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Attainment in public-sector and independent schools in Scotland, 1994, by social class and parental education: some results for discussion

by Lindsay Paterson

This Note arose originally in response to a request for a research briefing by BBC Newsnight Scotland, 16 October 2002. It compares attainment in Higher Grade examinations of children in the public and independent sectors of schooling in Scotland, paying particular attention to children with well-educated, middle-class parents.

• Data and methods
• Results
• Discussion
• References
• Tables

Data and methods

The data come from the 1995 Scottish School Leavers Survey, which was an approximately one-in-ten sample of leavers from school session 1993-4, excluding those registered as having special educational needs. Fuller details of the survey are provided by Lynn (1996). This is the most recent survey that is available in Scotland for detailed analysis of school attainment. The response rate was 70% (Lynn, 1996, p. 40). A weighting variable is used to correct for non-response bias. However, re-running the analysis reported below without the weights led to much the same results as here.

The School Leavers Surveys are available from the social science data archive at Essex University (http://www.data-archive.ac.uk/). They were funded by the Scottish Office, and were carried out by the National Centre for Social Research (http://www.natcen.ac.uk/). Data on examination passes were linked to the survey data directly from information held by the Scottish Examination Board: see Tinklin and Raffe (1999, p. 4). The analysis and interpretation reported here are the responsibility of the present author.

In the 1990s, the independent sector in Scotland educated about 5.6% of secondary pupils (Scottish Office, 1995, table 8). (For present purposes, the one grant-aided school and the one self-governing school are defined as independent; this involved only 6 sample members.) A history of the independent sector is provided by, for example, Walford (1988) and Highet (1969).

A few independent schools do not present their pupils for Scottish examinations, using the A level system from England instead. In an attempt to control for this, the present analysis omits the five independent schools in the data set where no leavers had passed at least 3 Highers. This probably slightly biases the analysis against the public sector, since some schools there also present some pupils for A levels as well as Highers. In the event, the omission made very little difference to the results. The total remaining sample size was 3212, of whom 189 were in the independent sector. As a weighted proportion, this was 5% in the independent sector, close to census figures. The sample for analysis then contained 32 independent schools, and 364 public schools.

Social class is collected in the survey by means of information on parental occupations, which is then recoded as Registrar General's class. This is available separately for mothers and fathers. Parental education is recorded as the age at which each parent left school. The distribution of these variables in the two sectors is shown in Table 1, where it can be seen that the independent sector has far more students with middle class or well-educated parents than the public sector.

Validly comparing attainment in the sectors is always fraught with difficulties, because the leavers survey contains no information on pupils' attainment upon entry to secondary school. Thus a truly 'valued added' analysis is not feasible. In the absence of such information, measures of socio-economic status are often used as a surrogate for educability (Paterson, 1991; Willms, 1992, pp. 52-4). This is undoubtedly not fully satisfactory, especially for working class children who might have entered the independent sector on bursaries which required them to demonstrate a certain level of prior academic attainment. In other words, the relatively small number of working-class children in the independent sector would not be comparable to the working-class children in the public sector. In the mid-1990s, about 2,600 children each year were in the independent schools on publicly funded bursaries under the Assisted Places Scheme (Walford, 1988). For this reason, attention towards the end of the present note is concentrated on a group for whom the available socio-economic indicators might be a more valid surrogate for educability - the children of well-educated, middle class parents. This is defined to be children whose father was in a professional occupation (the first two class categories) and who lived with two parents both of whom stayed on in school to at least age 17. Such families constituted 29% of the pupils in independent schools, and about 7% of all pupils. The marketing of independent schools is aimed particularly at this group (eg, Sunday Herald, 2002). Other data sources show that one half of such parents have some type of higher-education qualification (eg, the Scottish Election Survey, 1997). Extensive research from many educational systems suggests that such students can draw on a great deal of parental support at home (Paterson, 1991), which is the basis for saying that, in this group, measures of socio-economic circumstances are a reasonable surrogate for educability.

