17/2/09 1

MEASURING INEQUALITY IN RURAL ENGLAND: THE EFFECTS OF

CHANGING SPATIAL RESOLUTION

Meg Huby (Department of Social Policy & Social Work, University of York)

Steve Cinderby (Stockholm Environment Institute, University of York)

Piran White (Environment Department, University of York)

Annemarieke de Bruin (Department of Social Policy & Social Work, University of York)

(7224 words)

17/2/09 2

Abstract

The sustainability of rural development depends on the distribution of the social and

environmental resources needed to maintain and improve the vitality of rural areas. Here

we examine the complexity of measuring patterns of distribution using examples of

socio-economic data on rural poverty and affluence as well as data on environmental

quality and species richness. We demonstrate how changes in the base spatial units used

for analysis have different effects on different measures of inequality. The effects of such

changes in spatial resolution also depend on the underlying processes that generate the

data. The results of our investigations into the effects of scale on the assessment of

inequality suggest that where data come from both the social and natural science sources,

the most appropriate level for analysis is that of the finest common resolution. This may

result in redundancy of effort for some types of data but any such disadvantage is offset

by the benefits of identifying inequalities that are masked at coarser resolutions.

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Introduction

The achievement of sustainable rural development implicitly depends on the distribution

of social, economic and environmental goods and services that are needed to maintain,

reinforce or improve the vitality of rural areas. Although social and environmental

inequality is high on the policy agenda (HM Government, 2005; Warburton, 2006;

Coleman and Duarte-Davidson, 2007; Defra 2008) there has been little research

investigating specifically rural inequalities from an interdisciplinary perspective. The

term ‘inequality’ is used in this paper to refer simply to the dispersion of a distribution,

following precedents set by Litchfield (1999) and Kokko et al. (1999) in the social and

natural sciences respectively. This terminology distinguishes between inequality and the

more subjective term ‘inequity’ which we use to imply unfairness or injustice (Le Grand,

1991). Here we show how patterns of distribution in social and environmental conditions

can be measured and how measures of inequality are affected by the resolution of the data

used.

The identification of environmental and social inequalities requires data from a range of

sources and environmental and socio-economic studies tend to adopt different types of

spatial areas as their base units. Socio-economic studies are usually based on

administrative units such as local authority districts, wards or primary care trusts (Martin,

1996). In contrast, environmental data are mainly collected in units related to either

physical attributes of the environment such as watersheds, or regular sampling grids

related to the technology or methodology used to acquire or store the data.

In a previous study Huby et al. (2005; 2007) constructed a unique dataset integrating

information about both socio-economic and environmental conditions in rural areas

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(SECRA) of England using common base spatial units. An up-dated subset of the

SECRA data is used in this paper. Analytical results may, however, be sensitive to the

modifiable unit area problem (MAUP) (Openshaw, 1984; Wiens, 1989; Fotheringham

and Wong, 1991; Liu, 2001; Palladini, 2004).

Here we examine some of the resolution effects of the MAUP and their implications for

research into inequalities in rural England. There is much value in research that seeks to

examine rural and urban areas alongside each other and compare the two types of area

(Wheeler, 2004; Commission for Rural Communities, 2008). However, sufficient

comparative work has been done to suggest that specific conditions in rural areas make

them legitimate subjects for research interest in their own right (Noble and Wright, 2000).

Rural deprivation, for example, may be exacerbated by low benefit take-up rates

(Commission for Rural Communities, 2007) and is often dominated by accessibility

problems (Moseley and Owen, 2008). In rural areas housing availability is particularly

subject to the effects of inward migration of older people and younger commuters (Best

and Shucksmith, 2006) and employment and training opportunities are often limited

(Shucksmith, 2004). The relationship (and potential conflict) between social and

environmental protection is especially marked (Huby et al. 2005). There is a compelling

argument for research that examines the ways in which rural areas differ from each other,

not only in terms of social and economic inequalities but also in their ecological and

environmental conditions. Any such research, however, requires the selection of common

spatial units that takes into account the effects of the MAUP.

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Aims of this paper

We begin with a brief overview of the literature, distinguishing between statistical and

conceptual explanations of the MAUP and emphasising the need for a multi-scale,

empirical approach.

On the basis of statistical and technical considerations we hypothesise that changing the

units of analysis will affect some indicators of inequality more than others when all are

measured across the same geographical extent. We test this hypothesis by calculating

five different measures of inequality in income deprivation across rural England using

spatial data at four different resolutions.

Finally we test the idea that different types of variable are differentially affected by

changes in the resolution of spatial units of analysis. We use income deprivation, barriers

to housing, number of bird species and air quality. Because socio-economic and

environmental processes underlying these data operate at different spatial scales we

hypothesize that the level of resolution beyond which no further detail on inequality is

picked up will be different for each.

Resolution Effects of the MAUP

The effects of resolution on analytical results pose persistent problems in both the natural

and social sciences (Wiens, 1989; Levin 1992; Liu, 2001). The complex interactions in

multi-variable analysis make the theoretical anticipation of resolution effects extremely

difficult and empirical approaches are increasingly advocated (Fotheringham and Wong,

1991; Tranmer and Steel, 2001). While the selection of base units for analysis is often

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pragmatic and constrained by the availability of data (Maantay, 2002), the MAUP can be

addressed to some degree.

