Ethnic diversification and neighbourhood mixing: A rapid response analysis of the 2021 Census of England and Wales

This paper provides a rapid response analysis of the changing geographies of ethnic diversity and segregation in England and Wales using Census data covering the last 30 years (1991, 2001, 2011 and 2021), a period of significant social, economic and political change. Presenting the first detailed analysis of 2021 Census small area ethnic group

the geography of that diversity, with The Guardian and BBC choosing to report on the 'super diversity' (Vertovec, 2019) of the cities of Leicester and Birmingham. 1  While several sample surveys measure ethnic groups in some detail, the Census remains the 'gold standard' for research that seeks to understand local level populations (Stillwell, 2018).Only the Census can provide a comprehensive full population coverage (with 19 ethnic groups classified) at a fine spatial scale. 2 The publication of 2021 Census data thus represents a unique and important opportunity to explore new or emerging patterns and processes, allowing researchers the possibility of understanding how the nation's population and its geographies are changing over time.We begin with an overview of changes in ethnic group population numbers and shares for England and Wales from 1991 to 2021.We then turn our attention to geographical variation in these changes at local authority and neighbourhood scales, asking: what are the emerging geographies of ethnic diversity, residential segregation, and inter-ethnic mixing, and in what ways have they changed over time?This rapid response analysis of 2021 Census ethnic group data for England and Wales aims to explore the changing geographies of ethnic diversity and residential segregation for small areas across four time points : 1991, 2001, 2011 and 2021.Within this larger frame, we explore two temporal dimensions of the changing geographies of ethnicity in England and Wales: detailed diversity over the short(er) run (20 years) and broader trends over a longer time period (30 years).We explore ethnic group changes at three different spatial scales: the national (England and Wales), and the subnational scales of town and city districts, and neighbourhoods.

| Ethnic groups
Our analysis makes use of ethnic group data for England and Wales.The Census has asked about ethnic group identity since 1991.The inclusion of the Census ethnic group question was, and remains, politically contentious and empirically challenging (Aspinall, 2022;Finney & Simpson, 2009a).Its introduction in 1991 was given imperative by the introduction of anti-discrimination and race relations legislation in Britain from the 1970 s, and the desire to understand social inequalities remains a prominent driver of Census ethnic group data collection (ibid.).
In 2021, people were required to tick one box to 'best describe your ethnic group or background'.Ethnic group is a compulsory question, and completion of the Census form is a legal obligation. 3For the 2021 Census, following a series of user consultations, 4 one additional response was added to the range of ethnic groups available, allowing people to self-identify as Roma on their Census form.Additionally, search-as-you-type functionality 5 was introduced, to allow respondents who chose one of the 'other' ethnic group options to self-identify their ethnic group from a predefined list.A greater number of changes to the ethnic group question were made for earlier Censuses (see Jivraj & Simpson, 2015, for a detailed discussion).
Table 1 shows the ethnic groups that were reported for each Census since 1991.To enable comparison across time, ethnic groups recorded in later periods were combined in the analyses to make them consistent with earlier periods (see Catney, 2016a;Simpson et al., 2016).To investigate change during the four time periods for which we have ethnic group data (1991, 2001, 2011 and 2021)

