Breadth of study at secondary school and the attainment and progression of university graduates in Scotland, 1960–2002

The relationship between the breadth of the curriculum which university students followed at secondary school and their degree attainment or their entry to employment is studied using a series of surveys of graduates from Scottish universities between 1960 and 2002. The relationship of the school curriculum to the later experience of students who entered university has not been extensively studied. Scotland is a useful case study for this purpose because breadth of study at school was a core feature of school-leaving assessment from the origins of modern secondary schooling in the early twentieth century until the end of the century. Breadth of learning was also a principle of the dominant university tradition in Scotland from the mid-nineteenth century onwards. The conclusion of the analysis is that breadth was associated with propensity to enter professions rather than managerial occupations, and to avoiding low-status occupations. But also, for students with relatively moderate or low attainment from school, breadth was associated with a lower chance of gaining the highest attainment at university.


Introduction
The relationship between the curriculum which university students followed at secondary school and their degree attainment or their progression beyond graduation has received only intermittent attention. There is some evidence that some school subjects can strengthen graduates' position in the labour market, but the general conclusion from the small body of research is that there is no strong legacy of this kind.
Yet an alternative way of considering breadth is that it is the basis of educated citizenship, and thus, for graduates, the necessary preparation for taking on influential social roles. This tradition was the rationale offered for curricular breadth in Scotland, which is the empirical focus of the research reported here. Using surveys of graduates from Scottish 1 3 take a range of subjects that were external to their eventual subject of graduation. They also had the option of graduating after 3 years with what was called an Ordinary degree, in which breadth was mandatory, requiring students to take courses in science and humanities or social science. Unlike in England, these were not fail degrees. As we will see, nearly one half of graduates from the universities took Ordinary degrees until the early 1980s, but this fell to merely one in twenty in the first decade of the new century as these older universities concentred increasingly on specialist Honours provision.
Scotland provides an unusual case study of the potential meaning of breadth for university graduates. Dolton and Vignoles (2002b: 422) investigated one aspect of this by considering the comparison of Scotland and England as a natural experiment in the potential effect of curricular breadth on earnings; they still concluded that there was no such effect. We incorporate their definition of breadth in the models here, along with a definition that is defined explicitly in terms of the curricular traditions of the Scottish school leaving certificate.
We ask whether breadth was associated with the class of degree attained and with entry to different kinds of employment. We investigate also whether the answer varies according to overall attainment from school, to the broad discipline of the subject in which the student graduated, to sex, and to the social class of the graduate before entering university. The question about employment is further investigated according to the class of degree.

Data
The analysis uses three sources of data on graduates from first degrees at one of the eight older universities-four dating from the fifteenth and sixteenth centuries, and four founded (or upgraded from technological colleges) in the 1960s. The main analysis of any associations with breadth of study at secondary school covers the years 1960, annually 1983-1993, and 2002. In addition to some specific restrictions noted for each data source below, all the data were restricted to people who were living in Scotland when they first entered, and who entered by age 20 (because the relationship between attainment at school and at university for older entrants was different from that for younger students (Brown & Webb, 1990)). Graduates from courses related to medicine are omitted because they were not included in the 1960 survey.
The most extensive source comes from annual data in the Universities' Statistical Record (USR) for students who graduated between 1972 and 1993 (Kornbrot, 1987;Mancini, 2003;Smith & Naylor, 2005). These records are in effect a census of all students graduating in each year, linked to a survey of their first destination; the survey had a response rate of around 80% every year (Mancini, 2003: 11). We further restrict attention to students whose main school-leaving qualifications were either from the Scottish school examinations (Higher Grades) or from those used in the rest of the UK (A-levels and ASlevels). Confusion in several aspects of the coding in the available data forced us to restrict the USR data to the years 1983-1993, although we can use 1980-1982 for the purpose of describing outcomes (Figs. 1 and 2).
Before that, we have data from a survey in autumn 1966 of all women and half of men who graduated in 1960 from faculties other than medicine, dentistry and veterinary surgery (Kelsall et al., 1970: 1-7). We use weights to take account of this design. In addition to the four oldest Scottish universities, this survey also included a technological college that merged into a new university in 1964.
After 1993, we use data from a cohort study of students who were first surveyed at age 16-17 in spring 199716-17 in spring . They mostly left school in 199716-17 in spring -199816-17 in spring and were followed-up in 199916-17 in spring and 2004. We confine the data to people who had entered the eight older universities by 1999, thus giving close to a representative sample of entrants by age 19. The response rates, as percentages of the original target in 1997, were 68% in 1997, 39% in 1999, and 16% in 2004. Non-response in the whole sample was closely related to attainment, social  , 1960-2002 class and sex, and so weighting is used to compensate for differential non-response (Dobbie & Jones, 2005: 9-10); our restriction to people who entered university will itself have compensated for most of any distortion. We refer to this survey as 2002, the modal year of university graduation for this cohort.
The resulting sample sizes of graduates were 627 in 1960, between 4,671 and 5,657 each year from 1983 to 1993, and 242 in 2002. The statistical modelling takes account of this varying size, mainly through the standard errors of estimates.
The variables which we use from these surveys are:

Sex
This was recorded from the original questionnaires.

Father's class
The USR data include father's occupational title coded to a list that was based on the UK's official schemes of occupational classification (for example, OPCS, 1980). To convert this to a fully valid measure of social class would require also information about status at work.
In the absence of that, we impute the most likely value of Registrar General's social class for each occupational code, using data from the Labour Force Survey of 1984 (for students entering 1980-1993) or 1979 (entry 1972-1979). This is analogous to the method used by Elias and Gregory (1994: 13), Mancini (203: 28,158) and Kornbrot (1987: 519). In the 1960 survey, we code Registrar General's class from father's occupational title and whether he had any managerial responsibility (Kelsall et al., 1970;General Register Office, 1960). The data set from the 2002 survey already included the Registrar General's class of the father.

Relative school attainment
The purpose of this variable is to be a metric of relative academic ability in each graduating cohort before they entered (Bekhradnia & Thompson, 2002;Dolton & Vignoles, 2002b). The USR data include 'tariff' scores for each entrant, based on the number and quality of their school-leaving grades. We first converted these into standardised z-scores (mean 0 and standard deviation 1 within each year) for all entrants to any UK university whose main entrance qualification was Higher Grades. Separate standardisations of this kind were calculated for entrants with main qualification A-levels or AS-levels. The reason to define these z-scores in terms of entrants to all universities, and separately for the Scottish and non-Scottish qualifications, is to allow in the scoring for selection bias among people who crossed the Scottish-English border to enter university. This attention to all entrants was only for the purpose of calculating these scores: the actual empirical modelling reported below is only for entrants to Scottish universities from Scotland, to each of whom we gave the z-score corresponding to their attainment in their main entrance qualifications.
In the 1960 survey, the z-scores were simply based on the number of passes in schoolleaving examinations for students from Scotland, because no information was available on the grade attained in these passes. At this date, these would have been almost entirely in the Higher Grade (not A-levels). The absence of any measure of the quality of the passes makes this measure less valid as an indicator of high academic ability than is available in the later surveys. In the 2002 survey, we can take account of quality of pass by basing the z-scores on a measure that is analogous to the tariff scores used in the USR series: (number of passes) + 0.5x(number of A awards).
The purpose of our attainment variable is to control for relative attainment among people who sat school examinations in closely adjacent years. Changes in the modes of school assessment during more than four decades of extensive educational reform make invalid any attempt to compare over time the effects of nominally similar school qualifications (Goldstein & Heath, 2000).