One important consideration is the statistical effect of changing the resolution of the

analytical units. When data are averaged or summed to larger units, a ‘smoothing’ effect

occurs leading to reduced variance between units. As the level of aggregation increases,

correlation coefficients increase Fotheringham and Wong (1991). Tranmer and Steel

(2001) and Taquino et al. (2002) similarly demonstrate general patterns of higher

regression coefficients at coarser resolutions. However, there is little literature relating to

similar effects on statistical measures of inequality.

Liu (2001) and Taquino et al. (2002) argue that the selection of an appropriate unit of

analysis should be based on conceptual as well as statistical considerations. Manley et al.

(2006) demonstrate how the processes generating different types of data operate at

different spatial resolutions and thus different sized units are appropriate for their

representation. When data are collected at the same level as the processes generating

them, disaggregation to a finer resolution, while not losing information, will not reveal

any variation beyond that observed between the original units. Aggregating the same data

to a coarser resolution, however, can reduce the variability observed between units as

discussed above.

Methods

In this paper we use Lower Layer Super Output Areas (LSOAs) of rural England as initial

base units. The advantage of LSOAs is that they are designed to nest within other

administrative areas, allowing us to examine the effects on inequality measures of

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aggregating data from LSOA level to that of wards1, districts and Joint Character Areas2

(JCAs). Since our research is solely concerned with rural England, we use the UK

Government’s definition of rurality, based on both settlement size and context (ODPM,

2002). The indicators for the wards, districts and JCAs have been calculated only for

those parts of the larger units that consist of rural LSOAs. The indicators therefore only

apply to the rural parts of wards, districts and JCAs.

LSOAs are generally consistent in population size, with a mean of 1596 and median of

1538 residents in rural England. They are ideal for the analysis of social and economic

data collected and available at this level. The incorporation of environmental data,

however, requires that these data are assigned to LSOA polygons using boundary shape

files within a geographic information system. The methodological considerations of

combining data from different sampling regimes, scales and themes to a consistent unit of

analysis are described in Huby et al. (2007).

Analyses in this paper use indicators of income deprivation and barriers to housing that

have been allocated to LSOAs for the English Indices of Deprivation 2007 (CLG, 2007).

Our air quality variable is from the same source. Data on bird species richness were

attributed to LSOA level for the SECRA dataset using methods documented in Huby et

al. (2005; 2007). These social and environmental variables have values that can be

aggregated to larger units and their provenance is summarised in Table 1.

[Table 1 here]

1 http://www.statistics.gov.uk/geography/electoral_wards.asp

2 http://www.countryside.gov.uk/LAR/Landscape/CC/jca.asp

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Results

The effect of resolution on measures of inequality

There exists a plethora of techniques attempting to capture measures of inequality and

McKay (2002: p3) argues that ‘different inequality indices implicitly represent different

value judgements, notably on the relative weight given to different parts of the

distribution’. However, for a fixed number of analytic units and a fixed amount of

resource, Kokko et al. (1999) propose that almost any index is appropriate. Here we focus

on five inequality measures in common use in the social and natural sciences (Table 2).

[Table 2 here]

By calculating these measures for the same variable but different base units we can assess

the relative effects of spatial resolution. In the first instance we use a variable indicative

of income deprivation, taken from the English Indices of Deprivation 2007 and

representing the proportion of residents living in households in receipt of certain means-

tested benefits (CLG, 2007).

[Table 3 here]

Every measure used shows a decrease in inequality as the size of the base spatial unit is

increased (Table 3). Since the extent of the analysis remains constant, increasing the size

of the base units leads to a decrease in their number which will at least partly account for

the changes in the coefficient of variation and entropy measures. However, the Gini

coefficient is also lower at coarser resolution suggesting the effect on inequality is a real

one. This result is presented graphically as a set of Lorenz curves in Figure 1.

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[Figure 1 here]

The Lorenz curves plot the cumulative proportion of ‘resource’, in this case income

deprivation, against the cumulative proportion of base area units ranked in order of the

income deprivation they contain. If income deprivation were distributed evenly the graph

would be the straight diagonal line shown on Figure 1. The more the actual curve

deviates from this diagonal, the more inequality is present. Figure 1 shows decreasing

inequality as the size of the base units is increased.

These results suggest that in a wider study of rural inequalities, it would seem desirable to

use LSOAs in preference to larger spatial units as the latter may mask inequalities in

income deprivation. This decision nevertheless may need consideration in the light of the

scale of particular policy questions.

Differential effects of changes in resolution on different types of variable

Income deprivation as captured by the income domain of the English Indices of

Deprivation 2007 reflects household receipt of means tested benefits. This process

depends largely on local opportunities for employment and local rates of pay. Where

underlying processes operate at such a local level we might expect to find that analyses

using large base units such as local authority districts or JCAs mask inequalities that only

become evident at finer resolution such as that of LSOAs.

Other socio-economic variables, on the other hand, relate to processes occurring at higher

administrative levels. Opportunities for housing, for example, are likely to vary according

to local authority policies on social housing and homelessness as well as on house prices

and affordability. Here we hypothesise that using data at a finer resolution than

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administrative districts is unlikely to yield any further detail on inequality. The English

Indices of Deprivation 2007 provide a variable indicative of barriers to housing. The

derivation of this variable, combining data from both local and district levels, is described

in CLG (2007).

