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A2 Appendix 2: Modelling Inequalities in Attainment

A2.1 The focus of the current study is the extent to which inequalities in attainment have changed over the past two decades. In order to explore change over time in the effects of a number of different factors, the time-series data are analysed using multivariate linear regression models. The measures analysed are derived from comparable measures of:

• attainment at age 16 - the Standard Grade point score;
• attainment at 18/19 - the UCAS tariff score.

A2.2 These measures have been derived for all cohorts except the 1992 (reconstructed) cohort (see Section 2 for details).

A2.3 The estimates from the models are summarised in Tables A2.1 and A2.2, and include the effects of number of factors describing personal, family background and school characteristics. The main effect of each factor is estimated in comparison with a reference category; for example, average differences in attainment associated with sex are shown by the estimate for "female" compared with "male" which is the reference category.

A2.4 The models include "year" as a continuous measure, based on the year each cohort completed S4, in order to estimate overall change in attainment over time. The reference category for "year" is 1990, and the measure ranges from -6 (1984 cohort) to +12 (2002 cohort). In the model the estimates of changes in attainment over time are shown as change per year (compared with 1990). Thus the extent of change between 1990 and 2002 (a period of 12 years) can be calculated by multiplying the estimate by 12.

A2.5 Estimating change over time using "year" as a continuous measure assumes that attainment changed in a continuous - linear - fashion. However, the charts in section 5 suggest that change may have been steeper in the earlier cohorts than the later cohorts (or vice versa), and that change may be better represented as a curve. In order to control for this curvilinear trend a further measure of "year" in the model is "year squared". In the model, a negative estimate for "year squared" indicates that the upward trend in attainment has flattened out in later cohorts - and conversely a positive estimate indicates it has accelerated.

A2.6 The key question addressed by the models is whether inequalities by gender, family background and school location have changed over time. Therefore, the changing effects of each factor over time are estimated by the interaction of the factor with "year". The estimate for the interaction effect shows the extent of change in the effect of the factor each year. The estimate for the interaction effect should be compared with the main effect of the factor and the main effect of "year".

A2.7 The estimates show the effect of each factor after controlling for all other factors in the model.

A2.8 All the factors and interactions recorded in Tables A2.1 to A2.2 are statistically significant at the 95% confidence level. Factors that have been removed from the model because they are not statistically significant are denoted 'ns'.

Inequalities in attainment at age 16

A2.9 Table A2.1 shows the effects of each factor on attainment at age 16, measured by the Standard Grade point score. Results in the left side of the table are the "main effects" associated with each factor, and those in the right side are "interaction effects" indicating the extent of change over time.

Overall trends over time

A2.10 The estimate for "year" shows that on average the Standard grade point score increased by just over one point per year (the estimate is 1.03 per year). However, the negative estimate (-0.02) for "year squared" shows that the increase in attainment was steeper in the early period and levelled off for later cohorts.

Sex

A2.11 On average females achieved almost two points more than males (the estimate is 1.99). The interaction effects show that the female advantage increased over time by an average 0.08 points per year. Thus the gap associated with gender widened very slightly over the two decades.

Social Class

A2.12 The second estimate of inequality relates to parents' social class. The reference category for social class is managerial/professional, so the estimates compare the average attainment of intermediate, working class and unclassified pupils with the attainment of managerial/ professional pupils. The estimates show substantial differences in attainment between the classes (the estimate for intermediate class is -3.43; working class -8.12; unclassified -11.3). The estimates for interaction effects show that the difference between intermediate and managerial/professional students did not change over time (interaction effect for intermediate*year is not statistically significant). However, the difference in attainment between working class and managerial/professional students reduced over time by 0.17 points per year - showing that inequalities reduced over time. Similarly, differences between unclassified students and managerial/professional students reduced over time by 0.31 points per year.

Parents' education

A2.13 An important factor in children's education is their parents' educational level. From the SSLS, parents' education is indicated by whether or not they had some post-compulsory education. ¹³ Table A2.1 confirms that both father's and mother's education has a positive effect on their children's Standard Grade attainment (the estimates are 4.67 and 5 points respectively). The advantage associated with parents education decreased over time (-0.24 and -0.25 points per year).

Parents' main activity

A2.14 Previous studies have suggested that parents' main economic activity ¹⁴ may have an additional effect on pupils' attainment. Specifically, two aspects of parents' main activity - father unemployed and mother full-time unpaid in the home - have been found in previous analyses to influence attainment; these are included in the model, and compared with a reference category that includes full-time work, part-time work, retired, dead and "other". On average, having a mother full-time unpaid in the home is associated with higher attainment (1.03 points), but this advantage decreased over time (by 0.08 points per year). On the other hand, having a father unemployed is associated with lower attainment (-4.41) but this disadvantage decreased over time (by 0.11 points per year).

Family structure

A2.15 The last factor relating to family background in Table A2.1 is family structure; it compares the average attainment of young people living with step parents, lone parents or in "other" arrangements ¹⁵ with the attainment of young people living with both of their natural parents. In each case, family structures other than living with both natural parents are associated with lower attainment on average (the estimate for step parent families is -3.79; lone parent: -3.29; other: -6.25). However, the interaction effects show that the negative effect of living with a step parent diminished over the period (the estimate is 0.11 per year). The negative effect of living in "other" arrangements was exacerbated over time (the estimate is 0.32 per year).

