Technical Methodology Paper

June 2026

Introduction

About this technical report

This report presents the conceptual framework behind 3ni’s Social Capital Score. The measure has been created by 3ni’s research partner OCSI (Oxford Consultants for Social Inclusion) following a thorough literature review, evidencing the definitions, methodologies and indicators used across other research papers to measure social capital. The focus of this research was on different approaches to measuring Bonding, Bridging and Linking social capital and identifying any relevant indicators or proxy indicators which could be drawn on at neighbourhood level. It builds on the recent Social Capital 2025 series of papers published in partnership by 3ni, Local Trust and Demos, and the development of 3ni’s discovery tool to help identify community needs and
strengths at the hyper-local level.

This technical report provides an outline of the methodology for creating the Social Capital Score; the component indicators and dimensions and the decisions taken to inform the methodological approach. It also includes an analysis of the results, using visualisations to identify the neighbourhoods with low levels of social capital, including an exploration of how these areas fare on
other measures of social need such as the Indices of Multiple Deprivation 2025 (IMD) and Community Needs Index 2023 (CNI).

What is social capital?

Social capital is often understood as a kind of community asset, impacting a community’s capacity for resilience with a focus on neighbourhood cohesion, civic engagement and the availability of resources to maximise both. Following this widely accepted framework, social capital has been explored in this research through three interconnected dimensions:

• Bonding social capital refers to the strong, close-knit ties among individuals with similar backgrounds, such as family, close friends, or neighbours. These connections foster a sense of belonging, emotional support, and shared identity within relatively homogeneous groups. This form of social capital is often associated with internal cohesion and resilience at the local level (Norris et al., 2008; Ahn & Davis, 2020; ONS, 2022; Irfan et al., 2023).
• Bridging social capital captures the relationships that span across diverse social groups, linking people from different ethnic, socio-economic, or cultural backgrounds. These ties are characterised by more distant but broader networks that promote the exchange of information, increase tolerance, and support inclusive community participation (McCulloch, 2003; ONS, 2022; Irfan et al., 2023). Bridging ties are particularly important for social mobility and cross-community collaboration.
• Linking social capital refers to the vertical connections between individuals or communities and institutions, such as local government, public services, or other centres of power and authority. These relationships enable access to resources, opportunities, and influence beyond the immediate community, and are critical for navigating systems, improving outcomes, and addressing structural disadvantage (Szreter & Woolcock, 2004; Norris et al., 2008; Irfan et al., 2023; ONS, 2022).
  

Based on the above definitions, high levels of social capital generally suggest a stronger ability for collective action, mutual support and resilience in the face of challenges (like economic shocks, health crises, or environmental risks). Conversely, low social capital can indicate neighbourhood fragility, social isolation or barriers to accessing services and opportunities — all of which can undermine community wellbeing and resilience.

Creating the Social Capital Score at neighbourhood level

The Social Capital Score has been created as a measure of social capital that can be explored at the neighbourhood level using indicators and proxy indicators derived from established literature and available data sources. This approach captures the multi-dimensional nature of social capital (as defined above), while remaining sensitive to local context and the need for small-area
measurement to support local level change. The sections below outline the steps taken to develop the score.

Identifying dimensions to measure social capital

In order to develop this measure, each of these broad concepts of social capital have been constructed as a ‘dimension’ including a set of indicators or proxy indicators that were drawn out from the literature review. These dimensions have then been combined to create an overall measure of social capital at neighbourhood level. The dimensions can be summarised as follows.