[Table 4 here]

Although there is some decline in measured inequality when we change the base unit

from LSOA to ward, this is much less marked than for the income variable (Table 4). The

Gini coefficient for income deprivation, for example, falls by 19.9 per cent when we

move from LSOA to ward level. The corresponding fall for barriers to housing is only

five per cent. From ward to district level the fall is three percent although a steeper fall of

13 per cent occurs when we move from district to JCA level. The result supports the

hypothesis that reducing data resolution below district level reveals little further

inequality in the variable.

We turn next to examine ecological and environmental variables which we might expect

to be conditioned by processes operating at broader levels such as district or JCA. The

average number of wild bird species in areas, for example, is likely to vary with climatic

conditions as well as with more localised aspects of habitat suitability. Birds are found in

a wide range of habitats and are sensitive to environmental change making them useful

indicators of the general health of ecosystems (Gregory et al., 2005). Bird species

richness is commonly used an indicator of biodiversity (Dillon and Fjeldsa, 2005; Kleijn

and Sutherland, 2003; Orme et al., 2005). Although the movements of individuals of

some species may be quite limited, previous research has shown that population and

community processes in birds can operate at larger scales, for example across 25 km2

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units (Bennett et al., 2004). The hypothesis here then is that larger analytical units such as

JCAs will be well suited to identify inequality in bird species richness.

[Table 5 here]

This is not the case however. For every measure, more inequality is picked up by analysis

at finer resolution, with the greatest increase between district and ward level (Table 5).

We can only surmise the reasons for this finding. One possibility is that the processes

underlying bird species distributions are dominated by local conditions rather than simply

by broader scale climate and topography. However, the bird species we are counting in

one area may be different from those in another. There is scope here for analysis of data

generating processes at a number of different levels.

Our final variable is an indicator of air quality. Taken from the English Indices of

Deprivation 2007, it is a simple air quality index, also used by Wheeler (2004), based on

an index developed by Sol et al. (1995). For each of four pollutants - nitrogen dioxide,

particulates, sulphur dioxide and benzene - the ambient atmospheric concentration is

related to a guideline or standard value so that lower values imply better overall air

quality. The pollutants used in the indicator are largely, if not exclusively, linked to fuel

combustion so patterns of dispersion are expected to follow transport routes, cities and

industrial sites. Consequently we hypothesise that inequalities in the air quality indicator

will be largely independent of the resolution levels used in our analyses. Table 6 shows

that this is indeed the case, with marginally more inequality apparent when data are

aggregated to the level of JCAs.

[Table 6 here]

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Discussion

The use of rural LSOAs as base spatial units

LSOAs have many advantages for the type of methodological exploration we have

undertaken here but they also have disadvantages. One major drawback is that, while they

are relatively constant in terms of population size, they vary considerably in spatial size.

Anderton (1996) warns against the confounding of areas and populations in studies of

environmental equity but common spatial units are required for research hypotheses

relating environmental conditions to the characteristics of human populations in

particular places. The 6027 rural LSOAs in England have a mean area of 18km2 (median

9.66km2). Over three quarters are under 25km2 but 14 are over 200km2. Very large

LSOAs can appear to dominate cartographic representations of distribution as larger areas

attract the eye of the reader (Noble and Wright, 2000). A more important implication of

variation in size is that it makes the business of attributing data originating at other spatial

scales extremely complex. We have discussed this in detail in an earlier paper (Huby et

al., 2007) and note that the problem is particularly acute when using both socio-economic

and ecological-environmental variables in the same analysis.

In attributing numbers of bird species to each LSOA, for example, we have assumed that

the species are evenly distributed across the areas. We should ideally like to ensure that

the chance of observing them is the same for both large and small LSOAs. However,

depending on the actual numbers of birds of each species (for which no data are

available) and on the location and movements of the human population, this chance may

be higher for smaller LSOAs. Similarly open to criticism is the indicator of air quality

when used in the context of social health and well-being. This measure has been more

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widely used in work on environmental inequality (Walker et al., 2003; Wheeler, 2004;

Fairburn et al., 2005; Wheeler and Ben–Schlomo, 2005). Not only does it often assume

that human exposure to air pollution is distributed evenly across the spatial units but it

also fails to take account of the complex relationships between exposure and risk. It

should be remembered that research into environmental inequality is still in its infancy

and these are problems that may be eventually resolved.

Their designation as rural or urban under the official government definition (Bibby and

Shepherd, 2004) makes LSOAs useful for research focusing on the specific features of

rural areas. However, any such definition is open to criticism. There is no single perfect

way to define rural areas so there remain questions about the fuzziness of boundaries

between ‘rural’ and ‘non-rural’ parts of the wards, districts and JCAs used in this paper.

In spite of their drawbacks, LSOAs have enormous value in providing fine-resolution

units for use in integrated research.

Measuring rural inequality

We have shown above that, for analysis over a fixed geographical extent, inequalities in

income deprivation appear greater at finer resolution for each measure of inequality

tested. These resolution effects depend on the statistical measure used. When the base

unit of analysis is changed from LSOA to units of coarser resolution he greatest changes

occur in the coefficient of variation and in entropy (Table 7).

[Table 7 here]

Both of these measures are sensitive to changes in the size of the sample, a figure that

necessarily falls as the base units are increased in area. The smallest effect is seen in the

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interquartile range ratio, a measure that relies on only two data points. More interesting is

the effect on the Gini coefficient, a measure of inequality that captures the whole of the

distribution, is insensitive to sample size and is independent of the mean value.