Breadth of school attainment
We adapt the Scottish traditional definition of breadth by following Gray et al. (1983) in allowing a language to be replaced by a social subject or an aesthetic subject. This change is necessary because, by the eve of the university expansion of the 1960s, the range of subjects in the school curriculum was expanding to include social sciences. Thus breadth is defined as having a pass at Higher Grade (or A-level) in each of four domains: English, mathematics, a natural science, and either a language, a social science, or an aesthetic subject. As explained above, our measure of breadth is intrinsically dichotomous.
In order to compare our results with those by Dolton and Vignoles (2002b: 420), we also defined a version of breadth to be based on theirs. The range of school-leaving subjects was classified into the five domains which they specified (mathematics or computing, natural science, social science, humanities, and other). To parallel our dichotomous definition of breadth, a variable was created recording whether or not the student had a pass in each of at least four of these domains. We call this 'DV breadth'. Dichotomising this measure of breadth for the purposes of comparison with our measure does potentially lose information, and so we report also the results of varying that threshold.

University attainment
For all years except 2002, there is information on the class of degree attained, which we define as three dichotomies, gaining or not gaining: first-class degree; good Honours degree (meaning first, upper second or enhanced); Ordinary degree (including in this category only those outcomes which were explicitly labelled as such, not those described as 'pass'). The academic faculty of graduation is grouped into two: humanities or social science, and science or technology.

Destination
The work of graduates who entered employment was classified into four groups based on the successive official classification of occupations (General Register Office, 1960;OPCS, 1980OPCS, , 1990ONS, 2000): professional, managerial, associate professional and miscellaneous categories. Examples of the three main categories here are: • Professional: lawyer, scientist, accountant, teacher • Managerial: managers in production, hotels, marketing, public administration • Associate professional: scientific and engineering technician, quantity surveyor, nurse, journalist, graphic designer

Statistical models
The analysis uses binomial logistic regression to investigate the relationship between breadth of school-leaving attainment and seven measures of university outcome: For all graduates, comparing each category with not attaining that category: first-class honours; good honours (first-class, upper-second class, enhanced); ordinary degree; For graduates who entered employment: professions; management; associate professions; other occupations.
In the reported models, each of these occupations is compared with those below it in this list, and the last one with the first three, thus recognising an informal ordering of prestige.
The reason we use binomial regression rather than multinomial regression is to avoid having to specify a single reference category of outcome. The reason we have not used models for ordered categorical data is that these require restrictive conditions which are difficult to satisfy (Aitkin et al., 2009: 298-310).
The explanatory variables, as well as breadth at school, are school attainment, sex, broad faculty group, social class, interactions of these with breadth, and their variation over time. The control for school attainment is mainly to try to separate the statistical associations of breadth from the confounding associations with other educationally relevant characteristics, such as motivation (an approach also used by Dolton & Vignoles, 2002b: 420, 424). Towards the end of the Analysis, we summarise evidence that this control has been quite successful.
In restricting attention to people who entered Scottish universities from Scottish schools, we are analysing only part of the story, because in this period a growing proportion of undergraduates at Scottish universities came from elsewhere in the UK (Paterson, 1997: 38). The rationale for the restriction to Scottish schools is that our research question relates to the consequences of curricular breadth at secondary school, and so holding constant the secondary-school system removes the potential for confounding with other system-wide variables. The rationale for restriction to Scottish universities is the historical cultural association, outlined above, between these universities and the rest of the Scottish system of education.
The reason we nevertheless do not restrict the geographical destinations of graduates is that we are interested in all the opportunities with which breadth might be associated. In fact, in this period, over 80% of graduates in Scotland who were from Scottish schools remained in Scotland (Paterson, 1997: 38), but the more important point is that the graduate labour market was common across the UK (Raffe et al., 1999). Giving access to that wider market had long been an important role of the Scottish universities, a characteristic economic function of advanced education in many peripheral economies (Findlay et al., 2008).
The models were run in the R environment using the 'svyglm' function in the 'survey' package which allows weights to be included. Analysis of deviance tables in Sect. 1 of the supplemental material are shown using Type II tests (with the Anova function from the 'car' package in R), which are the summary results of dropping each term in turn from the model shown in the table. We show detailed results by means of selected regression coefficients (Tables 1 and 2) and also predicted proportions. (Comparing logistic regression coefficients for different models is not valid (Mood, 2010)). Where rates of entry are compared in the text (between students with and without breadth), the standard errors were calculated using the function 'vcov' in the 'survey' package. With as many as seven outcomes observed over 13 years, there is a risk of finding spuriously significant results by chance. So in the discussion we concentrate on those comparisons which relate explicitly to the theories about breadth which we are testing, mainly arising from the Scottish educational history sketched above, and we pay attention only to groups of years rather than individual years. Figure 1 shows the growth of upper-second-class degrees, from 6% in 1960, through 12% 1980, to over a third by the early 1990s. That trend is familiar elsewhere in the UK (Yorke, 2009), but the decline of the Ordinary degree is specific to Scotland. That degree was the most common outcome until the mid-1980s, with over 40% of graduates. Then, the proportion fell to around a third in the late-1980s, and 16% between the early 1990s and 2002 (the latter point not explicitly recorded in the figure). As university participation expanded in the late-1980s and 1990s, the relative school attainment of people achieving the different classes of degree changed. For example, the mean relative attainment of people who graduated with first-class Honours fell from around 0.8 in the early 1980s to around 0.6 in the 1990s, and the mean for good Honours moved towards the overall mean as that outcome become the norm (around 0.1 in the early 1980s to 0.02 in 1993). The relative mean attainment of Ordinary graduates was always below average, but moved towards the overall mean as that degree become less popular (from -0.3 in 1983 to -0.2 in 1993).

