.776 *** 4.256 8.640 1.35 Note : a * p < 0.05 , ** p < 0.01 , *** p < 0.001; b \(\:\varGamma\:\) is the odds of differential assignment to treatment due to unobserved factors; c the values refer to the threshold that the results would no longer be significant at the 5% significance level; d N/A means the PSM result is insignificant. [ Table 4 about here] For low-SES students, the results suggest a different story. Learning at integrated schools was positively associated with students’ academic performance in Districts 2, 3, and 4. The treatment effects were more pronounced in countries with Gini coefficients larger than 40. The values of \(\:\varGamma\:\) for these estimation models exceeded 1.35, indicating relatively robust results. Notably, low-SES students from countries in District 1 experienced a decrease in achievement compared to their otherwise similar counterparts who did not attend integrated schools. The data from PISA 2018 yielded similar results to those estimated using PISA 2015. However, two noteworthy differences emerged. On the one hand, attending integrated schools no longer negatively predicted high-SES students’ academic achievement in District 3. On the other hand, the treatment effect was not significant for low-SES students from countries in District 1. Discussion The existing literature has not examined the relationship between the socioeconomic diversity of national schools and income inequality. As such, it is still obscure whether a policy tool aiming to increase school diversity narrows students’ performance gap in a specific society. Motivated by making responses to those questions, this study applies the techniques of hierarchical linear modelling and propensity score matching to investigate the academic influencing mechanism behind school socioeconomic diversity. Our empirical analysis of PISA data reveals a Gatsby-like relationship between national school diversity and income inequality. However, this finding contradicts our initial hypothesis, as it demonstrates a positive association between national school diversity and Gini coefficients. This unexpected result may be attributed to the fact that, in meritocratic societies, greater inequality is often accompanied by lower mobility (Durlauf et al., 2022 ). This dynamic motivates parents to invest more in their children’s education to enhance their chances of future upward mobility within the meritocratic educational system. Although family background and high-quality schooling should more closely correlate in economically unequal countries, families often base their investment strategies on the observable links between higher education and upward mobility. In contrast, countries with relatively small or less visible income gaps may reduce family incentives to sacrifice living standards for their children’s access to high-quality schools. Therefore, this leads to a less diversified socioeconomic composition within schools in these countries. The findings partially support our second hypothesis, indicating a negative association between school socioeconomic diversity and academic performance in countries characterised by higher-than-expected national school diversity (countries above the curve illustrated in Fig. 1 ). Higher national school diversity implies a more equitable distribution of educational resources rather than equal opportunities for educational success. Students from socioeconomically disadvantaged backgrounds may face limited access to structured extracurricular activities, which are known to facilitate their understanding of the informal rules within the educational system (Tan et al., 2022 ). The presence of diverse socioeconomic backgrounds in schools can further accentuate disadvantaged students’ unfamiliarity with high-status cultural codes. Consequently, this situation contributes to a downward bias from teachers, potentially diminishing these students’ educational expectations and self-efficacy, which exacerbates their negative schooling experiences (Mckown, 2013 ). Although a few advantaged students may benefit from diversity, overall academic outcomes tend to decrease. It is noteworthy that such a negative impact is mitigated in countries with high income gaps and low national school diversity. A possible explanation is that learning at socioeconomically diversified schools simultaneously benefits and diminishes students’ academic performance. As economic and educational barriers become more impenetrable within a specific society, the scarcity of high-quality schooling resources may counterbalance the negative impact of unintentional cultural bias, thereby affecting students’ chances of success within the educational system. This study offers empirical evidence supporting our third hypothesis, which suggests that the effectiveness of school socioeconomic integration strengthens as the curve depicted in Fig. 1 evolves. Our findings indicate that integrated schools yield negative achievement for advantaged students in countries with relatively low income inequality. Implementing integration policies in such countries may lead to a decline in overall educational outcomes. However, attending integrated schools has a fuzzy negative impact on advantaged students and a solid positive impact on disadvantaged students in countries characterised by high income inequality and low national school diversity. It suggests that integrated schools may contribute to education equity in those countries without undermining advantaged students’ performance. The varied effectiveness of school integration can be attributed to different strategies employed to perpetuate intergenerational persistence in various countries. In societies with low income disparities, advantaged families struggle to monopolise educational resources. Therefore, they resort to utilising the qualitative differences in schooling to maintain children’s future socioeconomic status. Although the concentration of high-SES students does not directly enhance tangible resources in a school, it fosters a supportive school climate that facilitates students’ academic resilience and educational expectations through beneficial student-teacher relationships and emotional support (Agirdag, 2018 ; Berkowitz et al., 2017 ). It is important to note that while overall education equity, represented by high national school diversity, does not guarantee equal learning experiences, it does increase the value of school-level cultural resources for students. In a country characterised by relatively high income and education inequality, advantaged families can perpetuate their privileges through school segregation. It determines that advantaged parents have relatively low incentives to improve students’ academic competence outside the regular school hours. This situation resolves the major challenge of using school integration as an effective policy tool. Parental support may compensate for the academic losses experienced by affluent students who attend less advantaged schools. Surprisingly, school socioeconomic integration academically seemingly benefits all low-SES students, except those from countries with low income and education inequality. This may be attributable to a dearth of incentives to leverage the cultural mobility mechanism. As the narrowed income gap makes inequality more inconspicuous, low-SES students may be less motivated to assimilate unfamiliar cultural codes valued in the society. Three identified limitations within our current analysis invite future research for further clarity. First, our analytic process was not based on an experimental design. Given that students were not randomly assigned to environments with varying degrees of economic or educational inequality, it precludes our ability to analyse causal relationships. Second, there is a potential for omitted variable bias due to data restrictions preventing us from incorporating covariates indicating national education investment and societal recognition of education. These variables could influence parental and student educational expectations and self-efficacy. Third, our analysis fails to account for the varied impacts potentially spawned by the COVID-19 pandemic, which have led to dramatic shifts in education delivery methods and could widen the existing academic gap exacerbated by socioeconomic variance. Despite limitations, our study provides new insight into understanding the curvilinear relationship between national income and education inequality and the effectiveness of employing the school integration policy to further educational equity without negatively impacting overall academic performance. This article’s findings suggest that an effective integration policy is predicated on two conditions. First, visible income disparities need to exist to motivate the cultural mobility mechanism. Second, the unequal distribution of tangible educational resources should create a deficiency of quality schooling opportunities in society. The absence of these conditions may render a simple socioeconomic integration inadequate for success. Facing the challenges arising from diversified school socioeconomic composition, pedagogical and organisational adjustments must be instituted to assist students, particularly those with advantaged backgrounds, to acclimate to the new environment and mitigate potential schooling frustrations. Declarations Funding This study was supported by funding of Shandong Province Excellent Youth Innovation Team Project for Higher Education Institutions from Shandong Provincial Department of Education (2023RW095). Author Contribution Dr. Minda Tan completed the statistical part and wrote the main manuscript.Dr. Li Zhang was responsible for the research design and conceptual framework. Data Availability The data that support the findings of this study are publicly available from the Organisation for Economic Co-operation and Development (OECD) at https://www.oecd.org/pisa/data/.This article does not contain any studies with human participants performed by any of the authors. References Agirdag O (2018) The impact of school SES composition on science achievement and achievement growth: Mediating role of teachers’ teachability culture. Educational Res Evaluation 24(3–5):264–276. https://doi.org/10.1080/13803611.2018.1550838 Andersen IG, Jæger MM (2015) Cultural capital in context: Heterogeneous returns to cultural capital across schooling environments. 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Organizational Res Methods 16(2):188–226. https://doi.org/10.1177/1094428112447816 Lucas SR (2001) Effectively maintained inequality: Education transitions, track mobility, and social background effects. Am J Sociol 10(6):1642–1690. https://doi.org/10.1086/321300 Mckown C (2013) Social equity theory and racial-ethnic achievement gaps. Child Dev 84(4):1120–1136. https://doi.org/10.1111/cdev.12033 Mincer J (1984) Human Capital and Economic Growth. Econ Educ Rev 3(3):199–230. https://doi.org/10.1086/449834 Montt G (2011) Cross-national differences in educational achievement inequality. Sociol Educ 84(1):49–68. https://doi.org/10.1177/0038040710392717 Montt G (2016) Are socioeconomically integrated schools equally effective for advantaged and disadvantaged students? 