No-one thinks segregation is a good thing. Runnymede has long argued that policymakers should do more to ensure better integrated communities in Britain; a plea echoed across the political spectrum. The difference of opinion - and it is a big one - is in the ‘how?’.

It is broadly accepted that any move to make a positive change must begin at school. For our part we have advocated for the need for research into how school choice and faith schools affect the ethnic composition of schools in Britain.

In fact, our view is that the discussion on segregation is on the one hand too alarmist about the extent of segregation in Britain, but on the other hand unwilling to consider measures that would actually reduce it, particularly in our schools and workplaces. The evidence indicates that responding directly to inequalities and to racial discrimination will do more to promote integration and this is as true for schooling as for other domains of interaction.

But however we should promote integration in Britain, there is also a more technical question: how can or should we measure segregation?

A report by Ted Cantle and others suggests that we should measure segregation in schools in two ways. First, by comparing them to the population distribution of their ten nearest schools. Second, by asking whether the school is ‘double or half’, or ‘15 percentage points more’ than the average of those ten schools.

A flawed measurement of segregation

Comparing with the ten nearest schools raises a number of problems. The biggest problem is it compares very different populations to one another, especially in urban areas. In other words, a cluster of ten proximate schools will be very different in terms of the local ethnic population, and so we should expect those schools to be very different in terms of the pupil population too. The measure doesn’t help us understand if schools are more or less segregated than their local populations (or catchments) because it compares areas that are no longer ‘local’ or in the same catchment (and in some cases schools with almost no overlapping potential pupils).

Looking at ward level data shows that in most areas in Britain there are areas with twice as many ethnic minorities within a ward or two of one other. This is especially so in London, for example in Hackney where a number of the most diverse wards are directly next to the least diverse wards (using the Simpson index of segregation).

It isn’t really sensible to say that children attending a school in one of these most diverse wards are attending ‘segregated’ schools because schools in a neighbouring much less diverse ward are also less diverse. This is exactly what you would expect based on the residential living patterns, and it’s wrong to conclude from these data either that parents or schools are necessarily acting out of segregationist preferences.

That’s not to say that parents or schools are doing enough to encourage integration or ‘mixing’. Nor is it to deny that parental choice can encourage segregation. But this measure doesn’t help us understand whether or not this is the case, or if there is any school segregation over and above local area segregation. As with Cantle’s previous research (on ‘parallel lives’), the aim here isn’t merely to indicate whether or not segregation exists, but to show it is increasing, and that parental choice is as much to blame as institutional design.

Parents (and researchers) will be surprised and irritated to learn that they are being judged on the basis of their ten nearest schools, especially when in many areas parents are only allowed to indicate six choices on their application forms. Parents may also deliberately leave off nearby schools with small catchment areas knowing their child has no chance of being admitted.

If ten schools in urban areas is a poor measure because local area population varies so much even at small distances, it works no better in rural or semi-rural areas either. Here the closest ten schools will be many miles away, and some will even be in towns or cities that are of course more diverse than rural areas.

A further issue, but one that is hard to assess, is that in some areas a majority of the ten nearest schools may be selective or independent. This will inform not just the conclusion about the ‘segregation’ in those schools, but will bring down the mathematical average of non-white students for the nearest nine schools, as the nature of selective schools means that they are likely to represent a higher socio-economic demographic, and by extension include fewer BME students. The results, according to Cantle’s measurement, may implausibly suggest that the more representative state schools are more ‘segregated,’ because they are being compared to unrepresentative selective schools nearby.

A final problem with the ‘nearest ten schools’ criterion is that it results in very different outcomes for primary and secondary schools. There are nearly 16,800 state-funded primary schools, but only 3,400 secondary schools: nearly 5 times fewer. If we are going to compare like with like, and if we are going to use the arbitrary ‘ten closest’ criterion, then distances for secondary school will be many times greater than for primary schools. [i] We will, in effect, be comparing different areas, in geography and size.

When do we call a school ‘segregated’?

The other main element of the proposed segregation measurement does no better; Cantle suggests that an area or school is segregated if it is ‘half or double’ the ethnic minority population compared to a wide area, including the nine nearest schools. Statisticians and non-statisticians will intuitively balk at the results.

Is a school that has 6% black and minority ethnic (BME) pupils ‘highly segregated’ because the nine nearest schools have a 3% BME population? In areas with a relatively low BME population, this ‘half or double’ measure results in some implausible results. Can schools with less than 10% BME populations really be called ‘highly segregated’, as they are in this report? This is no minor consideration: 44% (234 out of 533) constituencies in England (and even more in Scotland, Wales and Northern Ireland) have populations that are under 5% BME.

Turning to the many towns in England that are say 10-20% BME doesn’t improve matters much. Here too, BME people may be concentrated in a few more densely populated areas, such that many schools will be 30% BME while others may even be 5%. Again, this is not a measure of schools themselves are increasing segregation; it is instead indicative of the underlying population distribution in these towns.

Finally consider the most diverse areas in London, Birmingham, Leicester or Manchester. Here we understand why the report has attached the further measure of ‘or 15% greater than the average’ for the 10 nearest schools. In London over half of all school children are ethnic minorities, so the ‘double’ measurement is mathematically impossible.