Analysis
The proportion in the two broad faculty groups was quite stable, with a slowly rising proportion of women who graduated in science and technology, from 36% in 1960 to 43% in 2002. The corresponding proportions of men were 68% and 61%. Because of a change to the recording scheme for the USR in 1984, there was a jump between 1983 and 1984 from 1 to 7% in the proportion of courses which could not be allocated to a faculty, followed over the ensuing years by a fall back to 1%. This short-term fluctuation seems likely to reflect unfamiliarity with a new recording system rather than any real-world changes, and so these cases have been omitted from the statistical models reported below.
The proportion who entered employment without further training rose from a third of the very small group of graduates in 1960 to around a half by the mid-1980s. For those who entered employment, the most notable trend (in Fig. 2) is the reduction in the share taken by professional work, from 80% of the small pool of graduates in 1960, to just under two-thirds in 1980, under a half in 1993, and one third in 2002. There was a concomitant growth of work as associate professionals (from 7% in 1960 to more than twice that in the 1990s). At the end of the series, there was also a large rise to over a third in the proportion entering miscellaneous occupations (see also Purcell et al., 2006). Accompanying this was a rise between 1983 and 1993 in the relative school attainment For full list of variables, and Type II chi-squared tests associated with these models, see Table A1.1 in the supplemental material. In brief, the explanatory variables are: curricular breadth from school, year, sex, school attainment, broad faculty of graduation from university, and interactive effects of curricular breadth with these other variables 1 Good honours means degrees classified as first, upper second, or enhanced Key for statistical significance levels: ** p < 0.01; * 0.01 < p < 0.05; (*) 0.05 < p < 0. For notes, see Table 1 The first and fourth dependent variables are each contrasted with all the others. The 'managerial' and 'associate professional' variables are contrasted only with the categories to their right For full list of variables, and type II chi-squared tests associated with these models, see Table A1.2 in the supplemental material. In brief, the explanatory variables are: curricular breadth from school, year, sex, school attainment, broad faculty of graduation from university, and interactive effects curricular breadth from school with these other variables of managers and a fall in that of professionals-for managers, from 0.07 to 0.17, and for professionals from -0.20 to -0.25. The average relative attainment of associate professionals fluctuated around a fairly stable trend in this same period, from -0.29 to -0.33 in 1993.
These graduates came from changing demographic origins. The female proportion was 42% in 1960, in the mid-40 s in the 1980s, and over a half in 2002. A growing proportion came from advantaged social-class origins, the proportion from classes I and II being 44% in 1960 and 60% from the mid-1980s, but this rise did not exceed the rise in the share of the population from these groups (Burnhill et al., 1988).
Our focus is on the indicator of curricular breadth at secondary school, the trends in which for male and female graduates are shown in Fig. 3. The proportion of female students with breadth rose from 25% in 1960, much less than the male proportion in that year (47%), to well over a half in the 1990s, thus nearly converging with the male proportion. The percentages fell back slightly with the overall expansion to 2002, when they were 54% of men and 51% of women. The main reason for the relative growth of breadth among female students was their growing participation in science: the proportion of women with a science pass from school was 38% in 1960, 59% 1983, around 80% in the early 1990s, and 70% in 2002. The male proportion changed less (in these years, 69%, 90% and 85%). Of the other components of breadth as we have defined it, the proportion with a language fell among both women (90% in 1960 to 41% in 2002) and men (69% to 17%). Women compensated for this to a greater extent than men by means of a growing proportion holding a pass in an aesthetic subjects: from 1960 to 2002, the proportion went from 3 to 17% among men, but 5% to 28% among women. In contrast, the trends in the proportion with mathematics was quite stable: for men, always around 80-90%, and for women rising from 65% in 1960 to around 75-80% from the 1980s onwards. Social subjects also rose similarly: from around 40-45% to around 65-75% for both men and women. The proportion with English was always over 90% for both men and women. Because the female proportion with breadth was lower than the male proportion, we might suspect that females with breadth would be higher-attaining at school than males with breadth. In fact, there was no evidence of this; if anything, the opposite was true until the early 1990s. In 1983, for example, the mean value of the standardised attainment variable among people with breadth was 0.23 for men (s.e. 0.02) and 0.056 for women (s.e. 0.03). A decade later, the values were both 0.12 (each with s.e. 0.02).
We now turn to the statistical models. We start with models that do not control for university attainment. Chi-squared tests for each term in the models are shown in Table A1.1 in the supplemental material. The logistic regression coefficients are in Tables 1 and 2, confined to terms involving breadth in order to economise on space. For each outcome, there is evidence either of an average statistical association between breadth and the outcome, or that the association varies by year, relative school attainment or faculty; there is hardly any sex variation in the association with breadth. We interpret these models in terms of the proportions of graduates which they predict would reach the threshold recorded in their dependent variable. A summary of these interpretations is in Table 3.
For only three outcomes was there no evidence of any statistical association with breadth: among science and technology students, gaining an Ordinary degree, entering an associate profession rather than other occupations, and avoiding other occupations. For most outcomes, there was reliable evidence of a statistical association with breadth, more commonly positive than negative (adjectives which we use in a numerical sense, not as evaluations). The patterns differ somewhat between the two faculty groups, and so we discuss them separately.