According to this measure, data at finer resolution are needed to capture existing

inequalities in the distribution of income deprivation in rural England. Indeed recent

research by OCSI (2008) suggests that, for many socio-economic indicators, analysis

even below LSOA level is necessary to identify the pockets of rural deprivation hidden in

analysis by larger areas. However, the advantages of working at finer resolutions may be

offset by the constraints placed on data availability by the need to preserve anonymity.

We have shown above that the effects of changing data resolution are also dependent on

the type of variables under analysis. The detailed results for different variables can be

summarised generally by the ‘aggregation effect’ introduced by Tranmer and Steel

(2001). This statistic is calculated as the ratio of the variance in data aggregated into

larger spatial units (coarser resolution) to the variance in data at the original spatial units

(finer resolution). Figure 2 shows the results for each of the four types of variable used in

our analyses.

[Figure 2 here]

A more detailed summary of the effects of changing resolution on the Gini coefficient for

each of our four variables is given in Figure 3.

[Figure 3 here]

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Here we see a significant fall in the Gini coefficient for income deprivation at each

decrease in data resolution. The only significant fall in the coefficient for barriers to

housing however is from LSOA to JCA level.

For bird species richness, Gini coefficients based on LSOAs and wards are similar but

those for districts and JCAs are significantly lower. There are no significant effects on the

Gini coefficients for air quality at any of the changes in resolution used here.

Figures 2 and 3 show that increasing the resolution of analytical units down to LSOA

level reveals more inequality in income deprivation than when larger units are used.

Inequality in barriers to housing, however, could be captured adequately at LSOA, ward

or even district level. Little information would be lost in examining inequality in bird

species richness at ward rather than LSOA level, while variation in air quality is likely to

be observed as well at JCA level as at finer resolution.

Research into relationships between social and environmental factors

Where research integrates data from both the natural and social sciences, the effect of

resolution can be complex. Wiens (1989) argues that ‘different patterns emerge at

different scales of investigation of virtually any aspect of any ecological process’ (p386).

Consideration of statistical techniques and data provenance may provide a rationale for

the selection of appropriate spatial base units for a single variable but the difficulty in

establishing a resolution suitable for a set of variables of different types is evident from

the range of units used in research into environmental inequalities. Cutter et al. (1996)

demonstrate how apparently contradictory findings can arise from environmental equity

analyses carried out at different spatial scales and argue that such discrepancies affect the

comparability of studies. Mitchell and Dorling (2003) illustrate the range of units used in

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UK air quality social equity studies (Table 1, page 912). In the past five years an even

greater range of units has been used in research into wider aspects of environmental

inequalities in Britain and other parts of Europe (Table 8).

[Table 8 here]

Where does this leave us if we want to examine multiple dimensions of social and

environmental inequality in rural England? The results presented here suggest a need for

compromise. By working at LSOA level we can be sure to capture inequality in those

phenomena that reflect broader processes. Even though working at this resolution may be

strictly unnecessary for certain variables, for others it may still not really be fine enough.

However, any advantages of attempting to increase the resolution of our analysis, for

example to the level of the output areas that make up the larger LSOAs, would be offset

by a reduction in the range of reliable data available. For socio-economic data this

reduction is related to the need for anonymity and the constraints of using non-disclosive

information. Ecological and environmental data covering the whole of England are not

available at units smaller than LSOAs and most data are not robust enough to

disaggregate to a finer resolution. Disaggregation even down to the level of LSOAs is not

a simple matter but demands a clear understanding of the scientific, social and

geographical context.

Policy implications

There is a growing recognition by policy-makers that environmental equity is a key

prerequisite for sustainable development. In the European Union the Aarhus Convention

on public access to justice in environmental matters has been in force since 2001 (Wates,

2005) and the idea of placing environmental protection in the context of social justice is

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gaining ground in the UK (Agyeman and Evans, 2004). In England and Wales the

Environment Agency has commissioned research to investigate environmental

inequalities in relation to flood risk (Walker et al., 2006), cumulative impacts (Stephens

et al., 2007), water quality (Damery et al., 2008a), and waste management (Damery et

al., 2008b). Defra is including environmental justice in the development of its Third

Sector Strategy and fairness is a main theme of a recent thematic review of food

production and consumption (Sustainable Development Commission, 2008).

Any policies aiming to reduce inequities require first a robust definition of where

inequalities exist. Where these inequalities concern both social and environmental factors

which are potentially inter-related, it is essential to base analyses on common spatial

units. Our results have shown that for rural areas in England, LSOAs are the most

appropriate units of analysis for highlighting inequalities. More generally, our work

suggests that inequalities can be identified most effectively by using the finest resolution

that can accommodate both types of data. This permits much greater precision in

identifying areas of inequality, and hence provides the potential for highly-targeted policy

initiatives to reduce inequity and unfairness in promoting sustainable development.

Acknowledgements

This paper forms part of a wider study, developing qualitative research techniques to

elaborate the findings of quantitative measurements of social and environmental

inequalities. The project ‘Social and environmental inequalities in rural areas’ is part of

the Rural Economy and Land Use (RELU) programme, funded by the ESRC, NERC,

BBSRC with additional funding from SEERAD and Defra. We should like to

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acknowledge the advice and support provided to the project by Nicola Lloyd and Justin

Martin of the Commission for Rural Communities and Kieron Stanley of the

Environment Agency.