The outcome variables are defined as four dichotomous indicators of attainment - passing 3 or more Highers, passing 5 or more Highers, gaining 3 or more A grades in Highers in school fifth year, and gaining 3 or more A grades in Highers in either fifth year or sixth year. The criterion of 3 or more Highers is often thought of informally as the threshold for entry to degree-level higher education. The criterion of 5 or more Highers indicates a very good level of school attainment. Gaining a good number of A grades, especially in one examination sitting, would generally be needed for entry to those universities where selection is most competitive. The proportions of the whole sample reaching these levels in the two sectors are shown in Table 2. For the first two criteria, comparison can also be made with the census-type information reported in official publications. These are also shown in the table, and the discrepancies of the sample from them can be seen to be relatively small, although there may be some overestimate of the proportion gaining 3 or more Highers in the independent sector; the consequence will be that, in the analysis below, there may be a small bias in favour of the independent sector for that criterion. With that exception, the sample seems to have been fairly representative.

The methods used are standard ones in research in this area. For example, the proportion passing 3 or more Highers was coded as a dichotomous variable, and then logistic regression was used to investigate the statistical effect of school sector with and without certain controls (Aitkin et al, 1989). The controls were father's and mother's Registrar General occupational class, and father's and mother's age of leaving full-time education, as in Table 1. The interactive effect of parental education and sector was added, to allow for different effects at different levels of parental education. Similarly, the interactive effect of father's class and sector was added too. The statistical package SPSS was used for the analysis, supplemented by the multi-level modelling software MLWin for the calculation of school-level residuals (Goldstein et al, 1998).

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Results

Tables 3 to 6 show the results of the logistic regressions, separately for each of the four criteria. They each have a common structure. In the first pair of columns, there is a null model showing the marginal effect of sector: this simply replicates the survey information in Table 2. The next pair of columns shows the results of controlling for the main effects of father's and mother's class, father's and mother's education, and school sector. For the two tables recording the numbers of A grades, reliable estimates could be calculated only if the final two categories of father's class (V and unclassified) were amalgamated, because no sample members from the unskilled manual class achieved 3 or more A grades. In the third pair of columns, the interactive effects of parental education and sector and of father's class and sector are added. The coefficients are the logarithms of the odds ratios of the proportion reaching the criterion in question in that category of the explanatory variable, compared to the omitted reference category as indicated in the table. (In SPSS parlance, this is using the 'simple' subcommand of the logistic regression command.) The standard errors of these coefficients are given in the second column of each pair. When interactive effects are added, the parameter estimates for the main effects no longer mean the same as they did when there were no interactive effects: for example, the main effect of school sector then means the effect among people whose father is not in a professional job and who do not have two parents educated to 17 years.

In all the tables, the class and parental-education gradients in the models labelled (2) are as might be expected, and merely confirm the results of many other studies. The average school sector coefficient is generally cut in half merely by adding the main effects of the socio-economic variables, and indeed the remaining sector effect is smaller than the largest of these socio-economic effects: thus even in this model, socio-economic circumstances are seen to matter more than sector. Table 7 illustrates this. It shows what the performance in the independent sector would be if that sector's socio-economic composition were the same as the composition of the public sector, allowing only for the main effects of socio-economic variables as shown in the models labelled (2) in Tables 3 to 6. For these illustrative purposes, the calculations are done holding constant the actual level of attainment in the public sector (as estimated from the sample, and shown in Table 2). Consider the calculation for 3 or more Highers as an example. The sector coefficient of 1.23 in Table 3 is the logarithm of the ratio of the odds of reaching this level in the two sectors. So the odds ratio is the anti-logarithm of this, which is 3.42. The actual odds ratio in the public sector is (from Table 2) 0.28/(1-0.28), which is 0.39. So the odds ratio for the independent sector is 3.42 x 0.39, which is 1.33, and hence the adjusted proportion for the independent sector is 1/(1+1.33), which is 0.57. That is the figure entered in Table 3.

As shown in Table 3, the proportion of the entire sector gap that may, in this way, be explained by socio-economic composition is 38% for the criterion of 3 or more Highers, 55% for 5 or more Highers, 76% for 3 or more A grades at Higher in fifth year, and 71% for 3 or more A grades in fifth or sixth year.