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Social Stratification: Class, Race, and Gender in Sociological Perspective, 116(4), 1023–1034. https://doi.org/10.4324/9780429494642-123 Rivkin SG, Schiman JC (2015) Instruction time, classroom quality, and academic achievement. Econ J 125(588):F425–F448. https://doi.org/10.1111/ecoj.12315 Schober P, Boer C, Schwarte LA (2018) Correlation Coefficients: Appropriate Use and Interpretation. Anesth Analgesia 126(5):1763–1768. https://doi.org/10.1213/ANE.0000000000002864 Tan M (2022) School socioeconomic desegregation and student academic performance: evidence from a longitudinal study on middle school students in China. Soc Psychol Educ 25(5):1135–1155. https://doi.org/10.1007/s11218-022-09710-w Tan M, Cai L, Bodovski K (2022) An active investment in cultural capital: structured extracurricular activities and educational success in China. J Youth Stud 25(8):1072–1087. https://doi.org/10.1080/13676261.2021.1939284 Von Hippel PT (2007) Regression with missing Ys: An improved strategy for analyzing multiply imputed data. Sociol Methodol 37(1):83–117. https://doi.org/10.1111/j.1467-9531.2007.00180.x Wu Y, Huang C (2017) School socioeconomic segregation and educational expectations of students in China’s junior high schools. Social Sci China 38(3):112. https://doi.org/10.1080/02529203.2017.1339449 Xu J, Hampden-Thompson G (2012) Cultural Reproduction, Cultural Mobility, Cultural Resources, or Trivial Effect ? A Comparative Approach to Cultural Capital and Educational Performance Author (s): Jun Xu and Gillian Hampden-Thompson Published by : The University of Chicago Press on. Comparative Education Review, 56(1), 98–124 Zhang P, Hu Y (2019) What role do schools play to help socioeconomically disadvantaged students succeed against the odds? China Econ Educ Rev 4(2):3–25. https://doi.org/10.19512/j.cnki.issn2096-2088.2019.02.001 Additional Declarations No competing interests reported. Supplementary Files Appendix12.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Feb, 2026 Reviews received at journal 09 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 26 Oct, 2025 Reviewers agreed at journal 26 Oct, 2025 Reviewers invited by journal 21 Aug, 2025 Editor assigned by journal 21 Aug, 2025 Editor invited by journal 21 Aug, 2025 Submission checks completed at journal 20 Aug, 2025 First submitted to journal 20 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7172805","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":506149147,"identity":"2dfd6a9d-a0b9-4faa-a9c7-9dad40e64fcd","order_by":0,"name":"Minda Tan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDACZgYGCTCDvQHKOECcFgMGBp4DxGphgGmRSCBSi24778EbPxj+yJtLPn94u7CNQY7vRgLj5wI8WswO8yVb9jAYGO6cnWNsPbONwVjyRgKz9Ay8WnjMJHgYDBg33M5hk+ZtY0jccCOBjZmHgBbJPwwG9htuHn8G0lJPlBZpoC1AwxnMQFoSDIjQYmwtY2CcvOEM0C885yQMZ5552CyNV8v5M4Y331TI2W44fvzhbZ4yG3m+48kHP+PTAgEGcBYoahgbCGoYBaNgFIyCUYAfAACAR0Qcpu85KgAAAABJRU5ErkJggg==","orcid":"","institution":"Shandong Normal University","correspondingAuthor":true,"prefix":"","firstName":"Minda","middleName":"","lastName":"Tan","suffix":""},{"id":506149148,"identity":"c3424aed-eadf-440b-b122-8fe4264d9d0c","order_by":1,"name":"Li Zhang","email":"","orcid":"","institution":"Central University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-07-21 03:23:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7172805/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7172805/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90192768,"identity":"01c128dc-c26c-47de-80d6-430b6c4dab4c","added_by":"auto","created_at":"2025-08-29 16:12:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":205502,"visible":true,"origin":"","legend":"\u003cp\u003eNational income inequality and school socioeconomic diversity\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7172805/v1/0ec11eb3f47ff67c40578d82.png"},{"id":90194022,"identity":"abcb1335-4686-4102-b348-4e37f9d632bf","added_by":"auto","created_at":"2025-08-29 16:36:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1336527,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7172805/v1/74177991-3be8-44fd-9b5a-976f370cd03b.pdf"},{"id":90192767,"identity":"53a0d7a6-fc72-4827-bf5c-81b2aba836aa","added_by":"auto","created_at":"2025-08-29 16:12:35","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":20329,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix12.docx","url":"https://assets-eu.researchsquare.com/files/rs-7172805/v1/7caea5918996cb2a36bed416.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Cross-national differences in the academic impact of socioeconomically integrated schools: The evidence from the PISA data","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIncome inequality has become a global concern due to its significant implication of reducing equal educational opportunities and resulting in low intergenerational mobility (Jerrim \u0026amp; Macmillan, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Analysing data from Organisation for Economic Co-operation and Development (OECD) economies, Miles Corak (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) found a negative relationship between income inequality and intergenerational mobility, illustrated by the Great Gatsby Curve (GGC). The link between income inequality and limited social mobility is primarily attributed to disadvantaged families\u0026rsquo; reduced capacity to invest in residences located in high-performing school districts. Further, school segregation contributes to refraining social mobility by impeding socioeconomically disadvantaged students\u0026rsquo; access to top-tier universities (Tan, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Nevertheless, according to the human capital theory, high income variance within a society can work as a motivating factor, leading parents to invest more to compete for high-quality school education (Mincer, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). Based on this assumption, countries with significant income disparities tend to show higher school socioeconomic diversity, although its influence on students\u0026rsquo; academic attainments remains unsettled (Park \u0026amp; Weng, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Parker et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite widespread interest in studying the education role of family socioeconomic composition (SEC), relatively few studies examine the academic influence of socioeconomic diversity and its heterogeneity across countries with differing levels of income inequality. Insufficient knowledge has been gathered regarding the efficacy of employing integrated schools to mitigate educational disparities across schools with varied economic inequalities. Therefore, using the Programme for International Student Assessment (PISA) data, this study aims to contribute threefold to the existing literature. First, similar to the GGC, we plot the Gini coefficient (income inequality) against national school socioeconomic variance (a school diversity measure) to categorise countries into specific education and income inequality groups. Second, we investigate school socioeconomic diversity\u0026rsquo;s effect on students\u0026rsquo; academic performance within different nation groups. Third, we analyse the impact of attending integrated schools based on student and national groups.\u003c/p\u003e\n\u003ch3\u003eTheoretical background\u003c/h3\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eThe Great Gatsby Curve and educational attainment\u003c/h2\u003e\u003cp\u003eThe Great Gatsby Curve depicts a positive association between earnings inequality, measured by the Gini coefficients, and intergenerational persistence, measured by the intergenerational elasticity of income (Durlauf et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This curve has attracted significant attention from high-ranking policy-makers and scholars as it challenges the widespread belief that equal opportunity for intergenerational mobility through education can counterbalance the social pressures arising from income inequality in the current generation (Durlauf \u0026amp; Seshadri, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Education is always regarded as a \u0026ldquo;social elevator\u0026rdquo; in intergenerational transmission. Although schooling can be unequal during childhood, educational attainment is essential to the relationship between parental earnings and offspring\u0026rsquo;s income (Jerrim \u0026amp; Macmillan, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The Great Gatsby Curve raises public concerns about whether education provides a placebo rather than a social mobility channel.\u003c/p\u003e\u003cp\u003eThree theories explain the role of education in the GGC, shedding light on the underlying mechanisms that link income inequality and intergenerational persistence. First, the classic model of social reproduction theory argues that social inequality perpetuates intergenerational transmission by transferring economic, cultural, and social capital (Bourdieu, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1986\u003c/span\u003e). As a key component in this process, the educational system unequally assigns academic rewards to students with varied accumulation of different forms of capital (Collins, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Lareau, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). With the income gap growing in a country, affluent parents have a greater capacity to secure educational advantages for their descendants, like school segregation. Such measures utilise education inequalities to enlarge offspring\u0026rsquo;s socioeconomic variance further.\u003c/p\u003e\u003cp\u003eSecond, cultural reproduction theory demonstrates that highly educated parents intentionally and unintentionally cultivate their children\u0026rsquo;s cultural habits, thereby facilitating their adaptation to formal schooling (Bourdieu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Lareau, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). These cultural experiences enable children to become familiar with the dominant cultural code embedded in the educational system, resulting in favourable treatment by teachers (J\u0026aelig;ger \u0026amp; M\u0026oslash;llegaard, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). In unequal countries, advantaged children tend to benefit more from their parents\u0026rsquo; educational experiences. Consequently, they are more likely to attain higher incomes due to their privileged position within the educational system (Jerrim \u0026amp; Macmillan, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThird, effectively maintained inequality (EMI) theory posits that socioeconomically advantaged parents seek out qualitative educational differences to perpetuate intergenerational persistence when schooling resources are no longer scarce (Lucas, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). These parents prefer to invest in residences in more affluent communities, facilitating their children\u0026rsquo;s human capital accumulation. However, this neighbourhood selection mechanism further perpetuates residential and school segregation between wealthy and low-income families, leading to disparate social interactions among children from different family backgrounds and the transmission of socioeconomic privileges across generations (Durlauf et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Durlauf \u0026amp; Seshadri, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). This situation is particularly evident in high-inequality countries with less public investment in education (Jerrim \u0026amp; Macmillan, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo summarise, privileged parents often take advantage of residential segregation to monopolise high-quality school resources. Therefore, this scenario may reduce the opportunities for low-SES students to succeed within the educational system. In contrast, high-SES students reap the benefits of segregation, thus perpetuating their inherited socioeconomic status. The magnitude of segregation is associated with the Gini coefficient, as high-inequality countries usually have more significant economic and social constraints that hinder students\u0026rsquo; access to quality education.