Participants

The sample was drawn from the Twins Early Developmental Study (TEDS), a representative sample of twins born in England and Wales between 1994 and 1996. Of the 16,000 twin pairs originally recruited, over 10,000 remain actively involved in TEDS. Their recruitment and representativeness has been described in detail elsewhere5,23. The present study included all individuals with educational achievement data available at 18. Participants with severe medical or psychiatric problems or whose mothers had severe medical complications during pregnancy were excluded from the analysis. We also excluded participants with unknown zygosity. Zygosity was assessed by a parent-reported questionnaire of physical similarity, which is over 95% accurate when compared to DNA testing24. For cases where zygosity was unclear from this questionnaire, DNA testing was conducted. After exclusions, the total number of individuals for whom data at 18 were available was 13,226 individuals (6584 twin pairs), of whom 2318 were monozygotic (MZ) twin pairs, 2146 were dizygotic same-sex pairs (DZss) and 2120 were dizygotic opposite-sex (DZos) pairs. A-level exam achievement results were available for half of the participants (the proportion of participants who took the A-level exams): 3308 twin pairs of which 1178 were MZ twin pairs, 1067 were DZ same-sex twin pairs, and 1063 were DZ opposite-sex twin pairs.

In the twin method, DZ twin pairs are needed to delineate genetic and environmental contributions to a trait, with same-sex DZ twins most often used because they provide a more appropriate control for MZ twin pairs, who are always the same sex4,25. When data are available from opposite-sex twin pairs, sex differences in the etiology of individual differences can also be explored. Sex limitation results are reported in the Results section. Because little evidence was found for significant sex differences for the achievement data and to increase power, we used the full sample, including opposite-sex twin pairs.

Measures

The TEDS sample has now completed compulsory education. In England and Wales, compulsory education ends with the General Certificate of Secondary Education (GCSE), a standardized examination typically taken at the age of 16. Completion of GCSE examinations marks a unique stage for pupils who are now, for the first time, free to choose whether to leave formal education or to continue their studies to complete further education (FE). In the UK, FE refers to courses offered in separate FE colleges or more commonly, available within the sixth-form part of a school, which are distinct from the undergraduate and graduate degrees typically offered at universities (http://www.cambridgeassessment.org.uk/Images/140668-popularity-of-a-level-subjects-among-uk-university-students.pdf). These FE qualifications are commonly taken over a two-year period, with official examinations held at the end of each year, leading to a formal qualification known as the General Certificate of Education Advanced level, or A-level, which is the focus of the present study. Alternative qualifications including the International Baccalaureate, NVQ (National Vocational Qualification) and BTEC (Business and Technology Education Council) are also considered FE but were not analyzed in the present study (https://www.studential.com/further-education/vocational-qualifications).

Unlike in previous school years, at A-level pupils are free to choose all of their courses from over 80 different subjects, typically choosing three to four subjects studied during the two-year period (http://www.cambridgeassessment.org.uk/Images/140668-popularity-of-a-level-subjects-among-uk-university-students.pdf). Grades achieved in both exams (GCSE and A-level) are converted into a points-based system (https://www.ucas.com/ucas/undergraduate/getting-started/entry-requirements/tariff), which is evaluated by the student’s chosen university along with previous school performance and teacher-predicted results, as criteria for university entry. However, some universities evaluate specific grades achieved, not just achievement based on the overall points-based system. A detailed description of the UK education system can be found on UK Department of Education website (https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/219167/v01-2012ukes.pdf).

A questionnaire, designed to obtain A-level and other post-16 qualifications as well as work destinations, was sent to all TEDS families at the end of the academic school year when twins reached age 18. The full questionnaire was completed either by twins themselves or by their parents. We have previously shown that self-reported exam results are accurate12. For GCSE (General Certificate of Secondary Education) exam results that children take at the age of 16 the grades were verified using the National Pupil Database (NPD; https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/251184/SFR40_2013_FINALv2.pdf) using the sample of 7367 twins, yielding a correlation of 0.99 for mathematics, 0.98 for English and >0.95 for all the sciences.

A-level examination grades (ranging from A* to E) were obtained for each twin and were coded from 6(A*) to 1(E) to ensure equivalent numerical comparisons. Because no subjects at A-level are compulsory and the range of subjects chosen is so wide, the sample sizes were too small to provide adequate power for analyses of separate subjects except for biology, chemistry, physics, history, geography and psychology. For this reason and to increase power generally, we created a composite STEM variable (science, technology, engineering and mathematics), which was derived as a mean grade of all sciences (mean of science, biology, chemistry and physics grades), technology (mean of technology and information communications technology grades), engineering (mean of engineering and mechanical engineering grades), and mathematics (mean of any core mathematics and further mathematics grades) courses. Composites were also created for English (mean of any English language and English literature grades), second language (mean of any second language course grade), and humanities (mean of history, religious studies, media studies and geography grades). An A-level mean grade, computed as the average grade achieved across all subjects in the dataset, was also created to ensure even those subjects with sample sizes too small to be considered separately were included in the analysis. In order to assess individual differences in subject choice we created categorical variables indicating whether or not pupils chose to take the individual or composite subjects described above. Finally, we created a categorical A-level choice variable to indicate whether or not participants chose to do their A-levels.