Further light is cast on these average sector differences by the results of a multi-level replication of the logistic regressions. The fixed parts of the models were dummy indicators of father's class, mother's class, and parental education, supplemented by the sample proportion of people with two parents educated to age 17 or beyond, a measure of the influence of the social composition of schools. (However, the results without that last variable were very similar to models that did not contain it.) The random levels were pupil and school, and only the constant term was allowed to vary among schools. So the school-level residual is a measure of the extent to which individual schools vary, controlling for the socio-economic status of their pupils; these residuals are measured on the same scale as the regression coefficients. A positive residual indicates a school where attainment is higher than would be expected from the socio-economic status of its pupils; likewise, a negative residual is lower-than-expected attainment.

The distribution of these residuals (as five percentiles) is shown in Table 8, for the independent schools, for all public-sector schools, and for public sector schools in those areas of the country where there was direct competition with independent schools. The average separation of the sectors is seen to be primarily to do with the independent sector's having a longer tail of schools with large positive residuals. For each outcome variable, and whether we look at all public sector schools or only at those in local competition with independent schools, the public schools with the largest positive residuals are well into the range of the above-average independent schools. Put differently, after controlling for socio-economic status, the residuals in the top quarter of the distribution for public sector schools are broadly comparable to the top half of the residuals for the independent schools, especially given the size of the standard errors.

For the reasons of validity of comparison of sectors noted above, we now concentrate attention on pupils in the category in which both parents left school at age 17 or older and the father was in a professional occupation (the first two classes). The raw figures for these students are shown in the first two columns of Table 9, and it can be seen that, even without any modelling, the sector gap among them (column 3) is far smaller than the sector gaps shown in Table 1. In the modelling, because there were so few students in the independent sector with no parent educated to 17 or over, the bottom four categories of the parental education variable were amalgamated for fitting this interactive effect, thus leaving three categories: both 17, one to 17, and the rest. The further models in each of Tables 3 to 6 show that, for each criterion, the difference between sector varies according to the level of parental education and father's class. The resulting fitted proportions for the independent sector are shown in Table 9, calculated in the same way as for Table 7. The relevant log odds ratios that are the starting points for the calculations are derived by adding together the appropriate coefficients in Tables 3 to 6. For example, for 3 or more Highers, the log odds ratio for the difference between sectors among students whose father was in a professional job and both of whose parents left school at age 17 or older is 1.24 - 0.49 - 0.33, which is 0.42. The calculation then proceeds as illustrated above for Table 7.

With the exception of the criterion of 3 or more Highers, the adjusted differences are even smaller than the raw differences (column 5), and are essentially negligible. This further reduction has happened because, even in the very socially advantaged group to which the table relates, the students who are in the independent sector are somewhat more socially advantaged (in terms of the full set of variables in the model) than their counterparts in the public sector. Even for 3 or more Highers, the adjusted gap (8 points) is only one sixth of the average gap between sectors for all students, as shown in Table 2.

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Discussion

This analysis should be interpreted as indicative only. Undoubtedly the variables available from the survey do not control for all the differences between students in the two sectors - in other words, do not control for all selection bias. Because the independent schools select on academic grounds explicitly and implicitly, if we did have a measure of attainment upon entry to secondary we would almost certainly find smaller differences between the sectors than have been reported here.

Although the survey is the most recent available for this work, it is nevertheless some seven years old. The analysis will be replicated when the 1999 leavers survey is released, due at the end of 2002. However, there are no reasons to believe that the results would be substantially different if more recent data were available. Indeed, inspection of descriptive statistics from earlier leavers surveys back to 1981 suggests that the results have been stable for some time, and so the present results do not seem to have been unduly influenced by the relatively small sample size which the independent sector yields in any particular survey. If anything, there might have been some convergence in attainment between the sectors recently, since the average attainment (not controlling for socio-economic characteristics) shows a small convergence between the mid-1990s and 1999, attainment in the public sector having risen more rapidly than attainment in the independent sector: in 1999, the gap for 3 or more Highers was 35.1 percentage points, compared to 37.7 in 1994; for 5 or more, it was 32.4 compared to 33.5 (Scottish Office, 1995, table 8; Scottish Executive, 2001, table 5).