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eCultural mobility theory and school socioeconomic diversity\u003c/h3\u003e\n\u003cp\u003eExisting research focusing on the academic impact of school factors suggests that both educational resources within schools, such as class size and teacher quality, and school climates, including a focus on learning and disciplinary policies, are positively associated with students\u0026rsquo; academic achievement (Gustafsson et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Montt, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Rivkin \u0026amp; Schiman, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Tan, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). With governments across countries realising the importance of developing public education, the variance in visible school factors has been narrowed since the 1990s (Baker et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). As a result, scholars have begun investigating the influence of invisible school characteristics, such as socioeconomic diversity.\u003c/p\u003e\u003cp\u003eAccording to cultural mobility theory, diversified socioeconomic composition within schools can simultaneously benefit both advantaged and disadvantaged students\u0026rsquo; educational attainment (DiMaggio, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1982\u003c/span\u003e). Disadvantaged students from low-SES families, who typically have limited cultural capital, benefit more from school resources than their advantaged peers (Andersen \u0026amp; J\u0026aelig;ger, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Lareau, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The presence of significant socioeconomic diversity in schools allows low-SES students, who come from communities with limited exposure to high-status cultural habits, to become more familiar with such school-valued habits and experience academic growth (J\u0026aelig;ger \u0026amp; Karlson, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Montt, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Meanwhile, due to the adequate cultural capital inputs from families, high-SES students\u0026rsquo; educational attainments are less vulnerable to the decreasing cultural resources resulting from increased school diversity (Xu \u0026amp; Hampden-Thompson, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). In light of the cultural mobility theory, promoting socioeconomic integration within schools can be seen as an effective policy measure to mitigate educational inequality, particularly in countries with high Gini coefficients.\u003c/p\u003e\u003cp\u003eEmpirical studies have yielded inconsistent results regarding the academic consequences of school socioeconomic diversity. The findings of some studies are consistent with the cultural mobility theory. J\u0026aelig;ger and M\u0026oslash;llegaard (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) argued that teachers\u0026rsquo; bias generated by socioeconomic variance is not permanent and has a minor impact on students\u0026rsquo; educational success. Thus, low-SES students tend to receive more educational returns from studying in high-SES and high socioeconomic diversity schools (Zhang \u0026amp; Hu, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Other studies aligning with this argument claimed that the education equity problem is attributed to school socioeconomic segregation, whose negative impact can be mitigated by increasing the diversity of school socioeconomic composition (Langenkamp \u0026amp; Carbonaro, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Palardy, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Wu \u0026amp; Huang, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). However, seemingly contradictory findings have been presented, indicating that school socioeconomic diversity consistently predicts negative student performance in Chinese secondary schools (Hu \u0026amp; Wang, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Tan (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), analysing the data from the China Education Panel Survey, explained this contradiction by highlighting that the positive effect of increasing school socioeconomic diversity is conditional. Specifically, low-SES students who are \u0026ldquo;overmatched\u0026rdquo; to top-tier secondary schools may encounter serious adjustment issues, which potentially hinder their educational trajectories.\u003c/p\u003e\u003cp\u003eIn conclusion, an effective policy aimed at promoting educational equity should narrow the achievement gap without deterring the overall attainment level in an educational system by diminishing the educational achievements of advantaged students (Montt, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The precise effect of socioeconomic integration within schools on students from diverse family backgrounds remains indeterminate. The consistency of these impacts across nations with varied income disparities remains unanswered.\u003c/p\u003e\n\u003ch3\u003eCurrent study and hypotheses\u003c/h3\u003e\n\u003cp\u003eUsing PISA 2015 and 2018 data, the present study explores the impact of within-school socioeconomic diversity on students\u0026rsquo; academic performance in countries notable for their income disparities. Our initial hypotheses stem from the premise of the Great Gatsby Curve, which posits that countries with higher economic inequality have lower socioeconomic mobility. Housing policies in numerous market economies facilitate sorting based on the ability to pay, rendering residential preferences vulnerable to family income levels and national income inequalities (Reardon \u0026amp; Bischoff, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). As a result, in countries with substantial income disparities, high- and low-SES families often remain segregated from the rest, which impedes the diversification of schools\u0026rsquo; socioeconomic composition (Dignum et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Given this, we hypothesise:\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 1\u003c/strong\u003e\u003cp\u003eNational school socioeconomic diversity is negatively associated with income inequalities (represented by the Gini index).\u003c/p\u003e\u003c/p\u003e\u003cp\u003eOur second hypothesis addresses the heterogeneous effects of school socioeconomic diversity on students\u0026rsquo; academic performance among countries clustered by a curvilinear relationship indicated between national school diversity and Gini coefficients. The inherent inequality in academic achievement across all educational systems stems from the unequal distribution of educational resources. A large socioeconomic variance within schools implies a broader spectrum of disadvantaged students accessing relatively high-quality educational environments. This situation should improve the overall academic performance in a country (Berkowitz et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Drawing upon the insights from the Great Gatsby Curve, we can deduce that promoting socioeconomic diversity within schools would be inversely associated with the Gini coefficient. This is because high-quality educational resources become particularly valuable in countries where significant financial and social barriers exist (Mincer, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Montt, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Integrating both theories, we assume that, due to its scarcity, a diverse student socioeconomic composition may yield larger positive effects in countries with relatively more educational and economic inequality. This leads us to propose our second hypothesis:\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 2\u003c/strong\u003e\u003cp\u003eSchool socioeconomic diversity is positively associated with students\u0026rsquo; performance in reading and mathematics. This effect is more pronounced in countries with greater educational and economic inequality.\u003c/p\u003e\u003c/p\u003e\u003cp\u003eFinally, we focus on the potential of utilising school socioeconomic integration as a policy tool to narrow the achievement gap. Two competing theories regarding heterogeneity in return to attend integrated schools in different countries exist. According to cultural mobility theory, disadvantaged students should benefit from schooling with more advantaged cohorts (Andersen \u0026amp; J\u0026aelig;ger, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; J\u0026aelig;ger \u0026amp; Karlson, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Therefore, learning in an integrated school should positively impact students from disadvantaged family backgrounds (Montt, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), especially in countries characterised by high levels of income inequality. Conversely, the cultural reproduction theory suggests that the educational system is designed to perpetuate social inequality and marginalise disadvantaged students by delivering negative signals in academic competitions (Mckown, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Tan, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). In that case, disadvantaged students hardly obtain extra support from learning in more diversified schools. This relationship should be consistent across countries with varying levels of income inequality. To test both theories, we put forward the fourth hypothesis:\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 3\u003c/strong\u003e\u003cp\u003eAttending an integrated school contributes to narrowing the income-achievement gap in countries with relatively high economic inequality but fails to work effectively as a policy tool to promote education equity among countries with limited income gaps.\u003c/p\u003e\u003c/p\u003e"},{"header":"Data and methods","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eData\u003c/h2\u003e\u003cp\u003eThe study analysed datasets from the PISA (Programme for International Student Assessment) 2015 and 2018 databases, as well as data from the World Bank. The PISA assessment, which covers 72 countries and regions, gauges the proficiency of 15-year-old students in reading, mathematics, and science literacy. Apart from standardised test results, PISA data provides insights into students\u0026rsquo; demographic characteristics, study habits, and the conditions of their school environments. Regarding educational resources and environments, the PISA data also includes school-level variables. Additionally, weights were applied to the data to ensure the sample accurately represents each country\u0026rsquo;s target population. Moreover, two country-level indices, GDP per capita and the Gini coefficients were retrieved from World Bank datasets and integrated with the PISA data.\u003c/p\u003e\u003cp\u003eIt is worth noting that the sizes of the analytical samples varied between PISA 2015 and 2018 due to some countries missing one or more of the PISA tests or standardised exams. To deal with the missing values in individual- and school-level variables, we applied the strategy of multiple imputations, then deletion (MID) to minimise potential bias (Von Hippel, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). We imputed 100 times and then excluded the imputed outcome variables from analytic procedures to promise reliability. The final samples for analysis included 61 countries with a total sample size of 282,289 for PISA 2015. For PISA 2018, the sample included 355,027 students across 69 countries for mathematics achievement analysis and 329,483 students for reading achievement analysis.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eMeasurement\u003c/h2\u003e\u003cp\u003eDependent variables\u003c/p\u003e\u003cp\u003eWe used participants\u0026rsquo; mathematics and reading test results to represent academic performance. Science scores were not included because students\u0026rsquo; mathematics performance is likely to affect their achievement in science tests (Rivkin \u0026amp; Schiman, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). PISA designed specific tests each round to enable cross-national comparisons in students\u0026rsquo; academic achievement. Instead of examining students\u0026rsquo; mastery of the curriculum, PISA tried to test the extent to which students emerging from school are adequately prepared to apply mathematics and reading tools to deal with issues and challenges in modern society. To achieve this purpose, PISA formed tests to measure students\u0026rsquo; proficiencies in three subject domains, respectively. Then, item-response theory (IRT) was used to estimate average mathematics and reading literacy scores for each education system. Ten plausible values were generated for each student, representing their true proficiency in mathematics and reading.