This year’s secondary school performance tables (‘league tables’) have been delayed a couple of weeks. To try and help pass the time, I’ve taken a look at whether, and by how much, attainment varies between schools.
This is all rather inconvenient for policy interventions that aim to improve low-attaining schools. Because low-attaining pupils are not clustered together conveniently in particular schools these policy interventions can only slightly reduce differences in attainment between groups of pupils.
Should we be looking elsewhere?
Performance tables publish school averages. They don’t tell us anything about the variation in pupil performance within each school.
This wouldn’t be a problem if the performance of pupils within each school did not vary much: the school average would be a useful statistic and attainment would be improved by focusing on the low-attaining schools.
But this is not the case in practice.
Other researchers have found that schools account for only a relatively small percentage of the differences in pupil attainment. For instance, research last year found that 15% of the variance in 2015/16 Progress 8 scores was between schools, the remainder being within schools (in other words, between pupils).
However, this research looked at an overall indicator of attainment – Progress 8 – derived from results in a number of subjects.
But what if we looked instead at all pupils’ results in each individual subject? How similar are they? And how much variation in schools is between departments? Or between classes?
Exploring the variation between schools
To answer these questions we’ll look at the pupils who reached the end of Key Stage 4 in state-funded mainstream schools in England in 2018. On average, these pupils entered 8.5 qualifications.
Grades in these qualifications have point scores for the purposes of calculating school performance indicators. Higher grades yield more points. Grades in non-GCSE qualifications are given notional GCSE equivalences – in other words, scored on the grade 9-1 scale.
Using a similar approach to that in the research mentioned above, we can break the differences we see between pupils’ KS4 point scores down into:
- differences between schools;
- differences between subjects;
- differences between pupils;
- differences within individual pupils’ results – that is, any remaining variation in the results that individual pupils get.
The chart below shows this breakdown.
In total, 12% of the variance in pupils’ KS4 point scores is between schools. A further 17% is between subjects within schools. Over half (51%) is due to differences between pupils. The remaining 20% is due to differences within individual pupils’ results. In other words, due to pupils achieving different grades in different subjects.
I should say that this sort of analysis assumes perfect measurement, which we know is not the case. Some of the remaining 20% may well be attributable to one of the other levels.
If we remove the effects of Key Stage 2 prior attainment, though, the picture changes somewhat – see the chart below.
The amount of variance in pupils’ results between schools reduces to 5%, largely because most of the variance is due to selection into grammar schools. In an ideal world, there would be zero (or close to zero) variation between schools once differences in intake had been controlled for as this would mean that, on average, schools would be achieving the same results given their intake.
The amount of variation the difference in KS4 attainment explained by differences between subjects within individual schools increases from 17% to 26%. (We’ve shown before that reducing this within-school variation would have far more effect on attainment than moving schools with a Progress 8 score below -0.5 to just above that score.)
Finally, and obviously, there is less variation between pupils as a result of controlling for prior attainment. And amount of variation within individual pupils’ results – that is, between the qualifications that an individual pupil takes – now accounts for a greater percentage of the variation in point scores.
Accounting for grading severity
We’ve seen previously that some qualifications tend to be graded more (or less) severely than others, though. We want to avoid this affecting results, so we can repeat the analysis using alternative point scores adjusted to account for variation in grading severity between subjects – see the charts below.
The results are broadly similar to those seen above, although there is much less variation between subjects – as we’d probably expect – and slightly more variation between schools and between pupils.
Nonetheless, there is still more variation between subjects within schools than between different schools after we’ve taken prior attainment at KS2 into account.
What implications does this have for policymakers?
Looking at the final chart shown above – where more of the difference in attainment is explained by each of the factors below school-level – this would suggest that policies to:
- improve poorly performing departments (‘between subject’ difference),
- help low-attaining pupils in all schools (‘between pupil’ difference),
- or even do more to boost subjects in which pupils seem to be struggling compared to their other subjects (‘within pupil’ difference)
would all be more effective at improving attainment than focusing efforts on whole schools.
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1. Not only that, but this fell to around 9% when the makeup of schools in areas such as gender, ethnicity and disadvantage were taken into account.
2. We need to focus just on those with Key Stage 2 results, giving 478,000 pupils in total. I’ve only included qualifications eligible for performance tables at least equivalent in size to a GCSE. This excludes free standing maths qualifications and graded music and drama.
3. I use a three-level multilevel model with the following nested structure: Schools | Pupils*Subjects | Results. In other words, results are nested within a cross-classification of pupils and subjects which is nested within schools.
4. Rather than portioning the total variance (as in the first chart), here we are partitioning the residual variance having controlled for prior attainment.