• Bonding: Capturing multiple dimensions of local social capital including socio-economic diversity, income inequality, neighbourhood relationships and support, crime levels and residential stability.
• Bridging: Reflecting civic engagement and community capacity through the presence of civic assets, third sector organisations, volunteering levels, unpaid care provision and occupational diversity.
• Linking social capital: Highlighting connections (or lack thereof) between communities and formal institutions of power and influence such as voter turnout, civic engagement, high social grade and public or third sector employment

Selecting the geographic unit of analysis

This section explores the approach for selecting the geography to use as the building block in constructing the Social Capital Score. In the absence of data at the level of individuals or households, a measure that identifies social capital should be constructed from data on small geographic units of a standard population size. This measure has therefore been developed as an area-based
indicator. An area can be characterised as having low social capital relative to other areas on the basis that a higher proportion of people in the area are experiencing barriers to social capital (e.g. poor social relationships or low civic engagement) or if the area as a whole is lacking in infrastructure to address low social capital (e.g. third sector organisations, occupational diversity). In other
words, both the experience of the people in an area and the areas’ infrastructure gives the area its Social Capital Score.

The selection of the unit of geography to use in an area-based analysis is important as it affects both the data we can draw from, and crucially, the focus areas for intervention and resource allocation which are identified as an outcome of the research.

The following key principles have been considered when selecting the appropriate unit of geography for the measure:

• It should be possible to align the geography units to statistical geography boundaries in order to link key socio-economic indicators to the geography units.
• Geography units should be of sufficient size in order to ensure they are not smaller than the smallest standard statistical geographies (Output Areas), so that it is possible to obtain key socio-economic indicators to be used in the analysis.
• Geography units should be at a neighbourhood (sub-Local Authority) level in order to capture inequalities in social infrastructure provision and participation.
• Geography units should be relatively homogenous in population size so that it is possible to make direct comparisons between communities in terms of their relative needs and community and civic strength.
• Geography units should be meaningful and recognised as areas by the people residing in them.

LSOAs were identified as the preferred unit of measure for a number of reasons:

• They only change after every census, so they are more consistent over time. Even when changes are made following census updates, these changes are capped, with a minimum of 95% of boundaries remaining unchanged. They therefore represent a more stable geography than wards.
• LSOAs are designed to be fairly homogenous in size (averaging at 1,700 people). They also nest directly with smaller statistical geographies (Output Areas).
• To support the identification of rural pockets of need, which tend to be revealed at smaller geographical scales. By contrast, single MSOAs and wards can encompass multiple villages with very different characteristics.
• Finally, LSOAs are a more commonly used geography and are increasingly used to disseminate key statistics releases.

Producing the Social Capital Score at LSOA level would therefore enable users to benchmark the performance of areas with low social capital against a wider range of socio-economic measures. This should increase the utility and analytical value of the indicator.

Identifying indicators

We have identified a set of measurable indicators and proxy indicators relevant to each dimension. The selection was guided
by studies that examined how social capital can be assessed using data available at small-area geographies. The table below summarises the dimensions and corresponding indicators used in this measure, alongside references to the key research sources that informed their inclusion.

The following table provides an overview of each of these indicators with metadata
concerning:

• Indicator name and description
• Timepoints the data is available for
• Data source
• Geographical unit at which the data is published
• Methodology notes
• Social capital source

Bonding

Bridging

Linking social capital

Overview of the methodology used to construct the Social Capital Score

This section provides an overview of the methodology used to construct the Social Capital Score, which (as outlined above) has been developed following a data driven evidence review of related literature on the subject. The construction of the Social Capital Score broadly consists of the following seven stages. These stages fulfil the purpose of defining the data inputs and data processing procedures and then producing the final measure.

• Dimensions of the Social Capital Score are identified
• The unit of geography is selected
• Indicators are chosen to provide the best possible measure of each dimension
  at the specified unit of geography
• ‘Shrinkage estimation’ is used to improve reliability of the small area data¹
• Indicators are combined to form the dimensions
• Dimension scores are ranked and the dimension ranks are transformed to a
  specified exponential distribution²
• The exponentially transformed dimension scores are combined using
  appropriate dimension weights to form an overall Social Capital Score at
  small area level. This stage completes the construction of the measure

The following steps outline the methodology of data processing used to construct the Social Capital Score.