School type and socio-economic characteristics

A2.16 Schools vary in the socio-economic characteristics of their pupil intakes - this is shown by the segregation indices described in Section 3. These differences in socio-economic characteristics may influence the experiences, aspirations and attainments of pupils attending each school. Three measures are included in the models in order to estimate the changing effects of school characteristics on attainment. The first indicates independent fee-paying schools compared with state-funded schools. Two other measures are derived from the percentage of pupils in the school with managerial/professional parents, and the percentage with working-class parents. In each case the percentage has been converted to a normal score with a mean of zero and a standard deviation of one - the estimates compare the effect of attending a school with a high proportion of managerial/professional parents, or a high proportion of working class parents, with the effect of attending a school where the class composition is average.

A2.17 Table A2.1 shows that on average the Standard Grade points score was lower in independent schools than in state-funded schools (-1.28), and this did not change over time. It is possible, however, that some of this difference in attainment can be explained by independent schools presenting their pupils for English qualifications such as GCSE that are not included in the Standard grade point score. Another explanation may be that the advantage associated with independent schools is derived from the high social-class intake of the pupils - and this is controlled for by the background factors included in the model.

A2.18 On average, pupils who attended a school with a high percentage of managerial/professional pupils had higher levels of Standard Grade attainment (the estimate is 2.01 points in a school where the % of managerial/professional parents is one standard deviation above the national mean). However, this advantage decreased over time (the estimated decrease is 0.1 points per year).

A2.19 On average, pupils had slightly lower attainment if they attended a school with a high proportion of working class pupils (the estimate is -0.36 points in a school where the % of working class parents is one standard deviation above the national mean). This disadvantage did not change over time.

School location

A2.20 Differences associated with school location are also estimated by the model. In view of the fact that pupils attending city schools are the largest category in SSLS (37%: see Section 2), city schools are used as the reference category in the model. All other things being equal, there is no difference in attainment between pupils attending city schools, schools in other urban areas, and schools in accessible town and rural areas. However, on average pupils attending schools in remote areas have higher average Standard Grade scores than pupils in city schools (the estimates are 1.76 in remote towns and 0.89 in remote rural areas). Over time the advantage accruing to pupils in remote towns did not change, but the attainment advantage of pupils in remote rural schools increased (the estimated increase is 0.17 per year).

Table A2.1 Factors influencing Standard grade attainment score at age 16 (estimates from regression model)

Inequalities in attainment at age 18

A2.21 Table A2.2 shows the effects of each factor on attainment at age 18, measured by the UCAS tariff score (for details of constituent qualifications see Table 2.4 in Section 2). The UCAS tariff is based on academic qualifications, and is used here because it offers comparability over time. The UCAS tariff underestimates overall attainment because it does not include vocational qualifications, but unfortunately information about more vocational qualifications has not been collected in a consistent manner by SSLS.

Overall trends over time

A2.22 The estimate for "year" shows that on average the UCAS tariff score increased by just over four points per year (the estimate is 4.44 per year). However, the positive estimate (0.15) for "year squared" shows that the increase in attainment was steeper in the later period than for earlier cohorts - suggesting that the increase in attainment has accelerated.

Sex

A2.23 Table A2.2 show that on average females achieved almost ten points more than males (the estimate is 9.7). The interaction effects show that the female advantage increased over time by an average 1.21 points per year. Thus the gap associated with gender widened over the two decades.

Social class

A2.24 Social class inequality in attainment of the UCAS tariff is very strong: managerial/ professional students have a marked advantage at age 18. Compared with managerial/professional students, all other social classes had substantially lower average attainment (the estimated difference for students of intermediate class is -39, working class -75 and unclassified -80). Over time, these inequalities increased still further (the estimated attainment gap increased by two points on average for each of the three lower social classes.)

Parents' education

A2.25 The education experienced by parents is a strong factor influencing students attainment at age 18. On average, students achieved higher UCAS tariff scores if their father and mother had some post-compulsory education (the estimates are 62.48 for father and 65.47 for mother). Over time, the advantage associated with father's post-compulsory education did not change, but the advantage associated with mother's post-compulsory education was reduced.

Parents' main activity

A2.26 Students whose mothers had been full-time unpaid in the home at S4 had higher average attainment at age 18 (estimate 16 UCAS tariff points), and this advantage did not change over time.

A2.27 Those whose fathers had been unemployed at S4 had lower average attainment at age 18 (estimate 23.86 points) and this disadvantage did not change over time.

Family structure

A2.28 At age 18, there were disadvantages in attainment associated with having step parents, lone parents and other living arrangements in S4. (The estimated reduction in attainment for having a step-parent is -37.25 points; lone parent -16.43; other living arrangements -56.02). Over time the disadvantage of having a step-parent did not change, but the disadvantage of having a lone parent or other living arrangements got worse).

School type and socio-economic characteristics

A2.29 Table A2.2 shows that students from independent schools have higher average UCAS scores than students from state-funded schools (estimate 64.89) and the advantage accruing to independent schools did not diminish over time. The difference in effect of independent schools at age 18 compared with age 16 is probably because more take Scottish qualifications at age 18 as entry qualifications for Higher Education.

A2.30 Students attending schools which had a high proportion of managerial/professional students also had higher average UCAS tariff scores (estimate 17.34) and this advantage did not diminish over time. Schools with a high proportion of working class students did not differ from the average in their attainment at age 18.

School location

A2.31 Students attending schools in urban areas and accessible towns had lower average UCAS scores than their counterparts in city schools. These differences did not change over time. In contrast to their higher performance at Standard Grade, there was no advantage accruing to students attending remote schools at age 18 (but note that students attending remote schools may have to move school and live away from home during the post-compulsory stages).

Table A2.2 Factors influencing UCAS tariff score at age 18/19 (estimates from regression model)

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