Here too the measure leads to a judgment that schools are ‘highly segregated’ when that seems far from obvious. For example, if the local area schools are generally 50% BME, is the one school that is 65% BME ‘highly segregated’ by comparison?

This raises a further problem for the measure, and one that is particularly acute in London with its more diverse population: the measure lumps all non-white British populations into one category. Say an area is 50% BME, but composed of 20% Asian, 20% Black and 10% Other children. On this measure, a school that is 50% Asian in this area is not at all segregated while one that is 25% Asian, 25% Black and 15% Other BME (even if roughly matching the local proportions) is ‘highly segregated’.

This outcome shows why standard academic measures of segregation compare each ethnic group’s likelihood of living near other specific ethnic groups. We have previously written about why segregation isn’t simply where white British people are a minority. It is disappointing to read further analysis that encourages a binary white / non-white distinction in Britain, especially at a time when we need to do more to bring people together.

How should we measure school segregation?

So using ten schools as a comparator doesn’t make a lot of sense. Instead we should follow Simon Burgess’s method of comparing school population with their actual neighbourhood or catchment area. If we are going to expand our analysis, the question should relate to distance and area populations, not a defined number of schools, and it certainly shouldn’t be the same for primary and secondary schools. This will then measure school-level segregation separately, rather than the result being a symptom of local area population distribution that tell us little about parental choice or schools policy.

Second, we should keep to the Simpson index of segregation, as used by local government, especially in London. This ensures we don’t lump all ethnic minorities together and encourage a simplistic white/non-white distinction. It also allows for more statistical rigour, in terms of using standard deviations from an average rather than the curious ‘half, double or 15%’ that produces counterintuitive results in rural, town and urban areas alike.

Understanding ‘choice’

Before concluding about what we might do to address integration or segregation, it’s important to address the reality that minority and majority populations confront choice differently. Given the way individual preferences aggregate and shape the choice-set of others, majority populations (of whatever sort) will always see their preferences better realised.

However, if a majority group has a preference that is too unrepresentative, then that can lead to ‘tipping points’ that result in no-one seeing their preference realised. For example, a majority white population of 60% has a preference that their child attends a school that has 70% white pupils. As schools drop below 70% white pupils, the white parents choose different schools, with the result that local schools can become more polarised or ‘segregated’ than their local catchment areas.

Meanwhile, most BME parents fully understand that their ethnic group is a minority, and do not expect their child to be in the majority ethnic group in their local school. Instead, they often seek a school with some minimum threshold of BME children - say 10% - so that their child doesn’t stand out as the only non-white pupil in the school.

Say I’m a minority parent and the majority and minority preferences in my local area that is 60% ethnic minority present me with two choices: a 95% white British school, or a 15% white British school. Which is the better ‘non-segregationist’ choice for me? In some of Britain’s cities, but particularly in London, parental preferences haven’t yet adapted to the reality of the diversity of local area populations. This is in large part because the workplace and other areas remain less integrated than they should be, and in part because Britain is more diverse today than it was 20-30 years ago when parents attended schools. White British (or better off) parents may then be surprised when they visit their local primary, because the pupil population is more diverse than they realised: in two-thirds of London schools no ethnic group is a majority.

If we defer to a white British preference that their children must always be a majority in local schools, then that will drive further segregation, especially in London.

On the other hand, minorities often face different challenges; we have interviewed Muslim parents in Oldham who would prefer to see their child in a more integrated school, but they don’t want their child to be the only Muslim in the school. This is hardly an irrational preference. In many ways, white British parents in London are now confronting a choice set more like that of minorities everywhere. The ability of middle class people to move to better off areas due to greater savings and assets means that in some areas in London the white population is more likely to be disadvantaged, but we’d need much better or more refined evidence to conclude that such parents reject their local school primarily because it is too diverse. We should not accept that London itself is ‘highly segregated’. No London ward - with populations of around 7500 people - contains any non-white group larger than 48%. By way of comparison, South Chicago, with a population of 750,000, is 3% White; 83% of the 1 million people in Detroit are African American; and the town of South Laredo, Texas, with 250,000 is 96% Hispanic.

How do we promote integration in schools?

Education policy could do more. It’s important to look beyond the catchment of a particular school, which could have narrowed artificially as wealthy parents cluster near an ‘outstanding’ school, with rising house prices. But what, then, are the solutions? The most obvious are far from easy to implement: introducing lotteries, to include a wider catchment than one school (though likely less than ten). The larger the number of schools we might include in that weighting, the more we must consider weighting these lotteries by distance, and implementing a widespread ‘school bus’ network across our urban areas in particular. In sum, we must reduce parental choice of school, and school selection of pupil.

Those policies, of course, are unpopular and difficult to implement, and may cut against the demand for a ‘local’ school. But given the population distribution of ethnic minorities (and indeed low income or free school meal children), the distribution of schools will always seem ‘segregated’ compared to the national average. And given the relative disadvantage and lack of assets of many ethnic minorities, they will be less able to ‘choose’ to move to better off neighbourhoods where schools may be better. We’re fortunate that London schools have improved so much in recent years to mitigate the effects of ‘well-off flight’. This suggests that improving local schools everywhere and responding to broader social ethnic and class inequalities is the best way to insulate against segregation, however we measure it.