Step 1: Convert all indicators to LSOA geography
The Social Capital Score has been produced at Lower-layer Super Output Area (LSOA) geography (using the updated 2021 version of the LSOA boundaries which were developed as part of the Census 2021 outputs). However, a number of the indicators in the measure are not published at 2021 LSOA level. It is therefore necessary to convert these indicators to 2021 LSOA geographies. The table below outlines our approach to converting indicators to 2021 LSOA level:

Step 2: Quality assurance of the data

The next step was to comprehensively check the distributions of all the indicators at LSOA level to ensure that all indicators have passed the relevant fitness tests and are “fit for purpose”. These tests include excluding indicators with high numbers of zeros or equal upper limits (for example where a large number of areas have values of 100%) which would distort the measure. All of the indicators selected above passed these quality assurance tests.

Step 3: Producing composite indicators

All indicators listed in the previous section are included in the final Social Capital Score. However, a small subset of conceptually related indicators were first amalgamated into composite indicators before being combined with the remaining indicators to create the dimension scores. The purpose of producing these composite indicators was to improve robustness and capture multiple facets of the same underlying concept. The table below therefore shows only the subset of indicators that were grouped together into composite measures; all other indicators from the full framework remain included individually within the index.

Step 4: Applying shrinkage to improve the robustness of indicators

Where a rate or other measure of social capital for a small area is based on small numbers, the resulting estimate may be unreliable, with an unacceptably high standard error. The technique of shrinkage estimation is used to ‘borrow strength’ from larger areas to increase the reliability of small area data; the impact of shrinkage will tend to move an LSOA’s score towards that of their parent higher-level area. Shrinkage moderates the levels of unreliability in the dataset and reduces the impact of chance fluctuations from year to year. Such scores occur most commonly where numbers are small at LSOA level and the event is thus relatively rare. This may be the case for the indicator as a whole or only for particular LSOAs. In shrinkage estimation the score for a small area is estimated as a weighted combination of that small area’s score and the mean value for a larger area from which the smaller areas within the larger area borrow strength. We have used the most up to date set of Local Authority Districts as the larger area in the shrinkage calculation for this measure. LSOAs within a single Local Authority District share issues relating to local governance. To a certain extent, they may also share issues relating to labour market sub-climates. Shrinkage has been applied to all indicators in the measure. Further details about the shrinkage technique are given in Appendix A.

Step 5: Ensuring that all indicators are “pointing in the same direction”

To combine the indicators into dimensions, it is necessary for each of the indicators to be orientated in the same direction. However, for some of the indicators included in the Social Capital Score, a high value indicates high levels of social capital – for example an area with higher voter turnout would be measured as having higher levels of social capital. By contrast, for other indicators, a high score denotes low social capital – for example areas with high income inequality or residential mobility. It is necessary therefore to ‘reverse the polarity’ for some scores to ensure that a high value is negative for all indicators – so they can be consistently combined.

Step 6: Standardisation

When combining measures, it is important to ensure that indicator scores are comparable and that the weighting of dimensions is not distorted by the variation in distribution across
different indicators. The indicators in the Social Capital Score are based on different metrics and each indicator in the measure needs to be standardised to ensure that they have a common distribution, so that indicators can be combined without a single indicator dominating due to having a wide distribution. Indicators in the Social Capital Score have therefore been standardised by ranking each of the indicators and then transforming to a normal distribution.

Step 7: Weighting

Because the Social Capital Score measure is a composite measure, decisions must be made as to the weight given to the various indicators and dimensions of the measure. There are a number of possible approaches to weighting the indicators in a dimension. Option 1 is to provide equal weightings to each of the indicators in a dimension. Option 2 is to apply different weights depending on theoretical judgements regarding the suitability of indicators in the model. Examples of this approach include applying higher weightings to indicators which are constructed from more robust administrative data sources and lower weightings to data from modelled data sources. Alternatively, higher weightings can be applied to indicators which more closely match the issue that is being captured – this can be ascertained through a Discrete Choice Experiment (DCE) – a survey of key stakeholders and people from impacted communities identifying the relative importance of indicators. Option 3 is to introduce a statistical technique called Maximum Likelihood Factor Analysis to determine the weights of the indicators within each dimension. Factor analysis works most effectively where there is a single overwhelming factor which explains the performance on a set of indicators within a dimension and where indicators within a dimension exert an influence on one another. A key advantage of using factor analysis is that it considers ‘double counting’ within dimensions.