\u003c/p\u003e\u003cp\u003eIndependent variables\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eSchool socioeconomic diversity\u003c/strong\u003e\u003cp\u003eThis study generates a variable indicating school socioeconomic composition by calculating the mean of students\u0026rsquo; economic, social, and cultural status (ESCS) per school. The coefficients of students\u0026rsquo; ESCS are measured and provided by PISA data. Then, this study calculated the standard deviation of students\u0026rsquo; ESCS in each school as the socioeconomic diversity at the school level.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eIntegrated schools\u003c/strong\u003e\u003cp\u003eIntegrated schools refer to schools with an average socioeconomic composition and high diversity of socioeconomic status.\u003c/p\u003e\u003c/p\u003e\u003cp\u003eControl variables\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eEconomic, social, and cultural status (ESCS)\u003c/strong\u003e\u003cp\u003ePISA 2015 and 2018 provide an index of students\u0026rsquo; economic, social, and cultural status, which is a composite measure representing the financial, social, cultural, and human-capital resources available to students (OECD, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; PISA, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Similar to the Trinity Model used to generate family socioeconomic status, the ESCS derived from several variables related to students\u0026rsquo; family backgrounds, including parental education levels, occupations, and home possessions, which can be taken as proxies for a family\u0026rsquo;s material wealth or cultural capital. The top and bottom 25% of the ESCS index are defined as high- and low-SES in this study, respectively.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eGini coefficients (World Bank)\u003c/strong\u003e\u003cp\u003eThe Gini index, supplied by the World Bank, evaluates income distribution disparities among individuals or households within an economy. It measures the deviation from perfect equality. An index of 0 symbolises ideal equality, while a score of 100 suggests total inequality. Typically, a Gini index surpassing 50 signifies a high income disparity.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eGDP per capita (World Bank)\u003c/strong\u003e\u003cp\u003eGDP per capita is the most commonly used indicator of living standards across countries. It is calculated by dividing the sum of gross value produced within an economy in a given year by midyear population. GDP per capita provides an essential measure of the value of output per person, which is an indirect indicator of per capita income. Although no officially defined standard cut-off values exist, some economists use 25,000 USD as the threshold for developed economies.\u003c/p\u003e\u003c/p\u003e\u003cp\u003eThis study also controlled students\u0026rsquo; demographic variables, such as gender and age, in the estimation models. Additionally, extensive covariates are included in the investigation process. Specifically, we isolated the effects of variables related to students\u0026rsquo; repetition records in lower secondary schools, the experience of attending a kindergarten, language spoken at home, and parental support at the school level. Moreover, we controlled for school-level variables such as the proportion of certified teachers, school challenges, and availability of teacher support. A detailed description and summary of the variables utilised in the estimation process can be found in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDefinition of Variables and Summary Statistics\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDefinition\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e2015\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e2018\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool-level variables\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eSD\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic diversity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe standard deviation of school ESCS.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.782\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.181\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.802\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.188\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic composition\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe school-level mean of students\u0026rsquo; ESCS.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.312\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.811\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-0.337\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.776\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFully certified teachers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndex proportion of all teachers fully certified.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.807\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.803\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.333\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eChallenges in school education\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRepresenting problems in school resources and climate. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.431\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.031\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.429\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEducation material shortage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIt measures the extent to which a school principal believed the lack of educational resources might influence school functioning.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e121.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e102.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e232.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e183\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStaff shortage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIt measures the extent to which a school principal believed the lack of stuff influenced might influence school functioning.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e100.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e106.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e222\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e220\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStudent improper behaviour\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIt measures a school principal\u0026rsquo;s perception of student behaviours that hindered learning at school.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e227.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e171.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1473\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e993\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTeacher improper behaviour\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIt measures a school principal\u0026rsquo;s perception of teacher behaviours that hindered learning at school.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e229.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e198.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e562\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e442\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAvailability of teacher support\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRepresenting the availability of teacher support to children. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.008\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.711\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-0.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.735\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInterest in students\u0026rsquo; learning\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe teacher shows an interest in every student\u0026rsquo;s learning.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.096\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.878\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.169\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.944\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExtra help\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe teacher gives extra help when students need it.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.135\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.855\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.188\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.920\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExtra assistance to learning\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe teacher helps students with their learning.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.149\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.881\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.278\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.900\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePatience of teachers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe teacher continues teaching until the students understands.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.093\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.899\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.156\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.946\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNation-level variables\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGini index\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCollected from the World Bank database.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e36.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e7.073\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e35.130\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e7.054\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGDP per capita\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCollected from the World Bank database.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e26994\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e23425\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e25517\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e21959\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStudent-level variables\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eESCS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAn index of students\u0026rsquo; economic, social and cultural status\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.312\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.131\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-0.337\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.121\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGrade repetition\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating students\u0026rsquo; repetition records in lower secondary schools.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.124\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.329\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.129\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.335\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParental support at the school level\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRepresenting parental supports concerning schooling process. This variable is generated by the application of the principal component analysis (PCA) on the correlation matrix using the following variables.