### Data

The dataset we use is the Annual Schools Census (ASC), formerly the Pupil Level Annual Schools Census (PLASC). This is administrative data that is collected for all maintained schools in England. Return of the census is compulsory, and so the dataset measures the whole school aged population. The ASC contains basic information for all pupils, including ethnicity, gender, whether they are eligible for free school meals (FSM) or have any special educational need (SEN). For this website, we use only the ethnicity of the pupil. We group ethnicity into 8 categories; White British, Black Caribbean, Black African, Indian, Pakistani, Bangladeshi, Chinese, and "Other". We also report a group named "Missing", which represents all cases for which we do not know the ethnicity of the pupil for some reason. We group ethnic groups so that there are enough pupils of each group for meaningful statistics.

All maintained schools in England are required to return the ASC. These schools include community (comprehensive) schools, voluntary aided, voluntary controlled, grammar schools and academies. For further information on school types, please see the DCSF webite.

The first year of data collection was in 2002. We present statistics from 2002 to the most recent year of data available.

### Sample

We present a number of statistics based on our sample. The sample of students is all pupils in all maintained schools in England. The statistics are calculated for each ethnic group in a given year, phase of education (POE), that is primary, middle or secondary, and Local Authority (LA).

Note that not all LAs have middle schools. In this case we do not report statistics for middle schools. Caution should be taken when comparing statistics between LAs if one has middle schools and one does not, as the age range of pupils in primary and secondary schools will be different.

Statistics for each ethnic group, year, POE and LA are available where applicable. In addition, comparison values for England as a whole are provided for each group, year and POE. We also provide the values for London as a whole for an additional comparison. For the Dissimilarity Index and Index of Isolation, the comparison value for England is a weighted average of all LAs. For London, the Dissimilarity Index and Index of Isolation, are calculated independently, as if the whole of London were a single LA.

### Minimum threshold

We present a number of statistics based on our sample. These statistics are calculated for each ethnic group in a given year, phase of education (POE), and Local Authority (LA).

We group ethnicity into 8 categories; White British, Black Caribbean, Black African, Indian, Pakistani, Bangladeshi, Chinese, and "Other". We also report a group named "Missing", which represents all cases for which we do not know the ethnicity of the pupil for some reason. We group ethnic groups so that there are enough pupils of each group for meaningful statistics.

A group may make up a small proportion of the total number of pupils in a given year, POE and LA. In this case, statistics may not be robust given the small sample to work from. For some statistics, for example the Dissimilarity Index and Index of Isolation, calculations would be biased by small sample sizes. We therefore present statistics for ethnic groups above a particular size threshold only.

The minimum size threshold we impose is as follows:

• For each ethnic group there must be 100 pupils of that ethnic group in the pupil population
• For each ethnic group the group must be at least 5% of the pupil population

Where pupil population refers to the year, POE, LA in question. We believe that this minimum threshold ensures that all statistics are robust and have a sensible interpretation. We do advise caution, however, when population sizes are close to this threshold. When looking at the statistics at a date, the percentage and number of the population in a given year, POE and LA can be found in the first two tables.

We do not present some statistics for situations where there are less than 3 schools being compared. In cases where calculations are based on between 3 and 10 schools, a warning note will appear as interpretations are based on so few cases.

### Percentile

A percentile is the value of a variable below which a certain percent of observations fall.

• The 25th percentile (p25) is the value of a variable below which 25% of observations fall.
• The 50th percentile (p50) is the value of a variable below which 50% of observations fall.
• The 75th percentile (p75) is the value of a variable below which 75% of observations fall.

### Information on statistics

There are many measures of segregation. This website presents proportions of ethnic groups, as well as more formal measures of segregation. Taken together, all the statistics give a representation of the level of ethnic segregation in each Local Authority (LA) in England.