However, if there is no underlying factor common among the indicators in a dimension, factor analysis is less effective. Factor analysis is also not statistically
robust with very few indicators (e.g. only two within a sub-dimension).

Having reviewed the indicators in each dimension, it was determined that an equal weighting would be applied to all of the indicators in each of the dimensions as well as when combining dimensions to create the overall social capital measure. This is largely due to the simplicity and transparency of applying equal weightings and because there is no clear rationale for assigning differential weightings within each dimension or to the overall score. Equal weights also reflect the equal importance afforded to each of the indicators within each dimension and the overall score.

Step 8: Standardising dimensions

The three-dimension scores are then combined to produce the overall Social Capital Score. However, each of the dimensions will be on a different scale to one another. It was therefore necessary to standardise the dimension scores before combining. The method of standardisation was to transform the dimensions to a specified exponential distribution using an exponential transformation function (see Appendix B for details). The exponentially transformed dimension scores were then combined to form an overall ‘Social Capital Score’ at LSOA level.

The exponential transformation method of standardisation differs from the normal distribution method as it gives more emphasis on the top end of the distribution (the areas with the highest scores) and so facilitates identification of the areas with the lowest social capital, in order to control cancellation effects (e.g. low social capital in one dimension is not completely cancelled out by high levels of social capital in a different dimension) and ensures that areas that perform particularly badly on one aspect of social capital are moved closer to the low end of the Social Capital Score spectrum even when they show positive outcomes on other indicators.

Step 9: Combining dimensions

Having standardised the dimensions, they were then combined to produce the overall Social Capital Score. The combination process involves summing each of the standardised dimension scores together to produce an overall Social Capital Score.

Analysis and outcomes

The maps below show the outcome of the Social Capital Score at Local Authority level, presenting the overall score. The map on the left shows the score as a comparison across all Local Authorities in England. The ‘Hotspots’ map on the right is based on the top 20% of areas across England only, specifically highlighting the Local Authorities with the lowest social capital.

Social Capital Score
Local Authority analysis
As highlighted in the map below, there are clear regional disparities in social capital across Local Authorities in England, with darker areas indicating lower levels of social capital. These areas are largely concentrated in the North of England, particularly around post-industrial urban centres such as Liverpool, Manchester, Sheffield and Middlesbrough, as well as parts of the Midlands, including Birmingham and Nottingham. While these patterns remain most pronounced in major urban areas, lower levels of social capital are also evident across a wider range of surrounding local authorities in these regions.

Coastal communities also feature prominently among the areas with the lowest levels of social capital, especially along the East and South coasts in places like Great Yarmouth, Thanet and Portsmouth. In contrast, rural areas across the South West, South East, and Welsh border regions tend to have higher levels of social capital, reflecting stronger community ties and
more stable populations.

These geographic patterns highlight where efforts to rebuild trust, civic participation, and community engagement may be most urgently needed to support long-term wellbeing and resilience.

LSOA analysis by region

The visualisations below show the Social Capital Score mapped at LSOA level by region across England.

South East: Social Capital Score by LSOA

Across the South East, most areas exhibit relatively higher levels of social capital compared to other regions. However, there are still distinct pockets of lower social capital, most notably in coastal communities such as Thanet, Hastings, Portsmouth, and parts of the Isle of Wight, as well as urban centres like Southampton, Reading, and parts of Medway and Slough. These areas are not confined to a small number of locations but are
distributed across a wider range of neighbourhoods within the region.

In contrast, much of the rural South East, including the South Downs, West Sussex, Surrey Hills, and the outskirts of Oxfordshire, display higher levels of social capital, likely reflecting stronger social networks, lower population turnover and greater local participation in community life.