References

Agyeman J, Evans B, 2004, "'Just sustainability': the emerging discourse of environmental

justice in Britain?" The Geographical Journal 170 155-164

Anderton D L, 1996, "Methodological issues in the spatiotemporal analysis of environmental

equity" Social Science Quarterly (University of Texas Press) 77 508-515

Bennett A F, Hinsley S A, Bellamy P E, Swetnam R D, MacNally R, 2004, "Do regional

gradients in land use influence richness, composition and turnover of bird assemblages in

small woods?" Biological Conservation 119 191-206

Best R, Shucksmith M, 2006, "Homes for Rural Communities", (Joseph Rowntree Foundation,

York)

Bibby P, Shepherd J, 2004, "Developing a New Classification of Urban and Rural Areas for

Policy Purposes - the Methodology", http://www.statistics.gov.uk/geography/nrudp.asp

Blowers A, Hinchcliffe S, 2003 Environmental Responses (Wiley, Chichester)

Boardman B, 1999, "Equity and the Environment", (Catalyst with Friends of the Earth, London)

Bowen W, 2002, "An analytical review of environmental justice research: what do we really

know?" Environmental Management 29 3-15

Bradshaw R, Cuff J, Rogers J, Watkins L, 2005, "Tackling Rural Disadvantage", (Commission

for Rural Communities, Cheltenham) p 19

Burningham K, Thrush D, 2003, "Experiencing environmental inequality: the everyday concerns

of disadvantaged groups" Housing Studies 18 517-536

17/2/09 19

Carter N, 2007 The politics of the environment: ideas, activism, policy (2nd Edition) (Cambridge

University Press, Cambridge)

CEH, 2004, "Centre for Ecology and Hydrology Land Cover Map",

http://www.ceh.ac.uk/data/lcm/LCM2000.shtm

CLG, 2007, "The English Indices of Deprivation", (Department for Communities and Local

Government, London)

Coleman G, Duarte-Davidson R, 2007, "Children's Environment and Health Action Plan",

(Health Protection Agency, Didcot)

Commission for Rural Communities, 2007, "Pension Credit take-up in rural areas. State of the

Countryside Update 4", (Cheltenham)

Commission for Rural Communities, 2008, "State of the Countryside 2008", (Commission for

Rural Communities, Cheltenham)

Cutter S L, Holm D, Clark L, 1996, "The Role of Geographic Scale in Monitoring

Environmental Justice", in Risk Analysis: An International Journal p 517

Damery S, Walker G, Petts J, Smith G, 2008, "Addressing environmental inequalities: water

quality", (Environment Agency, Bristol)

Damery S, Walker G, Petts J, Smith G, 2008, "Addressing environmental inequalities: waste

management", (Environment Agency, Bristol)

Defra, 2008, "Departmental Report 2008, Cm 7399", (Department for Environment Food and

Rural Affairs,, London)

Dillon S, Fjeldsa J, 2005, "The implications of different species concepts for describing

biodiversity patterns and assessing conservation needs for African birds" Ecography 28

682-692

17/2/09 20

Edwards-Jones G, Deary I, Willcock J, 1998, "Modelling farmer decision-making: What can

psychology do for agricultural policy assessment models?" Etudes et Reserches sur les

Systemes Agraires et le Development 31 153-173

English Nature, 2005, "Going, going, gone? the cumulative impact of land development on

biodiversity in England (Research Report 626)", (English Nature, Peterborough)

Evans K L, Greenwood J J D, Gaston K J, 2007, "The positive correlation between avian species

richness and human population density in Britain is not attributable to sampling bias"

Global Ecology and Biogeography 16 300-304

Fairburn J, Walker G, Smith G, Mitchell G, 2005, "Investigating environmental justice in

Scotland: links between measures of environmental quality and social deprivation (Project

UE4(03)01)", (Scotland and Northern Ireland Forum for Environmental Research

(SNIFFER), Edinburgh) p 153

Fitzpatrick S, 2005, "Poverty of Place. Centre for Housing Policy Working Paper", (Joseph

Rowntree Foundation, York)

Fitzpatrick T, Cahill M, 2002 Environment and Welfare: Towards a Green Social Policy

(Palgrave Macmillan, Basingstoke)

Fotheringham A S, Wong D W S, 1991, "The modifiable areal unit problem in multivariate

statistical analysis" Environment and Planning A 23 1025-1044

Friends of the Earth, 2001, "Pollution and Poverty - Breaking the Link", (FoE Policy and

Research Unit, London)

Gregory R D, van Strien A, Vorisek P, Mayling A W G, Noble D G, Foppen R P B, Gibbons D

W, 2005, "Developing indicators for European birds" Philosophical Transactions of The

Royal Society B 360 269-288

17/2/09 21

HM Government, 2005, "Securing the Future: delivering the UK sustainable development

strategy", (The Stationery Office, London)

Huby M, 1998 Social Policy and the Environment (Open University Press, Buckingham)

Huby M, Owen A, Cinderby S, 2007, "Reconciling socio-economic and environmental data in a

GIS context: an example from rural England" Applied Geography 27 1-13

Huby M, Cinderby S, Owen A, 2005, "Social and Environmental Conditions in Rural Areas:

report to accompany the SECRA dataset produced under the Rural Economy and Land Use

(RELU) programme", www.sei.se/relu

Kleijn D, Sutherland W J, 2003, "How effective are European agri-environment schemes in

conserving and promoting biodiversity?" Journal of Applied Ecology 40 947-969

Kokko H, Mackenzie A, Reynolds J D, Lindström J, Sutherland W J, 1999, "Measures of

inequality are not equal" The American Naturalist 72 358-382

Krebs C J, 1999 Ecological Methodology, 2nd Edition (Addison-Wesley, New York)