| Geographies
Local Authority (LA) districts and Lower Layer Super Output Areas (LSOAs) for 2021 are the base geographies used in our subnational analyses.LAs comprise single-tier unitary authorities and lower tier districts contained within shire counties (ONS, 2016).There are 331 LAs (hereafter districts) for which 2021 Census data have been released.They have a mean population of 180,053 and range in size from 2055 (Isles of Scilly) to 1,144,922 (Birmingham).LSOAs are a statistical geography built up from clusters (usually numbering four to six) of Output Areas (OAs)-small areas intended to have similar population sizes and also to be as socially homogeneous as possible based on housing tenure and dwelling type (see Martin et al., 2001 for an account of the procedures used in construction of these areas).LSOAs were selected in preference to coarser statistical geographies (e.g., Middle Layer Super Output Areas) which would lead to a loss of detail in our assessment of diversity, and also administrative geographies (e.g., wards), which are not designed to account for the underlying population characteristics (Martin et al., 2001).LSOAs offer a compromise between spatial detail and granularity that obscures the key spatial patterns.One of the challenges in using Census data over time are the changing boundaries.To overcome this issue, counts for 1991 Enumeration Districts (EDs), 2001 LSOAs and 2011 LSOAs were transferred to 2021 LSOAs using areal weighting, as detailed in the Technical Appendix (Supporting Information).There were 35,672 LSOAs in 2021, with a mean population of 1,671 people.LSOAs will be referred to as neighbourhoods from hereon in.All analysis and data processing were undertaken using the R computing environment (R Core Team, 2022).
Figure 1 shows the nine regions of England, plus Wales, and selected towns and cities that are useful references for the analysis sections.This map is a cartogram (Dorling, 1996), created by scaling LSOAs using the square root of their original geographical area (Harris et al., 2017).This means that geographically smaller LSOAs (which have higher population densities) appear relatively larger, while geographically larger LSOAs (with lower population densities) appear relatively smaller.The boundaries of distorted LSOAs allocated to a specific region/nation were dissolved to retain the region/nation boundary in cartogram space; the end result is as shown in Figure 1.The boundaries of Wales and the regions of England are superimposed on later maps (Figure 6) to aid interpretation.Traveller (57,680; 0.10%) Other White (2,485,942; 4.43%) White British (44,355,038; 74.42%) White Irish (507,465; 0.85%) Gypsy or Irish Traveller (67,768; 0.11%) Roma (100,981; 0.17%) Other White (3,667,997; 6.15%)

| THE CHANGING ETHNIC DIVERSITY OF THE ENGLAND AND WALES POPULATION
Table 1 tells us about the relative proportions of each ethnic group at the most recent Census, but also allows us to explore how the populations in each group have changed over time.The total number of people living in England and Wales in 2021 was 59,597,542 (Table 1, column 4).Of this total, 74.42% identified as White English/Welsh/Scottish/ Northern Irish/British (hereafter White British).The White British population has decreased since 2011, in a continuing trend of gradual decline since 2001.The White Irish population similarly experienced a decrease in group size.These declines may be explained by more deaths than births for these ethnic groups as a result of older age structures and ageing populations, from greater emigration than immigration, and, for the White Irish, changes in self-identification (Simpson & Jivraj, 2015).People who identified as 'Other White' accounted for slightly more than 6% of the England and Wales population in 2021.This is a diverse group and includes people with recent origins in, for example, mainland Europe (including Poland and Romania: the second and fourth highest non-UK countries of birth in England and Wales; ONS, 2022b).Growth of the Other White group constituted the largest proportional increase of all ethnic groups, an increase which ONS (2022c) suggest partly reflects the introduction of the search-as-you-type functionality, which assists people in self-defining their ethnic group by writing it in when completing their Census form online.Over 100,000 people identified with the newly added Roma ethnic group. 7The aggregated White group remains by far the largest ethnic group category, and continued to grow numerically, while experiencing a proportional decline since 1991.
The growth of ethnic diversity at the national scale is clear from Table 1.The population of all 'minority' ethnic groups apart from White Irish added to their populations between 2011 and 2021.The population in ethnic groups other than White constituted just over 18% of the England and Wales population in 2021 (up from 14.03% in 2011).Indian was the largest ethnic group not in the White category, making up just over 3% of the total population.The next largest were Pakistani (2.66%) and Black African (2.50%).The Black African group experienced particularly notable growth in the period from 2011 to 2021, increasing from approximately 990,000 to nearly 1.5 million people.We have also seen an expansion in the count of people identifying with a Mixed ethnic group: more than 1.7 million people self-identified as having a Mixed ethnicity in 2021 (White and Asian, White and Black African, White and Black Caribbean, or Other Mixed)-a considerable increase from just over 661,000 people in 2001, when the Mixed category was first included in the Census.This increase in people identifying with a Mixed ethnic group is expected, and predominantly reflects children born to people in mixed ethnicity partnerships (Lomax et al., 2020).
Several components of population dynamics will have, collectively, shaped these changes in ethnic group populations nationally: the balance of births and deaths which partly relate to the different age structures of ethnic groups; the balance of in and out migration; and changes in the number of people ticking a given ethnic group box, reflecting changes in how we see ourselves, or how we feel others see us (Finney & Simpson, 2009b;Simpson & Jivraj, 2015).Previous research has shown that some people change their ethnic group identification between Censuses (Simpson et al., 2016).
Figure 2 captures the sustained growth of ethnic diversity between 1991 and 2021.It shows the population in each of the six minority ethnic groups that, given changes in reporting (see Table 1), are most comparable across the four Censuses with an ethnic group question.What is most notable is the variation in ethnic diversity since ethnic group data were collected in the 1991 Census.The ethnic groups that have grown fastest since 1991 are groups that accounted for smaller proportions of the population when these data were first collected.Figure 2 also includes the Other category, which can be seen as a heterogeneous group.The considerable growth of this 'Other' group is an indicator of a diversification of diversity, where the pre-prescribed Census groups do not align with the self-identification of increasing numbers of people, despite the addition of new groups at every Census since 1991.The Any Other group, as measured in the 2021 Census, is the sixth largest minority ethnic group, demonstrating a continued mismatch in the predefined categories for almost a million people (see Table 1).

