Harris, R., Charlton, M., & Brunsdon, C. (2018). Mapping the changingresidential geography of White British secondary school children inEngland using visually balanced cartograms and hexograms. Journalof Maps, 14(1), 65-72.https://doi.org/10.1080/17445647.2018.1478753

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Mapping the changing residential geographyof White British secondary school children inEngland using visually balanced cartograms andhexograms

Richard Harris, Martin Charlton & Chris Brunsdon

To cite this article: Richard Harris, Martin Charlton & Chris Brunsdon (2018) Mapping thechanging residential geography of White British secondary school children in England using visuallybalanced cartograms and hexograms, Journal of Maps, 14:1, 65-72

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Social Science

Mapping the changing residential geography of White British secondary schoolchildren in England using visually balanced cartograms and hexogramsRichard Harris a, Martin Charltonb and Chris Brunsdonb

aSchool of Geographical Sciences, University of Bristol, Bristol, UK; bNational Centre for Geocomputation, Maynooth University, Maynooth,Ireland

ABSTRACTIn the context of debates about segregation within the UK, this paper maps the residentialgeography of two groups of White British school children, one of which was in secondaryschool in 2011 and the other in 2017. To present that geography, hexograms are introducedas a complement to visually balanced cartograms, both of which seek to address theproblems of invisibility and distortion encountered with more conventional choropleth andcartogram maps. The nature of these problems is introduced, our solutions discussed, andthe methods applied to the case study, which allow changes in the geography to be seen.

ARTICLE HISTORYReceived 8 March 2018Revised 15 May 2018Accepted 17 May 2018

KEYWORDSChoropleth map; cartogram;hexogram; segregation;England

1. Introduction

The objective of this paper is to chart any changes tothe geography of where White British children in twomiddle stages of secondary school education were liv-ing in England in 2011 and 2017. To achieve this, wepresent what we call hexograms as a way of mappingareal data. These are a visual method that allowsareas to be represented as equally sized hexagons onan underlying cartogram map. As such, they are across between visually balanced cartograms, hexagonalbinning and tile maps (see below), designed to tackletwo representational issues common to area-basedmaps of population distributions: the problem ofinvisibility, found in conventional choropleth maps,and the problem of distortion, created by cartograms(Harris, Charlton, Brunsdon, & Manley, 2017a).

The study considers the limitations of conventionalchoropleth and cartogram approaches for mappingspatial distributions across areas of varied size. Itdoes so in the context of a response to the UK Govern-ment-sponsored Casey Review: a review into opportu-nity and integration (Casey, 2016), which reigniteddebate on whether Britain is becoming more sociallyand ethnically divided. Newspaper headlines such asthat published in the national Metro newspaperimply that it is: ‘Diverse yet divided: UK is growingapart’ (December 5, 2016). However, such impressionsrun largely counter to a range of empirical studies thatshow residential ethnic segregation to have fallenwithin the UK between 2001 and 2011 (Catney, 2015;Harris & Owen, 2017; Johnston, Poulsen, & Forrest,

2013). There is an exception. Considered as a whole,the White British in London, metropolitan areas andother large cities are the only group for which segre-gation from other ethnic groups increased from 2001to 2011 in England and Wales (Catney, 2013). Cantleand Kaufmann (2016) have said that there is ‘a grow-ing isolation of the White majority from minorities inurban zones’.

A limitation of these existing studies is that they arebased on census data collected only once a decade, themost recentmeasuring theBritain of seven years past. Lit-tle is known about recent trends (but see Lan, Kandt, &Longley, 2018 for an innovative study using consumerdata). What we are interested in exploring is whetherthe apparent spatial contraction of the White Britishfrom urban locations has continued over recent years.

To that end, we follow Harris (2017) and turn to analternative source of data, which is the National PupilData (NPD) for England for the years 2011 (the yearof the last UK Census) and 2017 (the most recentdata). The NPD has been described by the Departmentfor Education as one of the richest education datasetsin the world, holding a wide range of informationabout students. However, it generally covers onlypupils in state schools in England (which is most:approximately 93% of all pupils are in state schools).The data used here are all pupils in two of the middleyears of compulsory secondary education, who areaged 13–14 or 14–15 and attending a state school.We look at where the White British of those pupilsare living and map any changes.

© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of Journal of MapsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricteduse, distribution, and reproduction in any medium, provided the original work is properly cited.