Each statistic is calculated separately for each of the largest ethnic groups in England and by phase of education (primary, middle, or secondary school). Unfortunately it is not possible to calculate the statistics for all ethnic groups in England; small sample sizes for some groups could bias the statistics. For this reason, we report statistics for the largest ethnic groups in England only; white British, Black Caribbean, Black African, Indian, Pakistani, Bangladeshi, and Chinese. All other ethnic groups are reported as 'Other'. Where a 'missing' group is reported, there is a group of students for whom we do not know their ethnicity for some reason. To reduce bias as much as possible we also introduce a minimum threshold for some statistics, so they are not presented for groups which make up a small proportion of an LA.

The website aims to give a rounded view of the level of segregation in schools in each LA. For this reason, we present various statistics, by ethnic group, phase of education and LA.

More information about indices of segregation can be found below. It must be recognised that no single measure of segregation captures all aspects of segregation, and all have some statistical shortcomings. The two formal measures of segregation, the dissimilarity index and index of isolation we present have intuitive appeal, and are the two most widely used in academic research.

### Number of each ethnic group in the LA

This set of statistics report the number of pupils of each ethnic group in each LA. The sample is the number of pupils enrolled in maintained schools in England in the given year. The statistics are reported separately for primary, middle and secondary schools.

For example, the table below shows that this fictitious LA had 1,110 Black Caribbean pupils in primary schools in 2007. This fictitious LA has no middle schools, and so statistics are not reported for this type of school.

Statistic: Number of each ethnic group

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
White 13,226 n/a 10,372 3,098,629 122,860 2,541,327
Black Caribbean 1,110 n/a 925 58,406 864 41,129
Black African 448 n/a 242 113,806 1,588 63,644
Indian 3,664 n/a 2,738 98,858 4,042 77,013
Pakistani 741 n/a 353 153,918 1,322 84,468
Bangladeshi 35 n/a 25 63,815 732 32,856
Chinese 40 n/a 39 13,647 432 12,816
Other 3,024 n/a 1,790 414,302 10,505 245,312
Missing 288 n/a 185 62,540 2,247 62,171
Total 22,576 n/a 16,669 4,077,928 144,592 3,160,736

The raw numbers for England as a whole are also given for comparison. For example, there were 84,468 Pakistani pupils in secondary schools in England in 2007. There were 62,171 pupils in secondary schools in England in 2007 whose ethnicity is unknown to us, and so we code as 'Missing'.

This statistic is useful for those interested in reporting raw numbers of different ethnic groups within the LA. The numbers may also be plotted over time using the graph section of the website. The comparison with England is less useful than with other statistics.

#### Mathematical notation

We write that the number of pupils of group i in LA l is given by:

$number_{il}=n_{il}$

### Percentage of ethnic group in the LA

This set of statistics report the percentage of pupils of each ethnic group in each LA, reported separately for primary, middle and secondary schools. The same statistic is also calculated for England as a whole for comparison. The sample is the number of pupils enrolled in state schools in England in a given year.

To illustrate the statistic, the table below gives the percentage of each ethnic group in a fictitious LA in 2007, compared with England in the same year. The table shows that 4.92% of pupils in primary schools in the fictitious LA in 2007 were Black Caribbean. Note that the fictitious LA has no middle schools, and so statistics are not reported for this type of school.

Statistic: Percentage of each ethnic group

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
White 58.58% n/a 62.22% 75.99% 84.97% 80.45%
Black Caribbean 4.92% n/a 5.55% 1.43% 0.60% 1.11%
Black African 1.98% n/a 1.45% 2.79% 1.10% 1.97%
Indian 16.23% n/a 16.43% 2.42% 2.80% 2.55%
Pakistani 3.28% n/a 2.12% 3.77% 0.91% 2.45%
Bangladeshi 0.16% n/a 0.15% 1.56% 0.51% 1.04%
Chinese 0.18% n/a 0.23% 0.33% 0.30% 0.35%
Other 13.39% n/a 10.74% 10.16% 7.27% 8.40%
Missing 1.28% n/a 1.11% 1.53% 1.55% 1.68%

The percentages of each group for England as a whole are given for comparison. For example, 2.45% of pupils in secondary schools in England in 2007 were Pakistani. 1.68% of pupils in secondary schools in England in 2007 are coded as 'Missing', as we do not have information on their ethnicity.