Laurian L, 2008, "Environmental Injustice in France" Journal of Environmental Planning and

Management 51 55-79

Le Grand J, 1991 Equity and Choice (HarperCollinsAcademic, London)

Levin S A, 1992, "The problem of pattern and scale in ecology" Ecology 73 1943-1967

Litchfield J A, 1999, "Inequality: Methods and Tools", http://worldbank.org/poverty

Liu F, 2001 Environmental Justice Analysis: Theories, Methods and Practice (CRC Press, Boca

Raton, Florida)

Lucas K, 2004 Running on Empty: transport, social exclusion and environmental justice (The

Policy Press, Bristol)

Lucas K, Fuller S, Psaila A, Thrush D, 2004 Prioritising Local Environmental Concerns: where

17/2/09 22

there's a will there's a way (Joseph Rowntree Foundation, York)

Maantay J, 2002, "Mapping environmental injustice: pitfalls and potential of geographic

information systems in assessing environmental health and equity" Environmental Health

Perspectives 110 161-171

Manley D, Flowerdew R, Steel D, 2006, "Scales, levels and processes: Studying spatial patterns

of British census variables" Computers, Environment and Urban Systems 30 143-160

Martin D, 1996 Geographic Information Systems: Socioeconomic Applications (Routledge,

London)

Martin D, 2002, "Geography for the 2001 Census in England" Population Trends 108 7-15

Martin D, Bracken J, 1993, "The integration of socioeconomic and physical resource data for

applied land management information systems" Applied Geography 13 45-53

Martin D, Nolan A, Tranmer M, 2001, "The application of zone-design methodology in the 2001

UK Census" Environment and Planning A 33 1949-1962

McKay A, 2002, "Defining and Measuring Inequality. Briefing Paper No. 1", (Overseas

Development Agency, London)

McLeod H, Langford I H, Jones A P, Stedman J R, Day J R, Lorenzoni I, Bateman I J, 2000,

"The relationship between socio-economic indicators and air pollution in England and

Wales: implications for environmental justice" Regional Environmental Change 1 78-85

Mikkelson G M, Gonzalez A, Peterson G D, 2007, "Economic inequality predicts biodiversity

loss" PLoS ONE 2 e444

Mitchell G, Dorling D, 2003, "An environmental justice analysis of British air quality"

Environment and Planning A 35 909-929

Mitchell G, Walker G, 2007, "Methodological Issues in the Assessment of Environmental Equity

17/2/09 23

and Environmental Justice", in Sustainable Urban Development Volume 2: The

Environmental Assessment Methods Eds M Deakin, G Mitchell, P Nijkamp, R Vreeker

(Routledge, London)

Mohan J, Twigg L, Barnard S, Jones K, 2005, "Social capital, geography and health: a small-area

analysis for England" Social Science & Medicine 60 1267

Moseley M J, Owen S, 2008, "The future of services in rural England: The drivers of change and

a scenario for 2015" Progress in Planning 69 93-130

Noble M, Wright G, 2000, "Identifying poverty in rural England" Policy & Politics 28 293-308

OCSI, JH Research, 2008, "Deprivation in rural areas: Quantitative analysis and socio-economic

classification", (Oxford Consultants for Social Inclusion, Brighton)

ODPM, 2002, "Urban and rural definitions: a user guide", (London) p 78

Openshaw S, 1984 The modifiable areal unit problem (Geobooks, Norwich)

Orme C D L, Davies R G, Burgess M, Eigenbrod F, Pickup N, Olson V A, Webster A J, Ding T

S, Rasmussen P C, Ridgely R S, Stattersfield A J, Bennett P M, Blackburn T M, Gaston K

J, Owens I P F, 2005, "Global hotspots of species richness are not congruent with

endemism or threat" Nature 436 1016-1019

Palladini S, 2004, "ArcObjects Development in Zone Design Using Visual Basic for

Applications", in Computational Science and Its Applications – ICCSA 2004 p 1057

Paskell C, Power A, 2005, "'The future's changed': impacts of housing, environment,

regeneration policy since 1997", (Centre for Analysis of Social Exclusion, London School

of Economics, London)

Power A, 2000, "'Poorer areas and social exclusion', in Social Exclusion and the Future of Cities

CASE Paper 35", (Centre for the Analysis of Social Exclusion, London School of

17/2/09 24

Economics, London)

Sang N, Virnie R V, Geddes A, Bayfield N G, Midgley J L, Shucksmith D M, Elston D, 2005,

"Improving the rural data infrastructure: the problem of addressable spatial units in a rural

context" Land Use Policy 22 175-186

Shucksmith M, 2004, "Young people and social exclusion in rural areas" Sociologia Ruralis 44

43-59

Sol V M, Lammers P E M, Aiking H, Boer J d, Feenstra J F, 1995, "Integrated environmental

index for application land-use zoning" Environmental Management 19 457-467

Stephens C, Willis R, Walker G, 2007, "Addressing environmental inequalities: cumulative

impacts", (Environment Agency, Bristol)

Sustainable Development Commission, 2008, "Green, healthy and fair: a review of government's

role in supporting sustainable supermarket food", (SDC, London)