CONTACT Richard Harris rich.harris@bris.ac.uk School of Geographical Sciences, University of Bristol, University Road, BS8 1SS, Bristol, UK

JOURNAL OF MAPS2018, VOL. 14, NO. 1, 65–72https://doi.org/10.1080/17445647.2018.1478753

2. Choropleth maps, cartograms and theproblems of representation

Our cartographic starting-point is Figure 1, whichmaps the percentage of the Census population thatwas counted as White British per English local auth-ority (LA) in 2011 and, alongside, the correspondingpercentage of the NPD data for the same year.

Measuring ethnicity is not unproblematic. Which ofthe pupils identifies as White British in each year is amatter of constrained choice: for the NPD, pupils ortheir parents select their ethnicity from a set of cat-egories that are similar to those used in the UK Census.They may also refuse to provide details (1.0% of thepupils in the 2011 data has an unknown ethnicity,including refusals; 1.3% in 2017). Because it is a partialchoice and a reflection of a person’s own, sometimeschanging self-identity, the ethnic classification fluctu-ates for some pupils over time (see https://nationalpu-pildatabase.wikispaces.com/Ethnicity). The growinginstability of ethnic identity has been identified in theCensus (Simpson, Jivraj, & Warren, 2016).

Nevertheless, there are interesting and potentiallyimportant differences between the two maps. Unfortu-nately, few of those are obvious because many occur inthe major urban conurbations where the spatial pat-terns are hard to see. This is especially true of the placesin and around London which form the conurbationtowards the bottom right of the map.

The problem, common to conventional choroplethmaps of area-based data, is that the areas to be mapped– the English local LAs – vary from one another in bothphysical and population size. Furthermore, the placeswith most people living in them are amongst the smal-lest in area: the Spearman rank correlation betweenarea and the 2011 Census count of residential popu-lation is –0.175. This means that many of the areas ofmost interest are amongst the ones rendered smalleston the map, some to the point of ‘invisibility’.

Potential solutions to the problem include using amap insert to redraw London at a larger scale thanthe rest of the country. However, whilst this mightwork for the capital, it would be of no use to anyother ‘invisible’ places in other parts of the map unlessthey too had their own map insert. An alternative,increasingly popular method, is the cartogram. Anymap is a distortion of the real world, selectively choos-ing methods of projection and visualisation for the pur-pose of its design. Nevertheless, cartograms are distinctin breaking the more usual link between the size of anarea displayed on the map and its true, physical size.Instead, areas are re-scaled in accordance to some attri-bute such as population size.

Cartograms are not new: their history is describedby Dorling (1996); a more recent review is providedby Nusrat and Kobourov (2016). Over the 20-yeargap between those publications, what was once an

esoteric method of cartographic visualisation hasbecome much more common as the range of softwareavailable to produce cartograms has expanded. Thereare several types of cartogram (see Table 1 of Nusrat& Kobourov); we specifically focus on contiguous car-tograms that modify the boundaries, areas and shapesof areas but maintain adjacencies. The cartogramsshown in Figure 2 employ the Dougenik, Chrisman,and Niemeyer (1985) algorithm but the arguments tobe made apply equally to Gastner and Newman’s(2004) diffusion method and others that have in com-mon the broad principle of re-sizing areas by stretchingand deforming them.

Elsewherewe have argued that ease of productionhasled to an uncritical adoption of cartograms in a numberof academic papers, reports and media presentationswith too little consideration to their effectiveness incommunicating the data available (Harris, Charlton,Brunsdon, & Manley, 2017b). In the present case, thecartogram has some success. Noting that blue shadingon the maps represents lower percentages (‘coldspots’) of White British populations, the cartogramsenable it to be seen that those are concentrated withinurban areas, including but not limited to London, andthat they are usually colder for the NPD than for theCensus population; that is, the percentages of the pupilsthat are White British in urban areas are often less thanthe percentages of the Census population.

It is possible that these differences are due to theNPD data being biased by the absence of pupils whoattend fee-charging schools. Against this, we are reas-sured by a close correspondence between the percen-tage of the White British population that is WhiteBritish per LA and the percentage of the NPD pupils:the Pearson correlation is 0.989. Fitting a regressionline with a forced zero y-intercept to predict the per-centage in the NPD data from the percentage in theCensus produces a coefficient (slope) of 0.978. This isvery close to a one-to-one relationship and has amodel fit, measured by the R2 value, of 0.997. Never-theless, such a model tends to over-predict the percen-tage of the NPD pupils that are White British in localauthorities where the Census percentage is less than60, which is 31 of the 324 local authorities, amongstwhich 26 are in London. The over-prediction suggeststhat in areas where the White British are less prevalentin the Census population then, relatively speaking, theyare even less so amongst the group of secondary pupils.This may imply that White British families and theirchildren are moving out from urban places perhapsas a process of school choice (Butler & Hamnett,2011). However, other explanations include broaderdemographic changes (the decreased number ofWhite British pupils enrolled in secondary schoolsnationally), and also the possibility that in places (nota-bly London) that are much more ethnically diversethan most of England, younger age groups are more

66 R. HARRIS ET AL.

comfortable expressing their ethnic identity as a cat-egory other than White British.