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.044\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.519\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.006\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.573\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAcademic support\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating whether parents are supportive when their children make efforts at school.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.657\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.593\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.264\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDealing with difficulties\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating whether parents provide supports to children when they are facing difficulties at school.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.665\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.251\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.630\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.266\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParental encouragement\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating whether parents encourage children to be confident.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.736\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.717\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.234\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpeak native language at home\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating whether children speak native language at home.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.883\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.321\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.850\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.357\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNever attend kindergarten\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating whether children have attended kindergarten before.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.052\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.222\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.074\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.261\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating surveyed students\u0026rsquo; age.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.438\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.481\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e9.454\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3.483\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGender\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicating surveyed students\u0026rsquo; sex.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.504\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003e\u003cem\u003eNote: The World Bank does not provide national economic data for each country every year. Thus, we use the index of the adjacent year to substitute the missing values in Gini and GDP per capita.\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e[Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eAnalytic procedure\u003c/h3\u003e\n\u003cp\u003eWe mainly conducted three analytic approaches to test the research hypothesis. Hypothesis \u003cspan refid=\"FPar1\" class=\"InternalRef\"\u003e1\u003c/span\u003e examined the relationship between national income inequality and school diversity. We calculated each country\u0026rsquo;s average school socioeconomic variance to obtain an estimated national school diversity. Subsequently, we plotted a curve representing the correlation between the Gini coefficients and national school diversity. This generated curve, intersected by a vertical line at Gini\u0026thinsp;=\u0026thinsp;50, categorises countries into four districts. Each district represents a distinct combination of school segregation and income inequality degrees.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 2\u003c/strong\u003e\u003cp\u003efocused on the heterogeneous impact of school socioeconomic diversity on student academic performance across differing districts. The PISA data, being nested within schools and countries, required the estimation of multilevel regressions. We used student and family characteristics, school factors, as well as national economic variables to predict students\u0026rsquo; achievement in mathematics and reading. This facilitated the construction of three-level random coefficient models, considering both sampling and replicate weights provided by PISA. Hierarchical Linear Modeling (HLM) proved highly suitable for this context, as the intercept and slope coefficients of students\u0026rsquo; ESCS and school socioeconomic variance may vary across countries. To ensure the robustness of our results, we adjusted the model specification, for instance, by integrating additional control variables and modifying weight variables. Our findings remained consistent across these modified models.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 3\u003c/strong\u003e\u003cp\u003eexplores the impact of attending integrated schools on students from high- and low-SES families across country districts. Given that school choice is not randomly assigned among students, it becomes difficult to gauge the unbiased effects of implementing integrated schools to promote educational equity. To tackle this complexity, we adopted the Propensity Score Matching (PSM) technique to formulate counterfactual models, thereby mitigating the selection bias in our estimation process. Our first step involved estimating a logit model using the set of observable variables mentioned above. This enabled us to obtain propensity scores, which are defined as the probability of students being educated at integrated schools. We then applied kernel matching to calculate the average treatment effect of attending integrated schools. To check the covariate balance, we ran t-tests to compare the means of covariates between the treatment and control groups performed pre- and post-matching. Moreover, we used the test for Standardised Bias (SB) to measure the extent of bias reduction. Finally, we conducted a test of Rosenbaum Bounding (RB) to investigate the potential vulnerability of our estimated effect to unobserved covariates, thereby determining the existence of any hidden bias (Li, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eThe Gatsby-like relationship between national school diversity and the Gini index\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e plots national school socioeconomic diversity against income inequality. The left-hand panel illustrates a relationship determined by the data collected from PISA 2015. A correlation coefficient of 0.50 (Spearman\u0026rsquo;s rank is also 0.50) suggests a moderate positive correlation between these two national attributes (Schober et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The right-hand panel delineates a curvilinear liaison based on PISA 2018 data. In this instance, the correlation coefficient stands at 0.67 (and Spearman\u0026rsquo;s rank at 0.64), which implies a moderate and positive correlation between school diversity in a nation and its corresponding Gini coefficients. Notably, the results are consistent across the two datasets.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e[ Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eThe graph features a sloping curve intersecting a vertical line at a Gini of 50, signifying an imbalance in the distribution of national income. This divides the participating countries into four discernible districts. District 1 includes countries experiencing non-severe income disparities, yet displaying a higher-than-expected level of school socioeconomic segregation. District 2 accommodates nations with relative economic equality alongside elevated national school diversity. District 3 encompasses countries with substantial income inequality and high national school diversity. District 4 comprises countries suffering from pronounced income inequalities while demonstrating higher levels of school segregation.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eThe academic impact of school socioeconomic diversity by nation districts\u003c/h2\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e outlines the disparate impacts of school socioeconomic diversity on mathematics and reading performance according to the PISA 2015 data. The findings reveal that greater school socioeconomic diversity resulted in lower mathematics and reading performance scores among students in Districts 1, 2, and 4. Despite the tenuous correlation with school diversity, the Gini index, indicative of income inequality, displayed a significant and positive association with the academic achievement of students from District 3. Notably, the impact of school socioeconomic diversity was more pronounced in countries with comparatively low levels of school segregation and income inequality. Considering other variables, school socioeconomic composition and family economic, social, and cultural status (ESCS) positively predict students\u0026rsquo; academic performance.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe effects of school socioeconomic diversity and national income inequality on academic performance in PISA 2015\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eDistrict 1\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eDistrict 2\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003eDistrict 3\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u003cp\u003eDistrict 4\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(1) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(2) Reading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(3) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(4)\u003c/p\u003e\u003cp\u003eReading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(5) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(6) Reading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(7) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(8) Reading\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool-level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic diversity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-35.73\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-35.83\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-24.92\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-17.51\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-10.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-10.