| Growth of ethnic diversity at the national scale
The increasing ethnic diversity of England and Wales indicated in Table 1 and Figure 2 can be measured more formally.The Reciprocal Diversity Index (RDI) allows us to compare levels of ethnic diversity over time (Catney, 2016b;Simpson, 2007).To analyse change in diversity for a greater number of ethnic groups, including a disaggregation of the White category, we restrict our analysis from 2001 onwards at this point, omitting the more limited data for 1991 and using the 16 comparable ethnic groups detailed earlier.RDI is computed with: where there are M ethnic groups (here, 16),    is the number of people in group m in area (e.g., district) i and there are    people in total in area i. RDI can be standardised to the range 0,1 by subtracting 1 and dividing by M−1 (Simpson, 2007).For ease of interpretation, the product is multiplied by 100.In this case, RDI scores can range from zero (one ethnic group only in an area) to 100 (equal share of all 16 ethnic groups; thus, each group comprises 1/16th of the total population).
As with the period 2001-11, ethnic diversity also increased from 2011 to 2021.The national level (England and Wales) RDI increased from 2.02 in 2001, to 3.56 in 2011, to 5.14 in 2021.

| Considering mix, rather than majority
This growth of national level ethnic diversity was mirrored across many of the major urban areas of England and Wales.The extent of these changes was a focus in the media at the time of the data release.In particular, the emergence of so-called 'minority-majority' cities 8 drew substantial attention, as it did at the release of the 2011 Census (for a critique, see Simpson, 2015).These places were labelled as such because more than 50% of their populations were either not White British or not White (the broader grouping including Irish and people claiming another White identity; see Table 1).While the number of 'minority-majority' districts increased by the time of the 2021 Census, the results are more nuanced than has largely been reported to date.
The use of the term minority-majority is too blunt for depicting the diversity within districts.We suggest that, rather than emphasis being placed on one ethnic group's threshold (usually White), the absence of White people in a place is better thought of as a signal of ethnic diversity.This is what the data show: the smaller the share of a district's White British population, the greater the ethnic diversity of that district.Put another way, districts being characterised as 'minority-majority' should instead be thought of as ethnically diverse places. 9This is depicted in Figure 3, which demonstrates that the relationship between the diversity of a district (measured by RDI 10 ) and the log of the percentage share of the population that is White British is almost perfect (correlation coefficient = −0.98).The log transformation linearises the relationship, which is necessary because the correlation coefficient calculated measures linear association.
For a moment, let us use this lens of diversity measured by RDI and centre the notion of 'minority-majority' as an object of inquiry.Figure 4 focuses in on Figure 3 to show only those places where the White British group constitutes less than 50% of the population.These places are mostly in London, but include a few districts outside: Birmingham, Leicester, Slough, Watford, Luton, Manchester.The relationship between RDI and percentage White British, now linear in this subset, weakens a little (correlation coefficient = −0.87).Thus, as the White British population drops below the majority threshold, its power to predict ethnic diversity weakens somewhat, suggesting that other factors (such as the share of other ethnic groups) drive the relationship.To illustrate the variability of the relationship, Leicester, Kensington and Chelsea, Hackney, and Waltham Forest all had approximately the same percentage of White British in 2021 (33%-34%) but had a wide range of ethnic diversity (RDI values of 21-33).All of these districts are diverse, but Leicester is less so (i.e., lower RDI), largely because two-thirds of its population is evenly distributed across two ethnic groups: Indian and White British (see Figure 5).By contrast, Ealing and Tower Hamlets exhibit substantially different RDI values from one another (a difference of around 16), yet both areas had approximately the same shares of White British people.The lower diversity in Tower Hamlets is nevertheless considerably higher than in all places where White British people are in the majority (see Figure 3).To understand the ethnic mosaic across England and Wales it is more illuminating to consider mix than majority.
To dive deeper into the ethnic mix of these diverse places, Figure 5 shows the ethnic composition in the six most diverse LA districts within and outside London in 2021.The selection of districts is based on the 16 group RDI; the charts show, for each of these districts, the percentage of people in each of the 19 ethnic groups reported in the 2021 Census.For London this is a subset of the diversity apparent in the city because 25 (of the 32 districts in London) are among the 30 most diverse districts of England and Wales.Outside of London, Slough (South East region) and Luton (East region) were respectively the sixth and ninth most diverse districts.It is also notable that of this group of districts, Watford and Slough are very much satellites of the London urban area, with Watford LA lying within the M25 ring road area.Luton is within the commuter hinterland of London as well.Increasing ethnic diversity in these locales is likely due to in situ growth of minority ethnic groups, and internal migration from districts in London (see Catney, 2016a, for earlier time points).
These rainbow charts challenge the problematic minority-majority binary and confirm that these spaces are in fact highly diverse, home to a number of ethnic groups.England and Wales' most-diverse district, Newham, is remarkable, with no group accounting for more than a sixth of the population.The high level of diversity in Newham and Brent is also notable in that the White British group is not the largest, while in the other four London districts it comprises between 23% and 31%.The significance here is that the compositions of Newham and Brent represent distinct outliers among districts of England and Wales, in terms of the form their ethnic diversity takes.The relative (in many cases substantial) dominance of the White British group in several of the example places outside London illustrates how, for most districts, diversity is anchored in the context of historical ethnic structures.

