Differences in exam performance between pupils attending selective and non-selective schools mirror the genetic differences between them

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.


Supplementary methods:
Page Methods S1 -Details on genotyping 2 Methods S2 -Creating the school type variables 4 Methods S3 -Hierarchical linear regression to calculate adjusted means for school type 8 Supplementary Tables: Table S1 -Analysis of variance (ANOVA) and planned contrasts for EduYears GPS between students of three school types: state non-selective, grammar and private schools 9 Table S2 -Analysis of variance (ANOVA) and planned contrasts for EduYears GPS between students of five school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools 10 Table S3 -Correlation matrix 11 Table S4 -Hierarchical regression analysis of EduYears GPS, controlling for selection factors for students of three school types: state non-selective, grammar and private schools 12 Table S5 -Hierarchical regression analysis of EduYears GPS, controlling for selection factors for students of five school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools 13 Table S6 -Regression analysis of predictors of mean GCSE for three school types: state nonselective, grammar and private schools 14 Table S7 -Regression analysis of predictors of mean GCSE for three school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools 16  Figure S1 -EduYears GPS plotted means (and 95% confidence intervals) for students of five school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools 19 Figure S2 -EduYears GPS plotted means (and 95% confidence intervals) controlling for selection factors between students of 3 school types: non-selective state, grammar and private 20 Figure S3 -EduYears GPS plotted means (and standard errors) controlling for selection factors between 5 school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private school 21 Figure S4 -The plotted means (and 95% confidence intervals) for unadjusted GCSE, GCSE controlling for EduYears GPS, GCSE controlling for SES, GCSE controlling for prior ability, GCSE controlling for prior achievement and GCSE controlling for all variables between 5 school types: nonselective schools in wholly selective areas, non-selective schools in partially selective areas, nonselective schools in non-selective areas, grammar schools and private school   After initial quality control and genotype calling, the same quality control was performed on the samples genotyped on the Illumina and Affymetrix platforms separately using PLINK 1,2 , R 3 , and vcftools 4 .
Samples were removed from subsequent analyses on the basis of call rate (<0.99), suspected non-European ancestry, heterozygosity, array signal intensity, and relatedness (IBD cut-off 0.05). SNPs were excluded if the minor allele frequency was <0.5%, if more than 1% of genotype data were missing, or if the Hardy Weinberg p-value was lower than 10 -5 . Non-autosomal markers and indels were removed. Association between the SNP and the platform, batch, or plate on which samples were genotyped was calculated; SNPs with an effect p-value less than 10 -3 were excluded . A total sample of 6,710 samples, with 3,617  individuals and 600,034 SNPs genotyped on Illumina and 3,093 individuals and 525,859 SNPs genotyped on Affymetrix remained after quality control.
Genotypes from the two platforms were separately imputed using the Haplotype Reference Consortium 5 and Minimac3 1.0.13 6,7 available on the Michigan Imputation Server as reference data. A series of quality checks was performed before merging data from the two platforms' imputation (e.g. platform effects, allele frequencies by imputation quality). For the present analyses we limited our analyses to variants genotyped or imputed at info >.70 on both platforms, allele frequency difference between platforms smaller than 5%, and Hardy Weinberg p-value was greater than 10 -5 . Using these criteria, 7,581,516 genotyped and wellimputed SNPs were retained for the analyses.
We performed principal component analysis on a subset of 42,859 common (MAF>5%) autosomal HapMap3 SNPs 8 , after stringent pruning to remove markers in linkage disequilibrium (r 2 > 0.1) and excluding high linkage disequilibrium genomic regions so as to ensure that only genome-wide effects were detected.
Of the final sample of successfully genotyped individuals, there were 4,814 people who also had information on school type and exam results at age 16 which were included in the present analysis.

Methods S2 -Creating the school type variable
To create the school type variable for the present study, we used TEDS data in combination with data from the National Pupil Database (NPD; https://www.gov.uk/guidance/nationalpupil-database-apply-for-a-data-extract).

TEDS data
When the individuals in our sample were 18, they received a questionnaire that included a series of questions asking what type of school they attended during their GCSEs.
Respondents were asked to indicate either 'Yes' or 'No' for different school types, including: home-school, comprehensive school, grammar school, independent (private) school, special school, sixth-form or further education college, faith school, academy and single-sex school. Respondents could select 'Yes' to more than one school type.
We classed all respondents who said they went to either a comprehensive or an academy school as 'State non-selective'. Because individuals were able to select more than one school type, we excluded those who also said they went to a grammar school (n = 22), independent school (n = 26) or special school (n = 17). We did not include 'sixth-form' or 'further education college' within the state non-selective school type as we did not have any information about their selection criteria. After exclusions, the total number of individuals attending a state non-selective school was 4,780.
To create the 'Grammar' group, we classed all respondents who said they attended a grammar school as 'Grammar'. Again, we excluded those who indicated that they also went to a private school (n = 24), comprehensive school (n = 22) or special school (n = 3). After exclusions, the total number of individuals in this group was 372. We classed all respondents who said they attended a private school as 'Private'. We excluded those who indicated that they also went to a comprehensive school (n = 26), grammar school (n = 24) or special school (n = 8). After exclusions, the total number of individuals in this group was 513. We could not class individuals who indicated that they went to a faith or single sex school only into one of the three school types, as these schools can be state non-selective, grammar or private schools.