Analyses

The data were described in terms of means and variance comparing boys with girls and MZ and DZ twins. Analysis of variance (ANOVA) was then used to explore sex and zygosity differences in means and variances and their interaction, for A-level grades. For subsequent analyses the achievement scores were corrected for small age and sex differences using the regression method because MZ twins are always the same sex, along with the mean effect of age, which is perfectly correlated across pairs, both factors which if uncorrected would inflate estimates of shared environmental influence26. Standardized age and sex corrected residuals were used for all subsequent analyses. Finally, prior to conducting twin analyses, the data were corrected for normality using the rank-based van der Waerden transformation27,28. Corrections were performed because achievement data were slightly positively skewed, showing a ceiling effect similar to data achieved from UK national statistics (https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/365986/SFR42_2014_provisional__A_level_and_level_3_SFR.pdf).

Twin analyses

In order to investigate the relative genetic and environmental contribution to individual differences in educational achievement, we used the twin design, a quantitative genetic method which exploits the known coefficients of relatedness between identical (MZ) and non-identical (DZ) twins, to apportion phenotypic variance into additive genetic (A), shared environmental (C) and non-shared or unique environmental (E) components. Genetic effects are perfectly correlated for MZ twin pairs who are 100% genetically similar compared to DZ twin pairs who, like non-twin siblings, share 50% of the segregating genes. Shared environmental effects are perfectly correlated for MZ and DZ twin pairs reared together while non-shared environmental effects are uncorrelated for members of a twin pair and do not contribute to similarities between twins. Based on these known relations and the standard quantitative genetic model (Falconer’s formula), heritability (A) can be roughly estimated by doubling the difference between MZ and DZ twin correlations. The residual familial resemblance not explained by heritability is accounted for by the C component, calculated by subtracting the heritability estimate from the MZ correlation. The E component represents the remaining variance and measurement error and is calculated by deducting the A and C components from unity, as the total variance cannot exceed 100%4,25.

The ACE parameters can be estimated more accurately using structural equation model fitting with maximum-likelihood estimation, which also provides 95% confidence intervals and formal model fit statistics. The structural equation modeling program OpenMx was used for all model fitting analyses29.

Power was calculated using Genepi Twin Power calculator30,31, which shows that the analyses had over 80% power for both the subject choice and achievement variables. The analyses had less than 80% power to detect C in specific subject achievement grades of second language, geography and psychology as is evident from the large confidence intervals around the estimates, but were reported for completeness.

Sex-limitation model

When data are available for both same sex DZ twin pairs and opposite-sex DZ twins, the standard univariate ACE model can be extended to a sex-limitation model to test the differences in the etiology of the trait of interest by comparing twin correlations across five zygosity groups: MZ males, MZ females, DZ males, DZ females and DZ opposite-sex twin pairs4,32. Quantitative sex differences refer to sex differences in the magnitude of ACE estimates. Qualitative sex differences test whether there are different genetic or different environmental factors influencing boys and girls separately, which is largely based on whether DZ same-sex twin correlations are higher than DZ opposite-sex correlations32.

The sex-limitation model was analyzed using the structural equation program OpenMx by fitting a series of nested models and testing the relative fit of the models29. In the full model, all parameters are allowed to vary across all five zygosity groups (genetic correlation between DZos, ACE estimates, variances, ACE estimates, DZss and DZos variances and correlations). To test for qualitative sex differences, the genetic or shared environmental correlation is constrained to expected values (1.0 or 0.5 respectively), while other estimates are allowed to vary in the model. Quantitative genetic differences are tested by a reduced model in which ACE estimates are equated for males and females and the DZos genetic correlation is constrained to 0.5. The sex-limitation model is described in more detail elsewhere4,6,32.

Liability threshold model

Because subject choice was measured as a dichotomous trait (choosing a subject or not), twin resemblance was assessed by concordances between MZ and DZ twins by comparing the twin who took an A-level course, to their co-twin. Concordance represents an index of risk, often encountered when assessing the presence or absence of a disease; but is used in the present study as the presence or absence of subject choice4,25. Analyses of categorical twin data assume that observed categories represent an imprecise measurement of an underlying normal distribution of liability25. The degree of agreement between MZ twin pairs who are genetically 100% similar is then compared to the degree of agreement between DZ twin pairs, who share 50% of their segregating genes on average using the correlation of liability (tetrachoric correlation). The liability threshold model is described in detail elsewhere25. The structural equation program OpenMX was used for the liability threshold model29.