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-21.70\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-21.03\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(4.410)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(4.711)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(5.567)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(5.637)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(5.433)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(5.345)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(6.886)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(6.861)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic composition\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e46.40\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e54.27\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e24.83\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e31.03\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e31.77\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e37.34\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e33.16\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e35.43\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(1.628)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(1.747)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(1.514)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(1.564)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(1.439)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(1.495)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(1.637)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(1.707)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNational level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGini index\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-2.125\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-1.729\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5.692\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.171\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-3.003\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-1.770\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-1.708\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.167\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.174)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.195)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.276)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.266)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.259)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.260)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.331)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.353)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGDP per capita (Thousand dollars)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.357\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.234\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.618\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.595\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.108\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.088\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-1.33\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-0.697\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.044)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.046)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.047)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.048)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.095)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.098)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.412)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.417)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStudent-level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eESCS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e17.12\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e16.58\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e12.25\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e11.84\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e8.873\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e8.150\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e9.001\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e9.322\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.555)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.486)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.422)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.433)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.476)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.626)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.711)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.648)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eControls\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e\u003cp\u003e\u003cem\u003eNote: Standard errors are reported in parentheses\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003csup\u003e*\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05, \u003csup\u003e**\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01, \u003csup\u003e***\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e[ Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents findings from the PISA 2018 data. While most results align with the 2015 dataset, a striking difference emerges in the context of school socioeconomic diversity. Increased diversity in schools was not associated with a decline in mathematics performance for students from District 2. Additionally, there was a weak but positive relationship between school socioeconomic diversity and academic achievement for students in District 3.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe effects of school socioeconomic diversity on academic performance in PISA 2018\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eDistrict 1\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eDistrict 2\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003eDistrict 3\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u003cp\u003eDistrict 4\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(1) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(2) Reading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(3) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(4) Reading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(5) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(6) Reading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(7) Mathematics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(8) Reading\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool-level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic diversity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-31.43\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-35.15\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.015\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-15.65\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6.751\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e8.434\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-16.20\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-17.37\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(4.485)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(4.341)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(3.804)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(4.601)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(4.897)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(5.264)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(5.219)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(5.373)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSchool socioeconomic composition\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e52.43\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e61.80\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e52.75\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e61.70\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e38.29\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e45.83\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e36.11\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e44.57\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(1.432)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(1.369)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(1.161)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(1.232)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(1.268)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(1.302)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(1.483)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(1.478)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNational level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGini index\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.676\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.295\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.788\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.900\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.630\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.191\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-0.241\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e3.340\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.157)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.154)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.169)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.190)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.327)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.330)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.250)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.247)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGDP per capita (Thousand dollars)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.217\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.154\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.141\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.022\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.44\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.986\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-0.613\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.28\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.041)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.041\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.034)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.035)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.044)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.045)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.338)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.347)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStudent-level:\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eESCS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e13.10\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e12.04\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e13.90\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e12.01\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e8.453\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e9.412\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e7.188\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e6.425\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(0.507)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(0.307)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(0.566)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(0.381)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(0.409)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(0.377)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(0.670)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(0.513)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eControls\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u0026radic;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e\u003cp\u003e\u003cem\u003eNote: Standard errors are reported in parentheses\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003csup\u003e*\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05, \u003csup\u003e**\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01, \u003csup\u003e***\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e[ Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e about here]\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eThe effectiveness of using integrated schools to promote education equity\u003c/h2\u003e\u003cp\u003eBefore estimating the treatment effects, we compare the covariate balance before and after matching. A summary of the covariate balance is provided in Appendix 1 and 2. Researchers typically consider a standard bias below 5 or 10% acceptable (Chiteng Kot, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). In this study, we observed a significant improvement in covariate balance, as none of the estimated models had a standard bias greater than 10%. In fact, 15 out of 16 estimated models had a standard bias of less than 5%.