National Pupil Database data
In order to increase sample sizes, we also accessed school type information through the National Pupil Database (NPD). NPD is a pupil-level database which matches pupil and school characteristic data to pupil level attainment in England. Within the TEDS sample, 13,392 individuals gave consent for us to access their NPD records, of which 12,717 individuals were successfully matched. Approximately 700 individuals who had given consent lived outside of the England (for example Wales or Scotland), and therefore individuals could not be matched. In addition to pupil-level data on attainment, NPD also includes information on what type of school an individual attended during their GCSEs which is limited in description to one school type (for a list of school types in NPD and corresponding sample sizes in our data, please see Table SM1). Students coded in NPD as attending: 'community', 'voluntary aided', 'voluntary controlled', 'foundation', 'city technology college', 'non-maintained', 'academy sponsor-led', 'academy-converter' or 'free schools' were classed as 'State non-selective' (n = 10,446). Because NPD does not include a separate category for grammar schools, we identified grammar schools using the Department for Education database 'EduBase' which we could link to NPD data through unique school reference numbers (URNs). This identified 314 students attending grammar schools within our NPD records. Therefore, after excluding these individuals, there were 10,132 individuals attending 'State non-selective' schools in NPD and 314 individuals attending grammar schools. Students coded as attending 'other independent' schools in NPD we classed as 'Private' (n = 998).

TEDS and NPD accuracy
There were 4186 individuals who had both TEDS data and NPD data. From this, we checked the accuracy of our groupings using descriptive crosstabs (see Table SM2). This shows the agreement between TEDS and NPD school type data. It revealed high accuracy for both the state non-selective and the private school groups. There were 75 individuals who had stated that they attended a grammar school in the TEDS data, but who actually attended a state non-selective school, as indicated by NPD. This is likely due to grammar schools converting to state non-selective schools, but keeping the title 'grammar' within their school name. We decided prioritise the NPD data in these cases.

School type totals
After combining TEDS and NPD school type data and prioritising NPD data with relation to grammar schools, there were a total of 12,923 individuals for whom we had school type data available. 11,434 attending non-selective state schools, 377 attending grammar schools and 1112 attending private schools. The proportion of students attending the three school types in the current study is representative of UK statistics: for example grammar school UK intake = ~4% 1 , our sample = 2.9%; private school UK intake = ~7% 2 , our sample = 8.6%.
Of this final number 4,814 also had GCSE data and genotype information, with 4,263 attending non-selective schools, 143 attending grammar school and 408 attending private schools. 2533 people also had data for the selection factors: family SES, prior ability and prior achievement.

State non-selective schools and local education authorities
Local education authorities (LEAs) are the local councils in England and Wales that are responsible for education within their jurisdiction. They can be non-selective (contains no grammar schools), partially selective (contains one or more grammar school) or wholly selective (over 25% of pupils in that LEA attends a grammar school). Previous research suggests that those attending non-selective schools in wholly selective areas perform worse than those in non-selective areas, so we further split our 'State non-selective' school type into three subcategories to test this.
Non-selective, partially selective and wholly selective local education authorities (LEAs) were identified from The Education (Grammar School Ballots) Regulations 1998 3 , which includes 10 'wholly-selective' LEAs and a further 26 partially selective LEAs. We matched this information to our own data through school LEA.
There were 331 students attending a non-selective school in a wholly selective area, 905 students attending a non-selective school in a partially selective area, and 3,027 students attending a non-selective school in a non-selective area. Numbers for grammar (n = 143) and private (n = 408) schools remained the same.