| Growing neighbourhood ethnic diversity
Progressing from these large-scale patterns of ethnic diversity, this section focuses on neighbourhood-level geographies of ethnic diversity, and how these have changed over time.Here, diversity is again measured using the RDI. Figure 6 shows the RDI for the 16 comparable ethnic groups between 2001 and 2021 for LSOAs across England and Wales.The maps illuminate several important patterns of change.Ethnic diversity has grown, in some cases markedly, across much of England and Wales.6c), fewer neighbourhoods than ever have low levels of ethnic diversity.By far the greatest number of neighbourhoods with high levels of ethnic diversity can be found in large cities, particularly in London, but also across the country, from Birmingham to Bristol, Manchester to Cardiff, and Nottingham to Southampton.In Birmingham, we see considerable increases in the number of neighbourhoods in the highest category of ethnic diversity.A similar pattern can be observed for other parts of the Midlands, and for cities in the North West of England.In London, a 'doughnut' pattern of growth is evident (Figure 6d), with greater increases in ethnic diversity in outer London, and slightly lower increases in inner London, perhaps reflecting minority dispersal away from immigrant settlement areas (Catney, 2016a), and housing (un)affordability/availability in the capital which disproportionately impacts Black and other minority ethnic Londoners (Gleeson, 2022).
The maps also tell a story of change outside urban spaces.Between 2001 and 2021 there was a clear diffusion of ethnic diversity beyond city boundaries.This expansion of diversity occurs across many parts of England where many formerly non-diverse neighbourhoods are now home to people from several ethnic groups.Decreases in ethnic diversity (Figure 6d) tend to have occurred in the most diverse districts.These decreases will partly be a function of how the index operates; even a small increase in one (relatively larger) ethnic group compared with other (smaller) groups will lead to a decrease in RDI.It remains for further investigation to examine how changes in diversity may be the result of local changes in housing provision across population groups.the most attention in academic research.In the UK context, residential segregation has consistently declined over time, with increasing ethnic mixing in neighbourhoods for White and other groups (Catney, 2016b;Johnston et al., 2016).The relationship between spatial integration and ethnic inequalities across life domains is considerably less well understood.This partly reflects the hitherto inadequate focus on geographical variation in the experiences of people from different ethnic groups, which illuminate the intersections between social and spatial inequalities (for exceptions for the UK context, see Catney & Sabater, 2015;Jivraj & Khan, 2015;Lymperopoulou & Finney, 2017).Indeed, in many senses, segregation is a spatial expression of social (and economic) inequalities within urban areas, with a reinforcing relationship between the residential distribution of people of different ethnicities and spatialities of opportunity structures in housing and employment (Peach, 1996).
The Index of Dissimilarity (D), which captures the evenness of the spatial distribution of two groups, is one of the most commonly used measures of segregation (Massey & Denton, 1988).Here, each named group is compared with all others (for example, people in the Pakistani ethnic group compared with all people other than Pakistani).Values of D can range from zero to one, where zero indicates a completely even distribution (all areas have the same proportion of the two groups compared) and one indicates a completely uneven distribution (all areas comprise 100% of one group or the other).D is computed with:  1) to facilitate analysis of change over 30 years; the results are shown in Figure 7.The Other group is included in the population total for the analysis, but the group's D value is not reported in Figure 7 given its heterogeneity (as discussed earlier).The largest values for 1991, at greater than 0.8, reflect historic immigrant settlement patterns.
The decline in neighbourhood ethnic residential segregation observed for previous periods continued in the most recent decade.For all ethnic groups, there was a pronounced decline in spatial unevenness between 1991 and 2021.Taking the most recent period first (2011-21), we observe the greatest reductions in segregation for the Black African and Black Caribbean ethnic groups.White segregation from minority groups also declined in the period.Looking across all four time points, we see steady declines in segregation for all ethnic groups: White and minority.The largest proportional decline in residential segregation between 1991 and 2021 was for the Black African group, with a decrease of 0.17.The Bangladeshi, Black Caribbean and Indian ethnic groups also experienced large decreases in neighbourhood residential segregation between 1991 and 2021.Data constraints preclude exploring trends in residential segregation between 1991 and 2021 for disaggregated White groups.White British segregation (not shown) remained the same between 2001 and 2011 (0.55), and decreased between 2011 and 2021 (to 0.53).