Positive statistical association: arts and social science
The clearest instance is entering professional employment rather than any other employment, illustrated in Fig. 4(a). Among female graduates from arts and social science who entered any employment, there was no reliable evidence of a statistical association with breadth in 1960 (p values at high, medium and low attainment being 0.60, 0.49 and 0.41). The male differences were similar (with the same p values). But after that year, the proportion entering professions among those who entered employment was higher among graduates with breadth than among those without breadth, though converging in 2002. For example, the proportion of female graduates entering professional employment with and without breadth in the decade 1991-2002 was 49% against 38% at high attainment, a difference of 11 points (p < 0.001). The differences at medium attainment were 8 points (p = 0.002) and at low attainment were 4 points (p = 0.059). For men, the corresponding associations with breadth were similar to these. Table 3 suggests that the affinity of breadth at school with the Ordinary degree for arts and social science students was confirmed even when the percentage taking that degree was declining. Among female high attainers, the percentage graduating with an Ordinary degree (as distinct from any other degree) in 1987-1990 was 25% with breadth and 17% without (p < 0.001); this 8-point difference was similar at medium and low school attainment. For males with high attainment, the proportions were 27% and 18% (p < 0.001), and again the gap was similar at medium and low attainment. Restricting the data to compare Ordinary against any good Honours degree, the association of breadth with the Ordinary degree was not changed.
For arts and social science graduates who did not enter professional or managerial occupations, breadth was associated with entering an associate profession rather than the category of miscellaneous other occupations, but this association did not persist into the 1990s. Indeed, in the 1990s, for people with low attainment from school, breadth was negatively associated with entering associate professions, suggesting perhaps that Fig. 4 Proportion entering professional employment, by broad faculty of university graduation, sex, relative attainment from school, year, and breadth of study at school. Source: predicted values from model 1 in Table A1.2 (supplemental material). Relative attainment from school: high = one standard deviation above the mean within year; average = mean within year; low = one standard deviation below mean within year some element of specialisation at school was required to avoid non-graduate employment at this level of attainment.