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the estimated average treatment effect on the treated of learning at integrated schools on high- and low-SES students\u0026rsquo; mathematics and reading performance across country districts. Additionally, we conducted a sensitivity analysis to test for potential bias resulting from unobservable variables. The sensitivity analysis results are displayed in the last column of each subject panel. Based on our analysis of PISA 2015 data, attending a school with a middle-level socioeconomic composition and high-level socioeconomic diversity was consistently associated with a decrease in mathematics and reading performance for students from high-SES families. However, the sensitivity check results indicate that the treatment effect estimated in District 1 and 2 were relatively robust, which respectively ceased to be significant at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:=1.65\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:=1.30\\)\u003c/span\u003e\u003c/span\u003e at the .05 significance level. In contrast, the findings from District 3 and 4 countries were highly vulnerable to hidden bias.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePSM results of attending integrated schools in different districts\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003eMathematics performance\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003eReading performance\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDistrict\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDifference\u003c/p\u003e\u003cp\u003e(Treated \u0026ndash; Control)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eS.E.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003et\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003ebc\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eDifference\u003c/p\u003e\u003cp\u003e(Treated \u0026ndash; Control)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eS.E.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003et\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003ebc\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003ePISA 2015\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eHigh-SES students\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-42.594\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.514\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-16.945\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-46.646\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.730\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-17.086\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.65\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-26.132\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.837\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-14.224\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-28.493\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.934\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-14.733\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-19.889\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.050\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-6.522\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-20.766\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e3.366\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-6.169\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-36.615\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e6.126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-5.977\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-42.438\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.483\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-7.740\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eLow-SES students\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-17.651\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.760\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-6.395\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-15.194\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.854\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-5.323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e10.107\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.702\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.939\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e14.441\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.718\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e8.403\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.40\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e34.817\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.911\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e18.218\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e41.997\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.054\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e20.449\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e41.230\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.349\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e9.481\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e43.776\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4.515\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e9.695\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003ePISA 2018\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eHigh-SES students\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-44.754\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.102\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-21.288\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-50.403\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.050\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-24.590\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-32.523\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.679\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-19.367\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-47.557\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.011\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-23.642\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4.585\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.520\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eN/A\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-0.181\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.918\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-0.062\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003eN/A\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-54.654\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5.547\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-9.853\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-66.649\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.824\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-11.444\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.85\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eLow-SES students\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-1.323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.287\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-0.579\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eN/A\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.121\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.029\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003eN/A\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e37.162\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.545\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24.055\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e35.156\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.779\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e19.758\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.75\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e54.669\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e26.964\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e63.767\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.114\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e30.170\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e2.45\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e37.137\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.176\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8.894\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e36.776\u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4.256\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e8.640\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003e\u003cem\u003eNote\u003c/em\u003e: \u003csup\u003e\u003cem\u003ea\u003c/em\u003e \u003cem\u003e*\u003c/em\u003e\u003c/sup\u003e \u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.05\u003c/em\u003e, \u003csup\u003e\u003cem\u003e**\u003c/em\u003e\u003c/sup\u003e \u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/em\u003e, \u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e \u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001;\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003csup\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eis the odds of differential assignment to treatment due to unobserved factors;\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003csup\u003ec\u003c/sup\u003e\u003cem\u003ethe values refer to the threshold that the results would no longer be significant at the 5% significance level;\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003csup\u003ed\u003c/sup\u003e\u003cem\u003eN/A means the PSM result is insignificant.\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e[ Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e about here]\u003c/p\u003e\u003cp\u003eFor low-SES students, the results suggest a different story. Learning at integrated schools was positively associated with students\u0026rsquo; academic performance in Districts 2, 3, and 4. The treatment effects were more pronounced in countries with Gini coefficients larger than 40. The values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varGamma\\:\\)\u003c/span\u003e\u003c/span\u003e for these estimation models exceeded 1.35, indicating relatively robust results. Notably, low-SES students from countries in District 1 experienced a decrease in achievement compared to their otherwise similar counterparts who did not attend integrated schools.\u003c/p\u003e\u003cp\u003eThe data from PISA 2018 yielded similar results to those estimated using PISA 2015. However, two noteworthy differences emerged. On the one hand, attending integrated schools no longer negatively predicted high-SES students\u0026rsquo; academic achievement in District 3. On the other hand, the treatment effect was not significant for low-SES students from countries in District 1.\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe existing literature has not examined the relationship between the socioeconomic diversity of national schools and income inequality. As such, it is still obscure whether a policy tool aiming to increase school diversity narrows students\u0026rsquo; performance gap in a specific society. Motivated by making responses to those questions, this study applies the techniques of hierarchical linear modelling and propensity score matching to investigate the academic influencing mechanism behind school socioeconomic diversity.\u003c/p\u003e\u003cp\u003eOur empirical analysis of PISA data reveals a Gatsby-like relationship between national school diversity and income inequality. However, this finding contradicts our initial hypothesis, as it demonstrates a positive association between national school diversity and Gini coefficients. This unexpected result may be attributed to the fact that, in meritocratic societies, greater inequality is often accompanied by lower mobility (Durlauf et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This dynamic motivates parents to invest more in their children\u0026rsquo;s education to enhance their chances of future upward mobility within the meritocratic educational system. Although family background and high-quality schooling should more closely correlate in economically unequal countries, families often base their investment strategies on the observable links between higher education and upward mobility. In contrast, countries with relatively small or less visible income gaps may reduce family incentives to sacrifice living standards for their children\u0026rsquo;s access to high-quality schools. Therefore, this leads to a less diversified socioeconomic composition within schools in these countries.