Unfortunately, the success of the cartogram comesat a price: the cost of re-scaling is to replace misrepre-sentation through invisibility with misrepresentationthrough distortion because the geography of thelocations is warped. This exchange is conducted onunfavourable terms because the cartogram, which isdominated by places assigned a large scaling term,also results in areas that are too small to see. As such,it has failed to resolve the problem of invisibility(only substituting one set of invisible places withanother) and compounded it with distortion.

The fundamental limitation that the cartogramencounters is that a scaling parameter with a stronglyskewed distribution (the areas of the local authorities)cannot be exchanged for another that also is stronglyskewed (the population counts) if the objective is toproduce a map over which the entirety of the geo-graphical patterning is legible. For the local authorities,the area of the largest is 10.3 times greater than theinter-quartile range. It would be about 2.86 if the vari-able was randomly sampled from a Normal distri-bution. For their population sizes, the ratio is verysimilar, at 10 so there is little visual gain. If we followothers and rescale not by population counts but by amore specific attribute, in this case, the numbers ofpeople that are not White British, the ratio increasesto 23.7. This draws attention to the places wherefewer White British are living but the greater theamount of skew the more unrecognisable the geogra-phy of the country becomes (Figure 3).

None of this discussion means that a cartogram isunsuitable in every usage. In some cases, distortingthe map to draw attention to a large presence (orabsence) of a feature is the desired aim (see Hennig,2014 and the examples at https://worldmapper.org/).In others, they can be used to show the clustering of,for example, disease cases amongst a variably sizedpopulation at risk. In all cases, cartogram producingsoftware are agnostic to the choice of scaling term; itis up to the user to decide. With that in mind, Harriset al. (2017a) propose what is described as a visuallybalanced cartogram, which is a cartogram where a bal-ance between visibility and distortion is sought byenlarging only those areas on the map that fall belowa minimum, interpretable size and, therefore, need tobe expanded in order to be seen. Although a cartogramcan be defined as a map that is scaled in proportion tosome thematic or population count of interest (therebycombining statistical and geographic information), ourview is that it is any map that rescales the size of areasin accordance to an attribute other than their physicalsize. For us, the most important attribute is their visualinterpretability. A similar logic is employed by Soetens,Hahne, and Walllings (2017), expanding areassufficiently to represent each of a point outbreak ofan infectious disease.

Figure 4 is based on this idea with the smallest inter-pretable unit set at a target of 0.02 squared-inches. If anerror is defined (loosely) as the percentage amount bywhich the original map and the cartogram do not over-lap, then the gain from the visually balanced cartogramis clear: for the population cartogram the error is 15%,

Figure 1. Showing the percentage of (left) the Census population, and (right) the cohort of secondary school pupils that were WhiteBritish in each English local authority in 2011.

JOURNAL OF MAPS 67

for the attribute based cartogram it is 24% and for thebalanced cartogram it is only 5.9. More precisely, theerror may be defined as:

e = 100− 50Ax>y1Ax

+ 1Ay

( ),

where Ax is the area of the original map, Ay is the areaof the cartogram, and Ax>y is the area of their geo-graphical intersection.

Another way to consider the amount of distortion isto calculate the average displacement of the area cen-troids from their locations on the original map totheir new locations on the cartogram. This is28.49 km for the population cartogram, 43.97 km forthe attribute cartogram and 13.78 km for the visuallybalanced cartogram. Both measures rely on the carto-gram being placed within the same broad boundingbox as the original map and oriented along the same

Figure 2. The maps of Figure 1 redrawn with a population-based cartogram (the scaling parameter is the 2011 Census populationcount per local authority).

Figure 3. Showing an attribute-based cartogram (the scaling parameter is the Census count of population who are not White Britishin each local authority).

68 R. HARRIS ET AL.

vertical and horizontal axes (i.e. there is no rotationapplied wholescale to the map nor a recentring of it).On these two measures, plus a third criterion of visi-bility, the visually balanced cartogram is the best ofthe maps.