South West: Social Capital Score by LSOA

The South West also exhibits higher levels of social capital compared to other regions, with the majority of areas shaded in lighter tones on the map. This is particularly evident across rural and coastal parts of Devon,
Dorset, Somerset, and Wiltshire, as well as in the National Park areas such as Exmoor and Dartmoor. However, there are some notable pockets of lower social capital, especially in and around larger urban centres such as Bristol, Plymouth, and parts of Gloucester, Swindon and Torbay. Isolated areas of lower social capital also appear in more rural locations like parts of North Devon and West Cornwall, likely linked to issues of remoteness and access to services.

North East: Social Capital Score by LSOA

The North East shows some of the highest concentrations of low social capital in England, particularly across coastal and urban areas such as Middlesbrough, Hartlepool, Sunderland, and South Tyneside. These areas are shaded darkest on the map, reflecting weaker community ties and lower levels of civic engagement. In contrast, inland rural areas of Northumberland and County Durham display relatively higher social capital.

North West: Social Capital Score by LSOA

The North West shows notable variation in social capital, with lower levels concentrated in many of the region’s urban and coastal areas. Notably, parts of Liverpool, Manchester, Blackpool, and Barrow-in-Furness are shaded darkest on the map. These areas often correspond with economic disadvantage and population churn. In contrast, more rural and suburban areas across Cumbria, Cheshire, and parts of Lancashire show relatively higher social capital, particularly around the Lake District and Ribble Valley, where community networks are likely more established and stable.

East Midlands: Social Capital Score by LSOA

The East Midlands presents a mixed picture of social capital, with lower levels concentrated in and around major urban areas such as Nottingham, Leicester, and parts of Derby, as well as smaller towns like Mansfield and Boston. In contrast, much of the surrounding rural and semi-rural areas, particularly across the counties of Lincolnshire, Rutland, and Northamptonshire, show relatively higher levels of social capital.

East of England: Social Capital Score by LSOA

The East of England displays a varied pattern of social capital, with the lowest levels concentrated in a number of coastal and rural areas. Notable clusters of low social capital appear in coastal communities such as Great Yarmouth, Lowestoft, Clacton-on-Sea, and Jaywick, as well as more rural parts of Norfolk and west Suffolk. Several market towns and urban centres, such as Peterborough, Luton, and parts of Bedfordshire, also show lower scores. In contrast, many areas across Hertfordshire, Cambridgeshire, and Essex’s commuter belt show relatively higher levels of social capital.

West Midlands: Social Capital Score by LSOA

The West Midlands shows notable concentrations of low social capital, particularly across the urban core of the region. Birmingham, Wolverhampton, and the Black Country stand out with notable areas shaded dark red, indicating weaker community networks and lower civic engagement. Similar patterns extend into parts of Coventry and Stoke-on-Trent. In contrast, rural and semi-rural areas across Shropshire, Herefordshire,
Warwickshire, and the Malvern Hills exhibit comparatively higher levels of social capital, reflecting more cohesive, stable communities.

Yorkshire and the Humber: Social Capital Score by LSOA

Yorkshire and the Humber shows some of the most extensive areas of low social capital in the country, particularly concentrated across South and West Yorkshire. Urban centres such as Leeds, Bradford, Sheffield, Doncaster, Barnsley and Wakefield are shaded darkest on the map, indicating weaker social capital. Coastal towns such as Bridlington and Scarborough also exhibit low social capital. In contrast, many rural and upland areas, especially across North Yorkshire and the Yorkshire Dales, show relatively higher levels of social capital.

London: Social Capital Score by LSOA

London shows widespread variation in levels of social capital across the city, with many neighbourhoods experiencing relatively low social capital compared to other parts of the country. The areas with the lowest levels of social capital are concentrated in East London, including Barking, Dagenham, and Newham, as well as parts of North London such as Enfield, Haringey and Tottenham. South London also contains several large
clusters of low social capital, particularly across Croydon, Lewisham, and Southwark, while areas of West London such as Brent and Hounslow display similar patterns. In contrast, pockets of higher social capital are more visible in outer London suburbs, including parts of Richmond, Kingston, Sutton and Bromley, reflecting more stable, less transient communities with stronger local networks.