Sutherland W J, 2004, "A blueprint for the countryside" Ibis 146 230-238

Taquino M, Parisi D, Gill D A, 2002, "Units of analysis and the environmental justice

hypothesis: the case of industrial hog farms" Social Science Quarterly 83 298-316

Tranmer M, Steel D, 2001, "Using local census data to investigate scale effects", in Modelling

Scale in Geographical Information Science Eds N J Tate, P M Atkinson (John Wiley &

Sons, London)

van Lenthe F J, Brug J, Mackenbach J P, 2005, "Neighbourhood inequalities in physical

inactivity: the role of neighbourhood attractiveness, proximity to local facilities and safety

in the Netherlands" Social Science & Medicine 60 763

Vanslembouck I, Huylenbroeck G v, Verbeke W, 2002, "Determinants of the willingness of

Belgian farmers to participate in agri-environmental measures" Journal of Agricultural

17/2/09 25

Economics 53 489-511

Walker G, Burningham K, Fielding J, Smith G, Thrush D, Fay H, 2006, "Addressing

environmental inequalities: flood risk", (Environment Agency, Bristol)

Walker G, Fairburn J, Smith G, Mitchell G, 2003, "Environmental Quality and Social

Deprivation (R&D Technical Report E2-067/1/TR)", (Environment Agency, Bristol)

Warburton D, 2006, "Social Dimensions of the Environment Agency's Work", (Environment

Agency, Bristol)

Wates J, 2005, "The Aarhus Convention: a driving force for environmental democracy" Journal

for European Environmental & Planning Law 2 2-11

Wheeler B, 2004, "Health related environmental indices and deprivation in England and Wales"

Environment and Planning A 36 803-822

Wheeler B W, Ben-Shlomo Y, 2005, "Environmental equity, air quality, socioeconomic status,

and respiratory health: a linkage analysis of routine data from the Health Survey for

England" J Epidemiol Community Health 59 948-954

White P J T, Kerr J T, 2007, "Human impacts on environment-diversity relationships: evidence

for homogenization from butterfly species richness patterns" Global Ecology and

Biogeography 16 290-299

Wiens J A, 1989, "Spatial scaling in ecology" Functional Ecology 3 385-397

17/2/09 26

Figure 1: Lorenz curves showing changes in inequality in income deprivation with

changing base units of analysis.

17/2/09 27

Figure 2: Aggregation effects of increasing the size of the base spatial unit from LSOA

level for each of four variables

17/2/09 28

Figure 3: Effects on the Gini coefficient of changing the resolution of units of analysis

showing 95% confidence intervals.

17/2/09 29

Table 1: Variables used in the analysis

Variable name Source Provenance

Income deprivation

Income domain of English Indices of Deprivation 2007

Derived for LSOAs as proportion of households in receipt of certain benefits (DWP, 2005; HMRC, 2005; NASS, 2006)1

Barriers to housing

Wider Barriers sub-domain of English Indices of Deprivation 2007

Derived for LSOAs using data from the 2001 Census, Local Authorities (CLG, 2005) and District level models (Heriot-Watt University, 2005)1

Air quality Indicator from the ‘outdoors’ living environment sub-domain of English Indices of Deprivation 2007

NAEI emissions of benzene, SO2, NO2 and PM10 modelled to 1km grid squares and allocated to LSOAs as summed proportions of defined standard values representing ‘safe’ maximum concentrations. (Geography Department at Staffordshire University)1

Wild bird species

SECRA dataset Bird diversity data (BTO, 1993) on a 10km grid intersected with LSOA boundaries. Number of species in each LSOA calculated using area weighted averaging2

1 See CLG, 2007 2 See www.sei.se/relu

17/2/09 30

Table 2: Inequality measures used in the natural and social sciences

Formula Value for an even

distribution

Value for maximum inequality

(monopoly)

Comments

Coefficient of variation

sxx

0 n Inequality increases with sample size

Entropy (Theils’ H) − pi ln pi

i=1

n

∑ 0 ln n Inequality

increases logarithmically with sample size

Interquartile range ratio

value at 75th percentile

value at 25th percentile

1 ∝ Not sensitive to outliers but only relies on 2 data points

Green’s coefficient of dispersion

(sx2 / x ) −1

xi −1i=1

n

∑

− 1(x)∑ −1

1 Nearly independent of population density & sample size

Gini coefficient (2i − n −1)xi

i=1

n

∑

n2µ

~0 1 Uses all parts of distribution and independent of sample size. Small transfer from top to bottom reduces inequality without affecting mean.

Adapted from Kokko et al. (1999) and Krebs (1999) Where: n = number of cases i = rank of case x = sample mean µ = population mean sx = variance pi = proportion of resource at ith case

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Table 3: Measures of inequality in distribution of income deprivation across rural areas of England

Base Unit of Analysis

Inequality measure Lower Layer Super Output Area (n=6027)

Statistical Ward

(n=2938)

District/Unitary Authority (n=269)

Joint Character

Area (n=154)

Coefficient of Variation 0.610 0.480 0.412 0.302

Entropy (Theil’s H) 0.157 0.100 0.075 0.043

Interquartile range ratio 2.076 1.753 1.656 1.560

Green’s F -0.00177 -0.00381 -0.04183 -0.07521

Gini coefficient 0.306 0.245 0.213 0.164

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Table 4: Measures of inequality in barriers to housing across rural areas of England

Base Unit of Analysis

Inequality measure Lower Layer Super Output

Area (n=6027)

