The dataset is available to download from the website of ‘The Detail’. The webpage carrying the story relating to the data is at:
http://www.thedetail.tv/issues/152/exam-results-2012/gcse-and-a-level-results-for-all-nis-schools
The actual dataset, available as an Excel spreadsheet, can be
downloaded from the following link that appears on the above webpage:
http://www.thedetail.tv/system/uploads/files/203/original/Full%20exam%20 result%20data%20released%20by%20the%20Department%20of%20 Education.xlsx?1354103023
The dataset provides information for 211 of the 215 post-primary
schools in Northern Ireland. The analysis below focuses on the following variables extracted from the dataset:
School type (two dummy variables representing grammar schools and integrated schools respectively. Secondary schools were therefore used as the reference category)
Management type (one dummy variable representing catholic schools, with all other schools representing the reference category in this case)
fsm - percentage of young people in each school entitled to free school meals (variable centred)
sen - percentage of young people in each school with special educational needs (variable centred)
size - total number of young people enrolled at the school (variable centred)
gcses - percentage of eligible young people achieving five or more GCSE A*-C grades, including English and maths (actual percentages)
Analysis
Various regression models were fitted to the data, with ‘gcses’ as the dependent variable. Details of the models are provided in Table 9. It can be seen that Model 1 is the most parsimonious model that best fits the data.42 As the variables ‘fsm’, ‘sen’ and ‘size’ have all been centred then the constant represents the estimated mean score for the reference category of schools, in this case secondary, non-Catholic schools.
As Model 1 indicates, on average, and when controlling for intake differences (namely, the percentage entitled to FSM, the percentage with SEN and the size of the school), 42.2% of young people attending non-Catholic secondary schools are likely to achieve the GCSE
benchmark of five or more A*-C passes, including maths and English.
The model also suggests that this figure increases by 8.8 percentage points for those attending a Catholic school and by a further
25.6 percentage points for those attending a grammar school.
42 The dummy variable ‘integrated’ was added to Model 1 but it was found not to add anything significant to the model and so was removed. What this indicates is that, once the other variables in the model are controlled for, there is no difference in the GCSE performance of young people in integrated schools compared to secondary schools (the reference category).
Models 2 to 5 confirm that this added value of attending a grammar school is not mediated by any of the other variables listed. In other
words, this grammar school effect of a boost in 25.6 percentage points is likely to consistent across all types of school.
Table 9: Linear Regression Models Fitted to School-Level Data (Coefficients with Standard Errors in Parentheses)
Model 1 Model 2 Model 3 Model 4 Model 5 constant
Adjusted R2 77.79% 77.75% 77.70% 77.73% 77.94%
Findings
From Model 1, we can estimate what a particular type of school is likely to achieve in terms of the percentage of its young people attaining the GCSE benchmark of five or more GCSE grades A*-C, including English and maths:
Non-Catholic Secondary Schools 42.2%
Catholic Secondary Schools 51.0%
Non-Catholic Grammar Schools 67.8%
Catholic Grammar Schools 76.6%
The figures above are based upon the school-level data and provide the best and most reliable estimate of what each of the four types of school is likely to achieve with an average intake of young people.43 In this case, the average intake is simply the mean scores for the three variables
‘fsm’, ‘sen’ and ‘size’. As such, the above estimates are based upon a school with:
21% of young people entitled to free school meals
22% of young people with special educational needs
total enrolment of 685 young people
To estimate the ‘grammar school effect’, Model 1 was run again but with the variable ‘catholic’ removed. This gave a coefficient for the constant of 45.530 (se = 1.276) and for the dummy variable ‘grammar’
of 29.236 (se = 3.041). This indicates that the average performance of non-grammar schools, based on an average intake, is estimated to be 45.53% of pupils achieving the GCSE benchmark. For the average grammar school, with the same intake, the performance is expected to increase by 29.24 percentage points to 74.77%.
From the above estimates, the odds of a young person achieving the GCSE benchmark if attending a non-grammar school is therefore 0.8444 (i.e. 45.53/54.47). Similarly, the odds for a young person attending a grammar school is 2.9645 (i.e. 74.77/25.23). Thus it can be concluded that odds of a young person achieving the GCSE benchmark will be 3.5 times higher if they attend a grammar school (i.e. 2.96/0.84).
43 These figures above are clearly different to the raw data. For example, and from the dataset, it can be calculated that the average for all Catholic grammar schools is 93.8%. However, it needs to be remembered that the percentage of young people entitled to FSM at Catholic grammar schools is much lower than average at just 10% and the percentage with SEN in such schools is just 8%. The figures quoted above are calculated from Model 1 and use the data for the whole sample to estimate what Catholic grammar schools would get if they had the average proportion entitled to FSM and who were SEN.
44 This odds ratio can be interpreted to mean that for every 84 young people who attend a secondary school with the average intake and who achieve the GCSE benchmark, there will be 100 who do not.
45 Similarly, this can be interpreted to mean that for every 296 young people at grammar school with the average intake and who achieve the GCSE benchmark, there will be 100 who do not.