SummaryThe most widely used measure of segregation is the so‐called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce adjustments to the index, based on an underlying statistical model. We specify the assignment problem in a very general way, with differences in conditional assignment probabilities underlying the resulting segregation. From this, we derive a likelihood ratio test for the presence of any systematic segregation, and bias adjustments to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that the use of bootstrap methods can improve the size and power properties of test procedures considerably. We illustrate these methods by comparing dissimilarity indices across school districts in England to measure social segregation.

On average, students attending selective schools outperform their non-selective counterparts in national exams. These differences are often attributed to value added by the school, as well as factors schools use to select pupils, including ability, achievement and, in cases where schools charge tuition fees or are located in affluent areas, socioeconomic status. However, the possible role of DNA differences between students of different schools types has not yet been considered. We used a UK-representative sample of 4814 genotyped students to investigate exam performance at age 16 and genetic differences between students in three school types: state-funded, non-selective schools (‘non-selective’), state-funded, selective schools (‘grammar’) and private schools, which are selective (‘private’). We created a genome-wide polygenic score (GPS) derived from a genome-wide association study of years of education (EduYears). We found substantial mean genetic differences between students of different school types: students in non-selective schools had lower EduYears GPS compared to those in grammar (d = 0.41) and private schools (d = 0.37). Three times as many students in the top EduYears GPS decile went to a selective school compared to the bottom decile. These results were mirrored in the exam differences between school types. However, once we controlled for factors involved in pupil selection, there were no significant genetic differences between school types, and the variance in exam scores at age 16 explained by school type dropped from 7% to <1%. These results show that genetic and exam differences between school types are primarily due to the heritable characteristics involved in pupil admission.

Background: Children in the UK go through rigorous teacher assessments and standardized exams throughout compulsory (elementary and secondary) education, culminating with the GCSE exams (General Certificate of Secondary Education) at the age of 16 and A-level exams (Advanced Certificate of Secondary Education) at the age of 18. These exams are a major tipping point directing young individuals towards different lifelong trajectories. However, little is known about the associations between teacher assessments and exam performance or how well these two measurement approaches predict educational outcomes at the end of compulsory education and beyond. Methods: The current investigation used the UK-representative Twins Early Development Study (TEDS) sample of over 5,000 twin pairs studied longitudinally from childhood to young adulthood (age 7-18). We used teacher assessment and exam performance across development to investigate, using genetically sensitive designs, the associations between teacher assessment and standardized exam scores, as well as teacher assessments' prediction of exam scores at ages 16 and 18, and university enrolment. Results: Teacher assessments of achievement are as reliable, stable and heritable (~60%) as test scores at every stage of the educational experience. Teacher and test scores correlate strongly phenotypically (r~.70) and genetically (genetic correlation~.80) both contemporaneously and over time. Earlier exam performance accounts for additional variance in standardized exam results (~10%) at age 16, when controlling for teacher assessments. However, exam performance explains less additional variance in later academic success,~5% for exam grades at 18, and~3% for university entry, when controlling for teacher assessments. Teacher assessments also predict additional variance in later exam performance and university enrolment, when controlling for previous exam scores. Conclusions: Teachers can reliably and validly monitor students' progress, abilities and inclinations. High-stakes exams may shift educational experience away from learning towards exam performance. For these reasons, we suggest that teacher assessments could replace some, or all, high-stakes exams. Key points• Teacher assessments are as reliable and heritable as standardized test scores (average heritability around 60%).• Teacher assessments and test scores correlate strongly phenotypically (r $ .70) and genetically (genetic correlation $ .80) both contemporaneously and over time.• Teacher assessments account for $ 90% of the combined prediction (teacher ratings and earlier test scores) of exam performance at ages 16 and 18.• Teacher assessments during compulsory education explain $ 13% of variance in university enrolment, while test scores add an additional $ 3% to that prediction.

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We study the market for teachers in England, in particular teacher turnover. We show that there is a positive raw association between the level of school disadvantage and the turnover rate of its teachers. This association diminishes as we control for school, pupil and local teacher labour market characteristics, but is not eliminated. The remaining association is largely accounted for by teacher characteristics, with the poorer schools hiring much younger teachers on average. We interpret this market equilibrium allocation as either deriving from the preferences of young teachers, or as reflecting the low market attractiveness of disadvantaged schools.