\u003c/p\u003e\u003cp\u003eThe findings partially support our second hypothesis, indicating a negative association between school socioeconomic diversity and academic performance in countries characterised by higher-than-expected national school diversity (countries above the curve illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Higher national school diversity implies a more equitable distribution of educational resources rather than equal opportunities for educational success. Students from socioeconomically disadvantaged backgrounds may face limited access to structured extracurricular activities, which are known to facilitate their understanding of the informal rules within the educational system (Tan et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The presence of diverse socioeconomic backgrounds in schools can further accentuate disadvantaged students\u0026rsquo; unfamiliarity with high-status cultural codes.\u003c/p\u003e\u003cp\u003eConsequently, this situation contributes to a downward bias from teachers, potentially diminishing these students\u0026rsquo; educational expectations and self-efficacy, which exacerbates their negative schooling experiences (Mckown, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Although a few advantaged students may benefit from diversity, overall academic outcomes tend to decrease. It is noteworthy that such a negative impact is mitigated in countries with high income gaps and low national school diversity. A possible explanation is that learning at socioeconomically diversified schools simultaneously benefits and diminishes students\u0026rsquo; academic performance. As economic and educational barriers become more impenetrable within a specific society, the scarcity of high-quality schooling resources may counterbalance the negative impact of unintentional cultural bias, thereby affecting students\u0026rsquo; chances of success within the educational system.\u003c/p\u003e\u003cp\u003eThis study offers empirical evidence supporting our third hypothesis, which suggests that the effectiveness of school socioeconomic integration strengthens as the curve depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e evolves. Our findings indicate that integrated schools yield negative achievement for advantaged students in countries with relatively low income inequality. Implementing integration policies in such countries may lead to a decline in overall educational outcomes. However, attending integrated schools has a fuzzy negative impact on advantaged students and a solid positive impact on disadvantaged students in countries characterised by high income inequality and low national school diversity. It suggests that integrated schools may contribute to education equity in those countries without undermining advantaged students\u0026rsquo; performance.\u003c/p\u003e\u003cp\u003eThe varied effectiveness of school integration can be attributed to different strategies employed to perpetuate intergenerational persistence in various countries. In societies with low income disparities, advantaged families struggle to monopolise educational resources. Therefore, they resort to utilising the qualitative differences in schooling to maintain children\u0026rsquo;s future socioeconomic status. Although the concentration of high-SES students does not directly enhance tangible resources in a school, it fosters a supportive school climate that facilitates students\u0026rsquo; academic resilience and educational expectations through beneficial student-teacher relationships and emotional support (Agirdag, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Berkowitz et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). It is important to note that while overall education equity, represented by high national school diversity, does not guarantee equal learning experiences, it does increase the value of school-level cultural resources for students.\u003c/p\u003e\u003cp\u003eIn a country characterised by relatively high income and education inequality, advantaged families can perpetuate their privileges through school segregation. It determines that advantaged parents have relatively low incentives to improve students\u0026rsquo; academic competence outside the regular school hours. This situation resolves the major challenge of using school integration as an effective policy tool. Parental support may compensate for the academic losses experienced by affluent students who attend less advantaged schools.\u003c/p\u003e\u003cp\u003eSurprisingly, school socioeconomic integration academically seemingly benefits all low-SES students, except those from countries with low income and education inequality. This may be attributable to a dearth of incentives to leverage the cultural mobility mechanism. As the narrowed income gap makes inequality more inconspicuous, low-SES students may be less motivated to assimilate unfamiliar cultural codes valued in the society.\u003c/p\u003e\u003cp\u003eThree identified limitations within our current analysis invite future research for further clarity. First, our analytic process was not based on an experimental design. Given that students were not randomly assigned to environments with varying degrees of economic or educational inequality, it precludes our ability to analyse causal relationships. Second, there is a potential for omitted variable bias due to data restrictions preventing us from incorporating covariates indicating national education investment and societal recognition of education. These variables could influence parental and student educational expectations and self-efficacy. Third, our analysis fails to account for the varied impacts potentially spawned by the COVID-19 pandemic, which have led to dramatic shifts in education delivery methods and could widen the existing academic gap exacerbated by socioeconomic variance.\u003c/p\u003e\u003cp\u003eDespite limitations, our study provides new insight into understanding the curvilinear relationship between national income and education inequality and the effectiveness of employing the school integration policy to further educational equity without negatively impacting overall academic performance. This article\u0026rsquo;s findings suggest that an effective integration policy is predicated on two conditions. First, visible income disparities need to exist to motivate the cultural mobility mechanism. Second, the unequal distribution of tangible educational resources should create a deficiency of quality schooling opportunities in society. The absence of these conditions may render a simple socioeconomic integration inadequate for success. Facing the challenges arising from diversified school socioeconomic composition, pedagogical and organisational adjustments must be instituted to assist students, particularly those with advantaged backgrounds, to acclimate to the new environment and mitigate potential schooling frustrations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis study was supported by funding of Shandong Province Excellent Youth Innovation Team Project for Higher Education Institutions from Shandong Provincial Department of Education (2023RW095).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eDr. Minda Tan completed the statistical part and wrote the main manuscript.Dr. Li Zhang was responsible for the research design and conceptual framework.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that support the findings of this study are publicly available from the Organisation for Economic Co-operation and Development (OECD) at https://www.oecd.org/pisa/data/.This article does not contain any studies with human participants performed by any of the authors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAgirdag O (2018) The impact of school SES composition on science achievement and achievement growth: Mediating role of teachers\u0026rsquo; teachability culture. 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A Comparative Approach to Cultural Capital and Educational Performance Author (s): Jun Xu and Gillian Hampden-Thompson Published by : The University of Chicago Press on. Comparative Education Review, 56(1), 98\u0026ndash;124\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang P, Hu Y (2019) What role do schools play to help socioeconomically disadvantaged students succeed against the odds? China Econ Educ Rev 4(2):3\u0026ndash;25. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.19512/j.cnki.issn2096-2088.2019.02.001\u003c/span\u003e\u003cspan address=\"10.19512/j.cnki.issn2096-2088.2019.02.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"School socioeconomic diversity, National income inequality, Integrated schools, Education equity, Academic performance","lastPublishedDoi":"10.21203/rs.3.rs-7172805/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7172805/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe link between national income inequality and school socioeconomic diversity complicates the effectiveness of using school integration as a policy tool to promote education equity without harming overall educational outcomes. Using hierarchical linear modelling and propensity score matching, this study investigated PISA 2015 and 2018 data. Three main findings include: (1) a Gatsby-like curve is observed that indicates a positive association between national school diversity and Gini coefficients; (2) school socioeconomic diversity harms the academic performance of students in countries above the estimated curve; (3)the effectiveness of school socioeconomic integration strengthens as the estimated curve evolves. These findings suggest that the effectiveness of integration policy depends on visible income disparities and unequally distributed tangible educational resources in society. The absence of these conditions may render a simple socioeconomic integration inadequate for success.\u003c/p\u003e","manuscriptTitle":"Cross-national differences in the academic impact of socioeconomically integrated schools: The evidence from the PISA data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-29 16:12:31","doi":"10.21203/rs.3.rs-7172805/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-16T13:25:10+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-09T06:21:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-07T14:21:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"151218386014472185682978894483175255948","date":"2025-10-27T03:41:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"24472960169603378538597599271188928605","date":"2025-10-26T15:45:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-21T16:01:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-21T15:59:55+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-08-21T07:25:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-20T12:51:20+00:00","index":"","fulltext":""},{"type":"submitted","content":"Humanities and Social Sciences Communications","date":"2025-08-20T12:38:06+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"39fa2c38-ecb4-4bb8-80fe-c49a0a148955","owner":[],"postedDate":"August 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":53761520,"name":"Social science/Development studies"},{"id":53761521,"name":"Business and commerce/Economics"},{"id":53761522,"name":"Social science/Economics"},{"id":53761523,"name":"Social science/Education"}],"tags":[],"updatedAt":"2026-03-04T15:08:06+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-29 16:12:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7172805","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7172805","identity":"rs-7172805","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}