There are three main conclusion of this analysis:

• A large part of the sector difference may be explained by the socio-economic status of the families from which the students come. The high rates of examination success in the independent schools is probably in large measure due to the parents of the students who attend them. (Table 7)

• The school-level residuals, after controlling for socio-economic status, of the public-sector schools have an upper tail which is not distinguishable from the upper half of the distribution of school-level residuals from the independent sector, whether we make the comparison nationally or locally. (Table 8)

• The sector difference is particularly small for students who might be expected to do well in any sector, because they can draw on a great deal of parental support at home - students whose father worked in a professional occupation and who lived with two parents both of whom stayed on at school to at least age 17. (Table 9)

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References

Aitkin, M., Anderson, D., Francis, B. and Hinde, J. (1989), Statistical Modelling in Glim, Oxford: OUP.

Goldstein, H., Rasbash, J., Plewis, I., Draper, D., Browne, W., Yang, M., Woodhouse, G. and Healy, M. (1998), A User's Guide to MLWin, London: Institute of Education.

Highet, J. (1969), A School of One's Choice, London: Blackie.

Lynn, P. (1994), The 1994 Leavers, Edinburgh: Scottish Office.

Paterson, L. (1991), 'Socio-economic status and educational attainment: a multi-dimensional and multi-level study', Evaluation and Research in Education, 5, 97-121.

Scottish Executive (2001), Scottish School Leavers and their Qualifications: 1998-99, Statistical Bulletin, Edinburgh: Scottish Executive.

Scottish Office (1995), Scottish School Leavers and their Qualifications 1983-84 to 1993-94, Statistical Bulletin Edn/E2/1995/14, Edinburgh: Scottish Office.

Sunday Herald (2002), 'Going private', Sevendays Section, 6 October, p. 2, col. 5.

Tinklin, T. and Raffe, D. (1999), Entrants to Higher Education, Edinburgh: Centre for Educational Sociology.

Walford, G. (1988), 'The Scottish Assisted Places Scheme: a comparative study of the origins, nature and practice of the ASPs in Scotland, England and Wales', Journal of Educational Policy, 3, pp. 137-53.

Willms, J. D. (1992), Monitoring School Performance, London: Falmer.

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Tables

 Table 1: Distribution of socio-economic variables, by school sector

percentage	public	independent
father's occupational class
I (professional)	6	31
II (semi-professional)	20	41
IIInm (routine non-manual)	8	8
IIIm (skilled manual)	28	5
IV (semi-skilled manual)	10	2
V (unskilled manual)	3	0
unclassified	25	13
mother's occupational class
I (professional)	1	7
II (semi-professional)	20	43
IIInm (routine non-manual)	24	14
IIIm (skilled manual)	4	3
IV (semi-skilled manual)	12	3
V (unskilled manual)	9	0
unclassified	30	30
ages at which parents left school
both 17 or older	9	35
one 17 or older	17	32
one 16, none 17 or older	31	19
both 15	24	2
one 15, one don't know	4	1
both don't know	15	11
sample size	3023	189

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Table 2: School attainment, by school sector

percentage	public	independent
survey estimate of proportion who left school with  3 or more Highers	28	75
population proportion who left school with  3 or more Highers*	28	66
survey estimate of proportion who left school with 5 or more Highers	16	54
population proportion who left school with  5 or more Highers*	16	50
survey estimate of proportion who passed 3 or more Highers at grade A in fifth year	3.5	18.6
survey estimate of proportion who left school with 3 or more Highers at grade A	4.3	22.7
sample size for survey estimates	3023	189

*source of population proportions: Scottish Office  (1995, table 8)

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Table 3: Results of logistic regression for 3 or more Highers