| SUMMARY AND CONCLUSIONS
This paper provides a first analysis of the changing geographies of ethnic diversity and segregation in England and Wales, spanning 30 years and four Census time points (1991, 2001, 2011 and 2021).The 2021 Census shows that the population of England and Wales is becoming increasingly mixed and diverse, continuing a trend of the past three decades.Residential segregation of all ethnic groups-White and minority-is declining.At the local level, many more neighbourhoods are ethnically diverse, and diversity has been spreading out to new locales.Our analysis challenges the 'minority-majority' binary that hinges on White/White British presence or absence in a place, centring instead on its mixture of ethnic groups.In doing so, we find ethnic diversity where the ethnic majority is less populous.
The 2021 Census provides a unique and important opportunity to understand the changing ethnic landscape of England and Wales.Our rapid response analysis of recently published data illuminates several key trends, but also raises many questions in need of urgent attention.What can be learnt from these new data about how neighbourhood ethnic diversity evolves?How do internal and international migration shape these changes in ethnic diversity?What are the geographies of ethnic inequalities (e.g., in housing or employment), and how do they relate to residential segregation?This article has focused on England and Wales 11 : are the trends we see here reproduced across the rest of the UK, or do they have their own unique characteristics?
Ethnic groups reported at each Census 1991-2021, and their population counts and proportion of the total population.

F
I G U R E 1 Area cartogram showing regions of England, Wales, and selected towns and cities referred to in the analysis.14754959, 2023, 1, Downloaded from https://rgs-ibg.onlinelibrary.wiley.com/doi/10.1111/geoj.12507 by Test, Wiley Online Library on [06/02/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

F 2
Population size of the minority ethnic groups (other than White minority) reported in the 1991, 2001, 2011 and 2021 Censuses of England and Wales.Ethnic groups are ordered by smallest to largest population size in 2021.Source: 1991 Census,

F 3
Ethnic diversity (measured by the Reciprocal Diversity Index [RDI]) and proportion of White British population in districts in England and Wales, 2021.Source: 2021 Census, Table TS021 (Crown Copyright).Authors' own calculations.