3. Methods

The Main Map displays the pupil data using what wehave described as hexograms. These are based on creat-ing a cartogram where the minimum size of each areais that which allows each LA to be represented by itsown, unique hexagon in a process of hexagonalbinning.

Hexagonal binning has become a popular method ofdata visualization that is used to aggregate points ofdata on a map or chart (such as a scatter plot) intogroups based on their location on the chart: a hexago-nal grid is overlaid upon the points, the number ofpoints in each hexagon is counted, and the hexagonis shaded to represent the number (and also, if thesize of the hexagon is fixed, the density) of pointswithin each hexagon. For geographical point data thisis useful for representing spatial variation in, forexample, the number of cases of a disease. Here, how-ever, we use hexagonal binning for a different purposewhere what we are seeking is a visual representation ofarea, not point data, and we want each area to be rep-resented by its own, unique hexagon.

There are two ways to achieve this. The first is toraise the number of bins to the amount producingno conflicts (no shared hexagons). This entails theleast geographic distortion of the map but the

resulting hexagons are too small to be visible. Thesecond is to increase the size of the areas where theclashes are occurring but this will distort the map.We therefore encounter the now familiar trade-offbetween invisibility and distortion: fewer bins meansgreater visibility; more bins means less distortion.There is no one perfect solution but in making a jud-gement, it is helpful to gauge the expected number ofconflicts for each number of bins as this will indicatehow many places need enlarging. A graph of the twosuggested that 23 bins are suitable for the presentstudy.

The algorithm creating the hexograms works as fol-lows. To begin, an initial cartogram is created thatincreases the size of the smallest areas in the map. Hex-agonal binning is then applied to the centroids of thecartogram, identifying areas that conflict. To addressthese conflicts, an attempt is made to move the cen-troids to different parts of the conflicted areas to seeif that will separate them. If not, the areas are enlargedsome more. The process iterates through these pro-cedures but, as a last resort, will attempt a third wayto achieve a resolution, which is to increase the numberof bins. As a final stage, some careful re-arrangement ofthe hexagons can return those that are less clusteredtowards the edge of the map back to their original pos-itions, resulting in a non-tessellating tile map that,where possible, reflects the initial geography of theLA controids in the original map. The centroids ofthe hexagons in the tile map have a displacement of26.34km from their original positions.

It might be argued that representing each area withequally sized hexograms suggests some equivalence

Figure 4. A visually balanced cartogram offering a better compromise between visibility and distortion.

JOURNAL OF MAPS 69

between places. That is correct: each represents oneobserved value, which is the percentage of the pupilsin each LA who are White British. This is a little differ-ent from when, for example, tile maps are used in UKelectoral studies, where each tile represents a constitu-ency and – although these do also vary in their popu-lation size – each counts equally under the nationalelection’s ‘first-past-the-post’ system: their equival-ence is determined by the electoral system. Since thatis not the case here, should the hexograms be scaledby population size, which is more usual for cartograms?That is a possibility and an area for future research. Fornow, however, our interest is in the rates of White Brit-ish population and how those are spatially distributedacross the LAs. The spatial distribution of the popu-lation size of each LA is not our immediate concernand we certainly do not want it to dominate themaps by the geographical distortion that cartogramstypically generate. What is of interest to us is the visualrepresentation of the percentages and the geographicalvariation.

Much of the computational time to produce the mapis spent on creating and re-creating the cartogram,which is slower than producing a tile map directly(see, for example, McNeill & Hale, 2017). However,there is advantage in having the hexogram producethe tile map as well as the cartogram. The tile map isvisually appealing, with all areas clearly visible withinit. It also ensures sufficient space (within each hexagon)to include additional annotation, marking on the mapthe places where the numbers of White British pupilshave grown. However, only the cartogram retains thetopological connections between local authorities.They therefore offer complementary representationsof the same underlying data and are employed togetherin the Main Map.

4. Results

The Main Map shows how the residential geography ofthe White British school pupils changes from 2011 to2017. The upper and middle rows map the percentageof the pupils that are White British, in 2011 and in2017. As before, the LAs are shaded to highlight‘cold spots’, where the percentages are relatively low.Evident is that the percentages have mostly fallenover the period: they decreased in 309 local authoritiesand rose in only 15. The biggest decrease is in Carlislewhich may reflect it having one of the country’s fastestrates of ethnic minority population growth.