	(1) sector only		(2) add main effects		(3) add interactive effects
variable (reference category)	coefficient	standard error	coefficient	standard error	coefficient	standard error
father's class (class V):
I			1.73	0.30	1.58	0.34
II			1.30	0.28	1.15	0.32
IIInm			1.16	0.29	1.15	0.29
IIIm			0.43	0.28	0.43	0.28
IV			0.44	0.29	0.44	0.29
unclass.			0.35	0.28	0.34	0.28
mother's class (class V):
I			1.76	0.36	1.74	0.36
II			0.86	0.17	0.85	0.17
IIInm			0.79	0.16	0.78	0.16
IIIm			0.29	0.23	0.30	0.23
IV			0.27	0.18	0.27	0.18
unclass.			0.26	0.17	0.27	0.17
parental education (both 15):
both 17			1.19	0.14	0.99	0.21
one 17			0.63	0.11	0.66	0.22
one 16			0.07	0.10	0.07	0.10
one 15, one DK			0.13	0.20	0.14	0.20
both DK			0.25	0.12	0.24	0.12
sector (public):
indep.	2.04	0.15	1.23	0.17	1.24	0.18
interactive effects:
indep. by both 17					-0.49	0.40
indep. by one 17					0.08	0.41
indep. by prof. father					-0.33	0.35
reduction in deviance			720.9		3.4
change in degrees of freedom			17		3

see text for explanation

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	(1) sector only		(2) add main effects		(3) add interactive effects
variable (reference category)	coefficient	standard error	coefficient	standard error	coefficient	standard error
father's class (class V):
I			1.71	0.41	1.40	0.43
II			1.33	0.39	1.01	0.42
IIInm			1.21	0.41	1.18	0.41
IIIm			0.39	0.40	0.38	0.40
IV			0.33	0.42	0.32	0.42
unclass.			0.44	0.40	0.41	0.40
mother's class (class V):
I			1.80	0.37	1.76	0.37
II			1.01	0.24	0.99	0.24
IIInm			0.81	0.24	0.79	0.24
IIIm			0.46	0.32	0.45	0.32
IV			0.39	0.27	0.40	0.27
unclass.			0.58	0.24	0.58	0.24
parental education (both 15):
both 17			1.31	0.15	1.12	0.21
one 17			0.56	0.14	0.49	0.21
one 16			0.09	0.13	0.08	0.14
one 15, one DK			-0.09	0.29	-0.08	0.29
both DK			0.21	0.16	0.19	0.16
sector (public):
indep.	1.85	0.13	0.95	0.15	1.09	0.16
interactive effects:
indep. by both 17					-0.46	0.36
indep. by one 17					-0.17	0.36
indep. by prof. father					-0.70	0.33
reduction in deviance			564.8		8
change in degrees of freedom			17		3

see text for explanation

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Table 5: Results of logistic regression for 3 or more A grades at Higher in fifth year

	(1) sector only		(2) add main effects		(3) add interactive effects
variable (reference category)	coefficient	standard error	coefficient	standard error	coefficient	standard error
father's class (class V):
I			1.71	0.31	1.57	0.36
II			1.26	0.29	1.11	0.35
IIInm			1.07	0.36	1.07	0.36
IIIm			0.30	0.35	0.33	0.35
IV			0.36	0.45	0.39	0.45
mother's class (class V):
I			1.97	0.73	1.94	0.73
II			1.28	0.65	1.24	0.65
IIInm			1.22	0.65	1.19	0.65
IIIm			-0.64	1.13	-0.65	1.13
IV			0.46	0.73	0.46	0.73
unclass.			1.12	0.65	1.11	0.65
parental education (both 15):
both 17			1.80	0.32	1.55	0.38
one 17			1.05	0.32	0.91	0.39
one 16			0.27	0.33	0.22	0.34
one 15, one DK			0.16	0.70	0.15	0.70
both DK			0.36	0.38	0.31	0.38
sector (public):
indep.	1.84	0.18	0.75	0.20	0.96	0.25
interactive effects:
indep. by both 17					-0.63	0.53
indep. by one 17					-0.25	0.55
indep. by prof. father					-0.36	0.52
reduction in deviance			252.3		2.5
change in degrees of freedom			16		3