Positive statistical association: science and technology
There were fewer positive statistical associations with school breadth among graduates in science and technology. For men with high attainment from school, there was a positive association with gaining a first-class degree in the mid-1980s, but not later: for high-attaining men in 1983-1986, 22% against 19% (p = 0.02); high-attaining women had a tendency in the same direction (a gap of 1.7% but with p = 0.15). That difference was then enough to yield also an overall difference for any good Honours degree. There were few differences relating to types of employment. Breadth was, however, probably associated in the 1990s with higher rates of entry to managerial occupations (rather than associate professions or miscellaneous occupations) among scientists in employment who had relatively low attainment from school: 22% against 19% for women (p = 0.089), and 22% against 18% for men (p = 0.103).

Negative statistical association
The positive statistical association of breadth with entering professions was mirrored by a mostly negative association with entering managerial employment (rather than associate professions or miscellaneous occupations). For high-attaining female graduates in arts and social science who entered employment, the proportion entering managerial jobs was 12% lower with breadth than without breadth in the 1990s (p = 0.001). The gap at medium school attainment was around 7% (p = 0.012). The pattern for men was similar, though now including the earlier periods at high attainment.
Something the same was the case among scientists in employment who had high attainment from school. In the 1980s, the proportion of high-attaining women and men who entered managerial jobs (rather than associate professions or miscellaneous occupations) was about 7-10% less with breadth than without. Moreover, not all scientists experienced a positive association between breadth and professional employment ( Fig. 4(b)). For those with low attainment in the late-1980s, the proportion entering professions was, for women, 52% with breadth and 57% without (p = 0.009), and, for men, 53% and 59% (p = 0.001). The gaps at medium attainment were about half of these.
The other notable negative statistical association was with gaining a first-class degree among students with medium or low relative attainment from school: for both women and men, the proportions from the 1980s onwards were around 1-2% lower among those with breadth than among those without. These small differences should be set in the context of the low overall percentages gaining a first shown in Fig. 1. The resulting similar difference in gaining a good Honours degree in arts or social science was very small in relation to the overall rise in that proportion. For example, in 1991-2001, the proportion of female arts and social science graduates with medium attainment from school who had a good Honours degree was 53% with breadth and 54% without; the proportions for men were 49% and 52%.

Controlling for degree attainment
Degree attainment was included by adding to the employment models a four-category variable recording type of degree (as in Fig. 1), and its interactive association with breadth (see Table A1.3 in the supplemental material); there was not enough data in some years to allow these interactive effects to vary over time. Predictions then were made using these four categories; for this purpose, the value of school attainment was set to be the mean value in the sample in each year for each degree category.
These additions did not alter the broad pattern. The conclusions which were shown for employment outcomes in Table 2 and summarised in Table 3 were observed at all levels of degree attainment with four changes. The first three are simply refinements of the pattern noted in Table 3: • After the 1980s, the positive association of breadth with professional employment among science and technology graduates was seen only for Ordinary graduates. • The negative association of breadth with entering managerial employment (rather than associate professions or miscellaneous occupations) among arts and social science graduates extended back to the 1980s from the 1990s noted in Table 3. • The negative association of breadth with entering managerial employment (rather than associate professions or miscellaneous occupations) in the 1980s among science and technology graduates was observed only for graduates with good Honours degrees.
Only one showed a different pattern from anything noted in Table 3: • For science and technology graduates in the 1990s, there was a positive association of breadth with entering associate professions (rather than miscellaneous occupations). In no instance was there a reversal of the direction of association with breadth.