Lower social sapital and higher need

This is further evidenced in the scatter plot charts below which explore the correlation between the Social Capital Score and the Indices of Deprivation 2025 Score and the Social Capital Score vs the Community Needs Index 2023 Score.

Corelation at LSOA level between Social Capital Score and IMD 2025 Score

Comparing the Social Capital Score with the IMD 2025 Score gives a correlation coefficient of 0.672, indicating a moderate to strong positive relationship between the two variables. The R2 value of 0.4520 suggests that approximately 45% of the variation in one variable can be explained by the variation in the other. This provides evidence of a moderate linear association between these two measures meaning that they are likely capturing similar underlying social or structural conditions in the neighbourhoods they cover.

Corelation at LSOA level between Social Capital Score and CNI 2023 Score

The Social Capital Score compared to the CNI 2023 Score gives an R2 value of 0.1569, indicating that around 16% of the variation in one variable can be explained by the variation in the other, while the correlation coefficient of 0.396 shows a moderate positive relationship between the two variables. This provides evidence of some degree of linear association between the two measures, but also suggests that while the variables are related, other factors may also be influencing the patterns observed in the neighbourhoods they cover.

1 See Methods for data processing: Applying shrinkage to improve the robustness of indicators and Appendix A for description of the shrinkage technique.
2 See Methods for data processing and Appendix B for description of the exponential transformation

References

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Appendix A: Shrinkage estimation

Improving the reliability of small area data values using shrinkage estimation

The shrinkage technique is designed to deal with the problems associated with small numbers in an LSOA. In some areas – particularly where the at-risk population is small – data may be ‘unreliable’, that is more likely to be affected by sampling and other sources of error.

The technique of shrinkage estimation (in other words empirical Bayesian estimation) is used to ‘borrow strength’ from larger areas to avoid creating unreliable small area data. Shrinkage estimation involves moving LSOA scores towards another more robust score, often relating to a higher geographical level. All LSOA scores will move somewhat through shrinkage, but those with large standard errors (in other words the most ‘unreliable’ scores) will tend to move the most. The LSOA score may be moved towards a ‘higher need’ or ‘lower need’ score through shrinkage estimation. Without shrinkage, some LSOAs would have scores which do not reliably describe the community need in the area due to chance fluctuations from year to year.

It could be argued that shrinkage estimation is inappropriate for administrative data which are, in effect, a census. This is not correct. The problem exists not only where data are derived from samples but also where scans of administrative data effectively mean that an entire census of a particular group is being considered. This is because such censuses can be regarded as samples from ‘super-populations’, which one could consider to be samples in time.

All the data from administrative sources and the 2021 Census are treated as samples from a super-population in this way, and the shrinkage technique was applied to indicators which use this data. The exceptions are the indicators supplied at Local Authority. District level

Selecting the larger areas from which unreliable small area data can borrow strength

The principle for selecting the larger area should be that the LSOAs within them share characteristics. In the current shrinkage methodology, Local Authority Districts are used. The LSOAs within a single district share issues relating to local governance and possibly to economic sub-climates. To a certain extent, they may also share issues relating to labour market sub-climates.

The shrinkage calculation

The actual mechanism of the shrinkage procedure is to estimate deprivation in a particular LSOA using a weighted combination of (a) data from the LSOA, and (b) data from another more robust score (in the case of the Indices, this is the Local Authority District score). The weight attempts to increase the efficiency of the estimation, while not increasing its bias. All LSOA scores are adjusted to some degree through the shrinkage process, but the magnitude of the adjustment will be greatest for areas with the least reliable scores. The amount of movement depends on both the size of the standard error and the amount of heterogeneity amongst the LSOAs in a Local Authority District.

The ‘shrunk’ estimate of a LSOA level proportion (or ratio) is a weighted average of the two ‘raw’ proportions for the LSOA and for the corresponding District. The weights used are determined by the relative magnitudes of within-LSOA and between-LSOA variability.