see text for explanation

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	(1) sector only		(2) add main effects		(3) add interactive effects
variable (reference category)	coefficient	standard error	coefficient	standard error	coefficient	standard error
father's class (class V):
I			1.80	0.30	1.75	0.35
II			1.41	0.28	1.36	0.34
IIInm			1.09	0.34	1.10	0.34
IIIm			0.60	0.31	0.63	0.31
IV			0.46	0.41	0.49	0.41
mother's class (class V):
I			1.51	0.57	1.49	0.57
II			0.92	0.47	0.88	0.47
IIInm			0.74	0.48	0.71	0.48
IIIm			-0.20	0.71	-0.19	0.71
IV			0.40	0.53	0.39	0.53
unclass.			0.57	0.48	0.58	0.48
parental education (both 15):
both 17			1.51	0.27	1.24	0.34
one 17			0.99	0.26	0.90	0.33
one 16			0.10	0.28	0.07	0.28
one 15, one DK			0.21	0.58	0.19	0.58
both DK			0.07	0.34	0.03	0.34
sector (public):
indep.	1.87	0.17	0.86	0.19	0.98	0.25
interactive effects:
indep. by both 17					-0.80	0.49
indep. by one 17					-0.11	0.50
indep. by prof. father					-0.10	0.50
reduction in deviance			274.9		4.1
change in degrees of freedom			16		3

see text for explanation

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Table 7: Sector difference, controlling for main effects of socio-economic variables

	actual in public schools (Table 2) (%)	adjusted in independent schools* (%)	adjusted gap (diff. of first two columns)	proportionate reduction from actual gap (see Table 2) (%)
3 or more Highers	28	57	29	38
5 or more Highers	16	33	17	55
3 or more As in fifth year	3.5	7.1	3.6	76
3 or more As in fifth or sixth year	4.3	9.6	5.3	71

* estimate of what the proportion would be in independent schools if their students  had the same socio-economic composition as students in the public schools, using sector coefficient in the  models labelled (2) in Tables 3 to 6.

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Table 8: Distribution of school-level residuals in models controlling for main effects of parents' class and education, and for proportion of well-educated parents, but not for school sector

	school-level variance (standard error)			percentiles of school-level residuals					average variance of school-level residuals
				10th	25th	50th	75th	90th
3 or more Highers	0.18 (0.06)	public, all Scotland		-0.21	-0.13	-0.04	0.12	0.25	0.14
		public, in areas with indep. schools		-0.25	-0.15	-0.05	0.07	0.21	0.15
		indep.		-0.06	-0.004	0.08	0.20	0.34	0.15
5 or more Highers	0.20 (0.07)	public		-0.19	-0.12	-0.04	0.08	0.25	0.16
		public, in areas with indep. schools		-0.21	-0.12	-0.05	0.07	0.20	0.17
		indep.		-0.24	-0.09	0.09	0.27	0.55	0.16
3 or more As in fifth year	0.36 (0.19)	public		-0.17	-0.10	-0.04	-0.002	0.23	0.32
		public, in areas with indep. schools		-0.21	-0.09	-0.03	-0.01	0.15	0.33
		indep.		-0.33	-0.13	0.02	0.14	0.61	0.30
3 or more As in fifth or sixth years	0.29 (0.16)	public		-0.15	-0.09	-0.03	0.03	0.19	0.26
		public, in areas with indep. schools		-0.15	-0.07	-0.03	-0.004	0.15	0.27
		indep.		-0.26	-0.11	0.04	0.21	0.47	0.24

 

*The models were multi-level versions of the models numbered (2) in Tables 3 to 6, but including as an extra explanatory variable the sample proportion of students who had both parents educated to age 17 or older, and without the variable for school sector: see text. The residuals are thus on a logistic scale, like the regression coefficients in Tables 3 to 6.

The areas with independent schools are defined to be the 10 (out of 32)  local authority areas where at least one respondent in the survey  left from an independent school. This covered 140 public sector schools, out of the 364 in the sample as a whole.

	(1)	(2)	(3)	(4)	(5)
	actual in public schools (%)	actual in independent schools (%)	actual gap (col 2 minus col 1)	adjusted in independent schools* (%)	adjusted gap (col 4 minus col 1)
3 or more Highers	72	78	6	80	8
5 or more Highers	57	61	4	55	-2
3 or more As in fifth year	19	25	6	19	0
3 or more As in fifth or sixth year	21	27	6	23	2
sample size	215	54

* estimate of what the proportion would be in independent schools if this group of students in these schools had the same socio-economic composition as the corresponding group of students in the public schools, using sector coefficient in the  models labelled (3) in Tables 3 to 6.

(Published Online: 2 November 2002, updated 7 November 2002)