Control for social class of origin
Social class was added to the models as an average association, the variation of that association over time, its interactive association with breadth and with sex, and the variation over time in the interactive association with sex. In only two instances was there any evidence of an interactive association of breadth with social class, both concerning arts and socialscience graduates: • The positive association of breadth with entering professional employment was greater for class I and II than for the other classes (but it was clearly positive for all classes). • The positive association of breadth in the 1980s with avoiding other occupations was observed only for class I and II.

Is breadth a surrogate for motivation?
We cannot be sure that the associations which we have found reflect causal effects of breadth, because people who take a broad curriculum may have other characteristics, notably motivation, that contribute to the outcome. The main way in which this analysis tries to allow for that is the control for school attainment. So the question is whether there might remain an un-measured effect of motivation over and above that which is reflected in attainment.
Other sources of data allow some assessment of this problem. The details are in Sect. 3 of the supplemental material. We use three data sources covering most of the period of our main data: a cohort of people born in 1958 (who, if they entered university from school, would have done so in the mid-1970s); a similar cohort born in 1970 (entering in the late-1980s); and surveys of school leavers who would have entered between the late 1980s and the early years of the new century. (The penultimate school-leavers survey provided the data on 2002 graduation in our main analysis.) There are two conclusions of this supplemental analysis. One is that, although following a broad curriculum is indeed associated with motivation and with attitudes to school, that association is explained statistically by control for attainment. Thus, the models in the main text, all of which control for school attainment, probably show the association of curricular breadth discounting motivation and attitudes. The second conclusion from the supplemental analysis is that students who are motivated by the explicitly curricular aim of studying a specific subject were probably rather less inclined to follow a broad curriculum than students who did not have that motivation. This indirectly suggests that following a broad curriculum is probably linked to students' curricular motivation, and is not merely a surrogate for general motivation; thus, even if an association with a broad curriculum does not reflect the content of the curriculum, it perhaps does reflect the idea that breadth is intrinsically worthwhile.
In this same context, it is worth noting that, in principle, controlling for school attainment might over-compensate, and underestimate the association with breadth. This would happen if, for example, breadth of study itself affected school attainment. However, this is less of a problem here than it might be in other contexts because the selection for entry to university was itself based on that attainment. Thus what we are truly interested in is the statistical association with breadth only at relatively high attainment.

Comparison with breadth defined by Dolton and Vignoles
Having thus detected several statistical associations of secondary-school breadth with university outcomes, our final step is to compare these results with an adaptation of the analysis of Dolton and Vignoles (2002b), which we refer to as DV breadth. The proportion with this definition of breadth rose from 20% in 1960 to 42% in 1983, 54% in 1991 and 58% in 2002. DV breadth was somewhat more restrictive than our measure. Of people with our definition of breadth, 51% had DV breadth in 1960, rising to 75% in 1983, 80% in the 1991, and 88% in 2002. On the other hand, of people with DV breadth, around 90% had our definition of breadth from 1960 to 1993, falling back only to 80% in 2002. The analysis was rerun with DV breadth in place of the definition which we have been using. A summary of the comparisons is in Sect. 2 of the supplemental material. The broad conclusions were similar, but the association with DV breadth was sometimes weaker, and it also had negative associations in several instances where our definition showed no association, notably on gaining a good Honours degree or an Ordinary degree in science or technology. Coding DV breadth as a categorical variable with three values (0-2, 3, 4 +) did not change the conclusions either, because the statistical associations with the three categories were mostly ordered: that is, the strongest association was with the category '4 or more', and the category '3' had an intermediate association. This conclusion suggests that no significant substantive information about the statistical associations with breadth is lost by treating it as a dichotomous variable.

