A1 Appendix 1: Modelling segregation
A1.1 As part of the EYT project a methodology was developed to estimate social segregation in terms of the "variance ratio", using multilevel statistical modelling (Croxford and Paterson 2006). The "variance ratio" may be thought of as measuring the extent to which working class pupils are concentrated in some schools, and upper class pupils are concentrated in others. A high variance ratio indicates that the social classes are isolated from each other in different schools, while a low variance ratio indicates that schools have mixed social intakes.
A1.2 Multilevel modelling allows data analysis to take account of the hierarchical nature of the education system. With respect to segregation indices, multilevel modelling makes it possible to analyse differences in the distribution of working class pupils between schools, while taking account of differences in the size of schools and local authorities, and to calculate whether differences in indices of segregation have statistical significance (or whether they are likely to have arisen by chance). The test of statistical significance is of particular importance when using survey data, such as SSLS, that are subject to sampling errors.
Differences in segregation across Scotland
A1.3 Figure A1.1 illustrates the index of segregation (measured by the variance ratio). The index focuses on the isolation of the lower two social classes (ie working class and unclassified) from the higher two social classes (ie managerial/professional and intermediate). It estimates the extent to which low- SES pupils are concentrated in low- SES schools.
A1.4 The estimates of segregation in Figure A1.1 are shown by the small squares 12. The line through each square shows the 95% confidence intervals for the estimate. (We can say with 95% confidence that the true measure of social segregation lies between the upper and lower bounds of the confidence intervals).
A1.5 Three estimates are shown for each cohort. The first (and lowest) point shows estimated segregation within the SSLS sample as a whole. The second point shows estimated segregation among the sub-sample (71% of the SSLS sample) who attend schools in urban or large city areas. The third (and highest) point shows estimated segregation among the sub-sample (37%) who attend schools within the four large cities (Aberdeen, Dundee, Edinburgh and Glasgow). It is clear from Figure 4.1 that segregation is considerably higher in the cities than in Scotland as a whole, or in urban areas more generally.
A1.6 We can make comparisons between the estimates by using the confidence intervals. For example, looking at the 2002 cohort on the far right of Figure A1.1, the estimate for "All" is a little lower than the estimate for "Urban", so it appears that segregation is higher in urban areas than in Scotland as a whole. However, the confidence intervals for "All" and "urban" overlap, so we must conclude that the level of segregation in urban areas is not significantly different from that in Scotland as a whole. By contrast, the estimate for "City", appears considerably higher than the estimates for "All" or "Urban" areas - and the confidence intervals do not overlap - so we can conclude that the levels of segregation in the four cities are significantly higher than in other parts of Scotland.
A1.7 The pattern of trends over time is less clear. In Scotland as a whole segregation appears to have risen slightly from 1984 to 1988, and subsequently fallen. Unfortunately, statistical tests do not provide support for these overall trends, so we cannot be sure whether they are real or merely the result of chance.
A1.8 One result that is statistically significant is that segregation in 2002 is lower than in 1988 - a result that may be the consequence of a number of additional factors including closure or merger of schools as the population has declined.
A1.9 Although in urban and city areas there also appears to have been an upward trend from 1984 to 1988 followed by decline -these trends are not statistically significant.
Figure A1.1 Segregation of lower social class pupils (working class+unclassified) by cohort and area
(Index derived from variance ratio with 95% confidence intervals)