Statistical Ward

(n=2938)

District/Unitary Authority (n=269)

Joint Character

Area (n=154)

Coefficient of Variation 0.178 0.172 0.165 0.143

Entropy (Theil’s H) 0.016 0.015 0.014 0.010

Interquartile range ratio 1.274 1.259 1.239 1.202

Green’s F -0.0000603 -0.0001249 -0.001349 -0.00241

Gini coefficient 0.100 0.095 0.092 0.080

Table 5: Measures of inequality in numbers of wild bird species across rural areas of

England

Base Unit of Analysis

Inequality measure Lower Layer Super Output Area (n=6027)

Statistical Ward

(n=2938)

District/Unitary Authority (n=269)

Joint Character

Area (n=154)

Coefficient of Variation 0.150 0.143 0.119 0.107

Entropy (Theil’s H) 0.012 0.010 0.007 0.006

Interquartile range ratio 1.216 1.207 1.167 1.140

Green’s F 0.0000018 0.0000029 0.00001 -0.0000013

Gini coefficient 0.084 0.080 0.067 0.060

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Table 6: Measures of inequality in air quality across rural areas of England

Base Unit of Analysis

Inequality measure Lower Layer Super Output Area (n=6027)

Statistical Ward

(n=2938)

District/Unitary Authority (n=269)

Joint Character

Area (n=154)

Coefficient of Variation 0.220 0.228 0.220 0.237

Entropy (Theil’s H) 0.025 0.026 0.025 0.029

Interquartile range ratio 1.319 1.337 1.328 1.418

Green’s F -0.0001897 -0.000401 -0.0040372 -0.007081

Gini coefficient 0.123 0.128 0.123 0.135

Table 7: Comparing the effects on different income deprivation inequality measures of

changing the base units of analysis

% change in inequality measure when Base Unit of Analysis is changed from LSOA to:

Inequality measure Lower Layer Super Output Area (n=6027)

Statistical Ward

(n=2938)

District/Unitary Authority (n=269)

Joint Character

Area (n=154)

Coefficient of Variation 0.0 -21.3 -32.5 -50.5

Entropy (Theil’s H) 0.0 -36.3 -52.2 -72.6

Interquartile range ratio 0.0 -15.6 -20.2 -24.9

Green’s F 0.0

Gini coefficient 0.0 -19.9 -30.4 -46.4

17/2/09 34

Table 8: Social and environmental inequality studies showing the range of spatial units used

Indicators used Associations observed Base units Reference

Annual mean NO2 concentration, age, Breadline Britain Index, NOx emissions from cars

Areas with fewest cars have highest pollution; more car ownership – cleaner air. More pollution where parents likely to live; less where elderly tend to migrate. Areas with most pollution emit the least and tend to be among the poorest.

Wards (Great Britain) Mitchell & Dorling (2003)

Index of Multiple Deprivation 2000, flood risk, IPC sites

Tidal floodplain residents include more people in poorest decile. Fluvial floodplain residents include more people in best-off decile. Residents within 1km of IPC sites include more people in poorest decile. Most deprived areas have highest concentrations of air pollution

Wards (England)

Wards in Wales show similar but less marked results

Walker et al. (2003)

Ambient air quality, chemical emissions, landfill sites, major accident hazards, Carstairs Index

Analyses strongly suggestive of inequities but associations vary with measures considered and with urban or rural context.

Wards (England & Wales)

Wheeler (2004)

Ecological boundary of heathland area, development measures

Habitats in S England face a number of cumulative impacts from development pressures

Special Protection Areas English Nature (2005)

Industrial pollution, derelict land, landfills, quarries, green space, river water quality, air quality, Scottish Index of Multiple Deprivation

People in most socially deprived areas more likely to be living near industrial and air pollution, derelict land and poor water.

Census data zones (Scotland) with approx equal populations (431-2813) but varying considerably in size

Fairburn et al. (2005)

Physical inactivity, education, occupation, employment, neighbourhood attractiveness, safety

In poorer neighbourhoods, increased probability of walking/cycling to shops/work. But lower probability of walking/cycling, gardening, sports in leisure time.

Neighbourhoods with average 2200 residents (Netherlands)

van Lenthe et al. (2005)

Social capital, geography, health outcomes

Little evidence at this spatial scale that social capital has a beneficial effect on health outcomes.

Electoral wards (England)

Mohan et al. (2005)

Index of Multiple Deprivation 2000, IPC sites

IPC sites disproportionately located and clustered in deprived areas.

Wards and buffered site locations

Walker et al. (2005)

Air quality, social class Urban lower social class households more likely to live in areas of poor air quality. In rural areas, association, if anything, was reversed.

Wards (England) Wheeler & Ben-Schlomo (2005)

Bird species richness, human population density

Species richness increases with human population density then decreases at very highest densities.

Raster grid of 10x10 km squares

Evans et al. (2007)

Butterfly species richness, growing season temperature, habitat heterogeneity, insecticide application, paved roads, human footprint map

In human dominated areas insecticide applications, habitat loss and road networks reduce spp richness but effects are relatively small.

Raster grid with 6.6 km pixcels

White & Kerr (2007)

Hazardous sites, income, employment, industrialisation, born abroad.

Towns with higher proportions of immigrants have more hazardous sites.

Towns or ‘communes’ (France) Average area 14.9 km2 with ‘a dozen to hundreds of thousands of residents.’

Laurian (2008)