Figure 6
Figure6makes clear the increased spatial complexity of ethnic diversity.By 2021 (Figure6c), fewer neighbourhoods than ever have low levels of ethnic diversity.By far the greatest number of neighbourhoods with high levels of ethnic diversity can be found in large cities, particularly in London, but also across the country, from Birmingham to Bristol, Manchester to Cardiff, and Nottingham to Southampton.In Birmingham, we see considerable increases in the number of neighbourhoods in the highest category of ethnic diversity.A similar pattern can be observed for other parts of the Midlands, and for cities in the North West of England.In London, a 'doughnut' pattern of growth is evident (Figure6d), with greater increases in ethnic diversity in outer London, and slightly lower increases in inner London, perhaps reflecting minority dispersal away from immigrant settlement areas(Catney, 2016a), and housing (un)affordability/availability in the capital which disproportionately impacts Black and other minority ethnic Londoners(Gleeson, 2022).The maps also tell a story of change outside urban spaces.Between 2001 and 2021 there was a clear diffusion of ethnic diversity beyond city boundaries.This expansion of diversity occurs across many parts of England where many formerly non-diverse neighbourhoods are now home to people from several ethnic groups.Decreases in ethnic diversity (Figure6d) tend to have occurred in the most diverse districts.These decreases will partly be a function of how the index operates; even a small increase in one (relatively larger) ethnic group compared with other (smaller) groups will lead to a decrease in RDI.It remains for further investigation to examine how changes in diversity may be the result of local changes in housing provision across population groups.

F
Ethnic diversity (measured by the Reciprocal Diversity Index [RDI]) and proportion of White British population in districts where the White British population is below 50% (England and Wales, 2021).Source: 2021 Census, Table TS021 (Crown Copyright).Authors' own calculations.F I G U R E 5 Ethnic group composition of the most ethnically diverse districts of England and Wales in (a) London and (b) outside of London, 2021.Ethnic groups are, for each district, ordered left to right by largest to smallest population size in 2021.Ethnic groups in the legend are ordered by population size in England and Wales in 2021.W&BCaribbean = Mixed White and Black Caribbean; White&Asian = Mixed White and Asian; W&BAfrican = Mixed White and Black African; GyIrTraveller = Gypsy or Irish Traveller.Ranks by Reciprocal Diversity Index out of all districts in England and Wales (331) are as follows: Newham = 1, Brent = 2, Redbridge = 3, Ealing = 4, Barking and Dagenham = 5, Hounslow = 7, Slough = 6, Luton = 9, Birmingham = 28, Leicester = 29, Watford = 30, Manchester = 32.Source: 2021 Census, Table TS021 (Crown Copyright).Authors' own calculations.
14754959, 2023, 1, Downloaded from https://rgs-ibg.onlinelibrary.wiley.com/doi/10.1111/geoj.12507 by Test, Wiley Online Library on [06/02/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 5 | ETHNIC RESIDENTIAL SEGREGATION Patterns of ethnic and racial residential segregation are important indicators of spatial integration and spatial inequality.The former-the extent to which there is mixing of ethnic groups in residential neighbourhoods-has received by far F I G U R E 6 Ethnic diversity (measured by the Reciprocal Diversity Index [RDI]) for LSOAs in England and Wales for (a) 2001, (b) 2011, (c) 2021 and (d) change 2001-21.Source: 2001 Census, 14754959, 2023, 1, Downloaded from https://rgs-ibg.onlinelibrary.wiley.com/doi/10.1111/geoj.12507 by Test, Wiley Online Library on [06/02/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License , we use an eight group categorisation (see column one) of: White (including, depending on time point: White British, White Irish, Gypsy or Irish Traveller, Roma, Other White), Indian, Pakistani, Bangladeshi, Chinese, Black African, Black Caribbean and Other (including, depending on time point: the four Mixed categories [Mixed White and Black Caribbean, Mixed White and Black African, Mixed White and Asian, Other Mixed], Other Asian, Other Black, Arab and Any Other).For analyses of change between 2001 and 2021, we include greater detail and merge the 16 (2001), 18 (2011) and 19 (2021) ethnic groups into a 16-group 6 categorisation of: White British, White Irish, Other White (including, depending on time point: Gypsy or Irish Traveller, Roma, Other White), Indian, Pakistani, Bangladeshi, Chinese, Black African, Black Caribbean, Mixed White and Black Caribbean, Mixed White and Black African, Mixed White and Asian, Other Mixed, Other Asian, Other Black, and Any Other (including, depending on time point: Arab and Any Other).Changes in national level ethnic group sizes are discussed in Section 3.
where    are the number of zones (here, 2021 LSOAs),    are the number of people in group m in LSOA i and there are   people in group m in England and Wales.   and   are the equivalent for group n.D is computed here across neighbourhoods for eight ethnic groups (see Table