Methods S3 -Hierarchical linear regression to calculate adjusted means for school type
To test the effect of school type on GCSE once selection factors (SES, prior achievement and prior ability) had been controlled for, we conducted hierarchical linear regression. In the first step, we entered the selection factors, which were first standardized so that the mean of these variables was 0, and in the second step of the model we entered school type. Because school type is a nominal variable with three categories (non-selective state school, grammar school and private school) without intrinsic ordering, we created two dummy coded variables to represent the three categories. This is a common way of entering nominal variables into multiple linear regression in order to capture all of the categories. Dummy coding requires one of the categories to be the reference category, in which the other categories are compared with; in this analysis we chose to use state non-selective schools as the reference category to look at the effects of selective schools on GCSE performance (see Supplementary Methods S3 for further information).
Conducting hierarchical linear regression enables us to observe the R² change between the two steps in the model, indicating the amount of variance in mean GCSE score explained by school type once selection factors have been controlled for. In addition, it also allows us to test whether mean GCSE score differs between school types whilst keeping the selection factors constant. For example, in the case of grammar schools, the mean would be calculated using the equation below: Ŷ = β 0 + β 1 1 + β 2 2 + β 3 3 + β 4 4 Where Ŷ is the mean GCSE for grammar schools, β 0 is the intercept in the second step of the model which, in this case, is the expected mean GCSE of state non-selective schools when all other independent variables are 0 (which have been standardized so that 0 represents their mean), 1 , 2 , 3 and 4 are the independent variables: school type, SES, prior ability and prior achievement and β 1 , β 2 , β 3 and β 4 are the beta coefficients associated with the change in dependent variable when school type goes from state non-selective school to grammar school, whilst keeping the other independent variables constant. We observed the t statistic and its associated significance in order to see whether the mean GCSE differed between groups, once accounting for selection factors. Note: n = number of participants in each group; SD = standard deviation; 95% CIs = 95% confidence intervals around the mean; F = test of overall ANOVA model; ɳ² = eta squared variance explained; N = non-selective state school students; G = grammar school students; P = private school students; dcohen = adjusted cohen's d statistic; CI = confidence intervals; *** = p < .001

Table S2 -Analysis of variance (ANOVA) and planned contrasts for EduYears GPS between students of five school types: nonselective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools
Note: n = number of participants in each group; SD = standard deviation; 95% CIs = 95% confidence intervals around the mean; F = test of overall ANOVA model; ɳ² = eta squared variance explained; WS = non-selective school in wholly selective area; PS = non-selective school in partially selective area; NS = non-selective school in non-selective area; N = non-selective state school students; G = grammar school students; P = private school students; dcohen = adjusted Cohen's d statistic; CI = confidence intervals.* = p <.05; ** = p < .01; *** = p < .001.

Table S4 -Hierarchical regression analysis of EduYears GPS, controlling for selection factors for students of three school types: state non-selective, grammar and private schools
Step 1 Step Note: SES = Socioeconomic status; CIs = confidence intervals; * p < 0.05; ** p < 0.01; *** p < 0.001. School type was dummy-coded into two variables with state non-selective schools as the reference category. Constant = mean of state non-selective schools when all other variables held constant; Model step 1: selection factors (SES, prior ability and prior achievement) were entered into the model; Model step 2: selection factors and school type were entered into the model together.

Table S5 -Hierarchical regression analysis of EduYears GPS, controlling for selection factors for students of five school types: nonselective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in non-selective areas, grammar schools and private schools
Step 1 Step

Figure S2 -EduYears GPS plotted means (and 95% confidence intervals) controlling for selection factors between students of 3 school types: non-selective state, grammar and private
Note: There were no significant EduYears GPS mean differences between state non-selective and grammar school students (t = 1.853, p = 0.064) or between state non-selective and private school students (t = 1.739, p = 0.082) or between grammar and private school students (t = .432, p = 0.665). The 95% confidence intervals are larger here than in Figure 1 because the sample sizes were reduced when data for the three selection factors were required (N = 2533).

Figure S3 -EduYears GPS plotted means (and standard errors) controlling for selection factors between 5 school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, non-selective schools in nonselective areas, grammar schools and private school
Note: There were small significant differences between students in state non-selective schools in wholly-selective vs partially selective areas (t= -2.579, p =.010) and students in wholly selective areas vs non-selective area (t= -2.442, p = .015), controlling for selection factors. The 95% confidence intervals are larger here than in Figure S1 because the sample sizes were reduced when data for the three selection factors were required (N = 2533). Figure S4 -The plotted means (and 95% confidence intervals) for unadjusted GCSE, GCSE controlling for EduYears GPS, GCSE controlling for SES, GCSE controlling for prior ability, GCSE controlling for prior achievement and GCSE controlling for all variables between 5 school types: non-selective schools in wholly selective areas, non-selective schools in partially selective areas, nonselective schools in non-selective areas, grammar schools and private school Note: For GCSE controlling for all the variables, there were no differences between non-selective school students in varying selectivity areas. However, there were differences between wholly-selective and both grammar (t = 2.223, p = .026) and private (t = 5.029, p <.001) and between partially selective areas and both grammar (t = 1.997, p = .046) and private (t = 5.348, p <.001) and non-selective and both grammar (t = 2.375, p = .018) and private (t = 6.146, p <.001).