If the rate for a particular indicator in LSOA j is r_j events out of a population of n_j, the empirical logit for each LSOA is:

$m_j = \log\!\left[\frac{r_j + 0.5}{\,n_j – r_j + 0.5\,}\right]$

whose estimated standard error s_j is the square root of:

$s_j^2 = \frac{(n_j + 1)(n_j + 2)}{n_j (r_j + 1)(n_j – r_j + 1)}$

The corresponding counts r out of n for the district in which LSOA j lies gives the district-level logit:

$M = \log\left[ \frac{r + 0.5}{n – r + 0.5} \right]$

The ‘shrunk’ LSOA level logit is then the weighted average:

$m_j^* = w_j m_j + (1 – w_j) M$

where w_j is the weight given to the ‘raw’ LSOA-j data and (1-w_j) the weight given to the overall rate for the district. The formula used to determine w_j is:

$w_j = \frac{1/s_j^2}{1/s_j^2 + 1/t^2}$

where t² is the inter-LSOA variance for the k LSOAs in the district, calculated as:

$t^2 = \frac{1}{k – 1} \sum_{j=1}^{k} (m_j – M)^2$

Thus large LSOAs, where precision 1/s2^j is relatively large, have weight w_j close to 1 and so shrinkage has little effect. The shrinkage effect is greatest for small LSOAs in relatively homogeneous districts. The final step is to back-transform the shrunk logit m_j* using the ‘anti-logit’, to obtain the shrunk LSOA level proportion for each LSOA:

$z_j = \frac{\exp(m_j^*)}{1 + \exp(m_j^*)}$

Appendix B: Exponential transformation

In order to combine the dimensions into an overall measure of need, the dimension scores first need to be standardised. Any standardisation and transformation should meet the following criteria:

• Standard distribution: It must ensure that each dimension has a common distribution, so that dimensions can be combined, without one dimension dominating due to a much larger distribution.
• Identify areas of need: It must facilitate the easy identification of the areas with highest levels of need.
• Scale independent: It must not be scale dependent (in other words confuse population size with level of need).

One possible standardisation approach involves each of the dimension scores being ranked, and then the ranks are transformed to an exponential distribution. The exponential distribution has a number of properties that satisfy the criteria above.

Standard distribution

The exponential distribution transforms each dimension so that they each have a common distribution, the same range and identical maximum/minimum values. The process starts by ranking the scores in each dimension to standardise the dimension scores (from 1 for the lowest need to 33,755 for the most highest need), before applying the exponential transformation procedure to create a standardised dimension score ranging from 0 (lowest need) to 100 (highest need).

Cancellation

The exponential transformation procedure gives control over the extent to which lack of need in one dimension cancels or compensates for high need in another dimension. It allows precise regulation, although not elimination, of these cancellation effects. The scaling constant (23) used produces roughly 10 per cent cancellation. This means that in the extreme case, an LSOA which was ranked most deprived on one dimension but least deprived on another would overall be ranked at the 90th percentile in terms of levels of need. This compares to the 50th percentile if the untransformed ranks or a normal distribution had been used instead.

Identify deprived areas

The exponential transformation effectively spreads out that part of the distribution in which there is most interest – that is the ‘tail’ which contains the areas with the highest levels of need in each dimension. The scaling constant ensures that the most deprived 10 per cent of areas cover 50 per cent of the distribution of scores (in other words, scores between 50 and 100 after exponential transformation).

Scale independent

The transformation is not affected by the size of the LSOA’s population.

The exponential transformation calculation

The transformation used is as follows:

For any LSOA, denote its rank on the dimension R, scaled to the range [0,1]. R=1/N for the least deprived and R=N/N (in other words R=1) for the most deprived, where N=the number of LSOAs in England.

The transformed dimension score X is given by:

$X = -23 \ln\left( 1 – R \left( 1 – \exp^{-100/23} \right) \right)$

where ‘ln’ denotes natural logarithm and ‘exp’ the exponential or antilog transformation.