Conclusions
The main strengths of the analysis lie in the length and quality of the time series. In most respects, we have been able to consider graduates over four decades, from 1960 to 2002, thus including all three main phases of university expansion in that time-the 1960s, the 1980s and the 1990s. The data allowed us to include historically specific definitions of curricular breadth at school in Scotland. However, some of these strengths are obtained at the price of important weaknesses. The data come from three different sources, and so comparability of survey methods and of forms of coding cannot be guaranteed. The sample sizes available in 1960 and 2002 were small, and we could not extend the analysis beyond 2002. These considerations have forced the analysis to be in terms of broad categories of university faculty, attainment, and employment.
Our general conclusion is that high-school curricular breadth is indeed associated with several important long-term outcomes, but that these associations are neither uniformly positive nor uniformly negative. Breadth was associated with entry to professions rather than to managerial occupations, and to avoiding low-status occupations. For arts and social science graduates who did not enter full professions or management, breadth was associated with entering associate professions. All these positive associations were more true of arts and social science than of science and technology. In science and technology, breadth also led to attaining an upper-second-class degree or better. In arts and social science, breadth was linked to the Ordinary degree, which was the traditional Scottish expression of breadth at university, but which was taken by drastically declining student numbers in this period.
These are all positive associations with breadth (though negative from the point of view of managerial careers). There were also specific negative associations. Breadth was associated with not reaching the highest levels of degree for students with middling or low relative attainment from school. These levels of attainment are high by the standards of most school leavers, but it may be that breadth at school could have detracted from the specialist focus which relatively weaker students would require to attain most highly. The rising relative school attainment of entering management along with the negative association with breadth may similarly be a reflection of greater specialisation of recruitment. The positive association of breadth with the Ordinary degree may be read in this way too-that people with a specialised curriculum from school were more likely to gain an Honours degree than an Ordinary. Thus, the decline of the status of the Ordinary degree would have been reinforced if specialised study was rising in status (McPherson & Neave, 1976: 104-23;Neave & Cowper, 1979).
This question of the association between school curricular breadth and university outcomes has rarely been investigated previously, partly because there are few education systems that, like Scotland, provide a mixture of university students with and without breadth and also a standardised measure of school attainment. Baccalaureate systems make breadth compulsory among entrants from secondary school. Free-choice systems (such as with A-levels) often produce only a small minority of students with the kind of breadth which we have considered here. The most notable free-choice system globally is in the USA, but it does not have the standardised measures of school attainment that is available in Scotland and in other European systems. Because about one half of the graduates in our data had breadth from school, the scope for comparing people with and without breadth was strong.
We have compared our findings with the results obtained when rerunning the analysis using the definition of breadth from one of the few previous studies to have considered these questions, by Dolton and Vignoles (2002b). They looked only at earnings and found no association with breadth, including in Scotland. Replicating their measure of breadth gave similar results to ours, though weaker in several respects, and also gave additional negative associations. It is possible that one explanation of these authors' finding of no association may be that positive and negative associations at the stage of education which we have investigated might cancel each other. For example, the negative association with the Dolton and Vignoles measure of breadth of gaining a first-class degree and of entering managerial occupations might depress earnings, while the positive association with entering professions and avoiding low-status occupations might increase them.
Acknowledgements I am grateful to the UK Data Archive for data from the National Survey of 1960 University Graduates (study number 67036) and from the Universities' Statistical Record (study number 3456), and to Dr Linda Croxford and the UK Data Archive for data from the Scottish School Leavers ' Survey, 1996' Survey, -2004.

Funding The research was funded by a Leverhulme Major Research Fellowship (grant number MRF-2017-002).
Code availability From author.

Declarations
Ethics approval The analysis uses secondary data, for which the original consent is described in the documentation held by the UK Data Archive (see 'availability of data' above). Ethical approval for the secondary data analysis was given by the research ethics committee of the School of Social and Political Science, Edinburgh University, on 27 March 2017.

Conflicts of interest None.
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