Across the country, the number of White Britishrecorded in the extracts from the NPD data decreasedfrom 870613 in 2011 to 751067 in 2017, a reduction of13.7%. At the same time, the number in other ethnicgroups rose from 246453 to 304404, an increase of23.5%, which includes an increase in the Mixed eth-nicty group from 41671 to 51695 (24.1%), and in the

White Other from 38154 to 54255 (42.2%). The latter,especially, reflects immigration from EU and othercountries but a component of the reduced number ofWhite British might not just be demographic changesand migration but also the instability of the White Brit-ish category discussed earlier (i.e. an increased willing-ness to identify with and to choose categories otherthan White British for oneself).

Given these national changes, the LAs have beenclassified on two dimensions. First, those where thepercentage loss of White British is greater than thenational trend (higher–…) and those where the per-centage loss is less than nationally (lower–…). Second,those where the percentage gain of other ethnic groupsis greater than nationally (…–higher), and those whereit is less (…–lower). That gives four types of LA:higher–higher, higher–lower, lower–lower and lower–higher. Of particular interest are places where the lossof White British is greater and so too is the gain ofother ethnic groups. These (higher–higher) authoritiesare the ones likely to experience increased residentialseparation of the White British from other groups.Also of interest are places where the loss of White Brit-ish is relatively low and the gain of other ethnic groupsis relatively high. These (lower–higher) local auth-orities are likely to have more residential mixing.

The Main Map shows that it is too simple to portraythe loss of the White British pupils as a purely urbanphenomenon. Rates of loss are higher in some ruraland smaller town locations, especially along the eastcoast, where the rates of growth of other ethnic groupsare higher. At the same time, many of the locationswith a lower rate of decrease in the White British arealso locations with a higher rate of increase of othergroups (albeit sometimes from a low base). This isespecially true of the suburban, semi-rural and ruralareas around London but also around other citiesand urban conurbations too. In just a few locations,the number of White British pupils increased from2011 to 2017. Three of those are in London. The hex-ograms enable the visualisation of information thatwould be obscured or hidden in conventional choro-pleth and cartogram maps.

5. Conclusions

In this paper, we have shown how balanced cartogramsand hexograms can be used to tackle the (mis-)rep-resentational issues limiting more conventional choro-pleth and cartogram mappings, and to map thechanging residential geography of two cohorts of sec-ondary school pupils, one from 2011, the other 2017.Our approach is not a panacea but it is informed bythe knowledge that more judicious selection of a scal-ing variable will better balance the problems of invisi-bility and distortion that affect area-based maps ofpopulation distributions.

70 R. HARRIS ET AL.

The methods have been implemented as a proof ofconcept built on existing software libraries and arenot at all optimised for speed. With the 324 local auth-orities, the hexogram took 5 minutes to produce on aone-year-old, regular Windows-based laptop. A tutor-ial on how to apply the methods using the free andopen source software, R, is available at https://rpubs.com/profrichharris/hexograms.

With reference to the geography we have mapped,although the spatial retrenchment of the White Britishinto more semi-rural and rural locations appears tohave continued beyond the 2011 Census, it does notfollow that the country is becoming more segregatedbecause the evidence is that those locations are becom-ing more ethnically mixed (Harris, 2017) and someurban locations have had an increase in their WhiteBritish populations. The notion of ‘white avoidance’raised by Cantle and Kaufmann (2016) seems, at aminimum, to be an over-generalisation of more com-plex demographic changes and their causes. For longerterm understanding of segregation patterns, thosedemographic factors must be considered more fully:whereas the numbers of White British have decreasedin the secondary school years over the period, withinprimary schools they have increased from 785,717 to852,735 over the period (an increase of 8.5%)

Software

Each of the maps and methods was implemented anddrawn in R, version 3.4.3. The main software librariesused were cartogram version 0.0.2 (Jeworutzki, 2016),fMultivar version 3042.80 for the hexagonal binning(Wuertz, Setz, & Chalabi, 2017), and the spatiallibraries GISTools version 0.7-4 (Brunsdon & Chen,2014), sp version 1.2-7 (Bivand, Pebesma, & Gomez-Rubio, 2013; Pebesma & Bivand, 2005), rgdal version1.2-16 (Bivand, Keitt, & Rowlingson, 2017) and rgeosversion 0.3-26 (Bivand & Rundell, 2017) to spatiallymanipulate and visualise the data. The Main Mapwas finished in Serif Affinity Designer.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This publication has emanated from research supportedunder the Economic and Social Research Council’s UrbanBig Data Centre (http://ubdc.ac.uk/), ES/L011921/1 and bya research grant from Science Foundation Ireland (SFI)under grant number 15/IA/3090.

ORCID

Richard Harris http://orcid.org/0000-0001-7943-9005

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