This statistic is more useful than numbers when comparing percentages for one LA with the statistics for England or another LA. This is because the size of the LA is accounted for when calculating the percentage. The percentage of each group may also be plotted over time using the graph section of the website.

#### Mathematical notation

The percentage of ethnic group i in LA l is defined as the number of pupils of group i, divided by the total number of pupils in LA l. This number is then multiplied by 100 to give the percentage.

$percentage_{il}=\left({\frac{n_{il}}{N_l}}\right)\ast100$

Where nil is the number of pupils of group i in LA l. Nl is the total number of pupils in LA l.

### Percentage of schools that are "majority" white

This statistic calculates the percentage of schools within an LA in which at least 80% of the pupils are white British, reported separately for primary, middle and secondary schools. The percentage of schools is calculated without giving more weight to schools with more pupils. The same statistic is also calculated for England as a whole for comparison. The sample is the number of pupils enrolled in state schools in England in a given year.

This statistic shows the percentage of schools which have a white 'majority'. The statistic is affected by the degree of segregation between white and non-white groups, but importantly, also the raw percentages of each group. For example, if an LA has a very low non-white percentage, then the percentage of schools which have a white 'majority' will be high. In LAs with a higher percentage of non-white students, the statistic can be more clearly interpreted as a measure of segregation.

An example is given below.

Statistic: Percentage of schools that are "majority" white

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
Percentage 16.25% n/a 16.67% 73.67% 83.18% 71.64%

Compared with the percentage in England, the fictitious LA has a low percentage of schools which have at least 80% White British pupils. In secondary schools, 71.64% of schools in England have at least 80% White British pupils, compared to 16.67% in the fictitious LA. This may reflect a larger degree of integration between White and non-White pupils in the fictitious LA, but is also partly due to the composition of the LA. The table showing the proportion of the fictitious LA that is White British shows that a much lower proportion of White British pupils the fictitious LA than the proportion in England.

#### Mathematical notation

The percentage is defined as the number of schools where at least 80% of the pupils are white British in the LA, divided by the total number of schools in the LA. This number is then multiplied by 100 to give the percentage.

$percentage_{s80,l}=\left({\frac{s80_l}{S_l}}\right)\ast100$

Where s80l is the number of schools in LA l where at least 80% of pupils are white British, and Sl is the total number of schools in LA l. Note the weight for each school is constant; larger schools have the same weight as smaller schools.

### Percentage of schools that are "minority" white

This statistic calculates the percentage of schools within an LA where at most 20% of the pupils are white British, reported separately for primary, middle and secondary schools. The percentage of schools is calculated without giving more weight to schools with more pupils. The same statistic is also calculated for England as a whole for comparison. The sample is the number of pupils enrolled in state schools in England in a given year.

This statistic shows the percentage of schools in which white students are in the minority. The statistic is affected by the degree of segregation between white and non-white groups, but also the raw percentages of each group. For example, if an LA has a very low non-white percentage, then the percentage of schools which have a white 'minority' will be low. This may be the reverse in LAs with a higher percentage of non-white students.

An example is given below.

Statistic: Percentage of schools that are "majority" white

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
Percentage 11.25% n/a 5.56% 5.96% 5.22% 5.67%

Compared with England, the fictitious LA has a very similar percentage of secondary schools with at most 20% White British pupils. The fictitious LA has a much larger percentage of primary schools with at most 20% White British pupils, however.

#### Mathematical notation

The percentage is defined as the number of schools where at most 20% of the pupils are white British in the LA, divided by the total number of schools in the LA. This number is then multiplied by 100 to give the percentage.

$percentage_{s20,l}=\left({\frac{s20_l}{S_l}}\right)\ast100$

Where s20l is the number of schools in LA l where at most 20% of pupils are white British, and Sl is the total number of schools in LA l. Note the weight for each school is constant; larger schools have the same weight as smaller schools.

### Percentage of pupils in schools that are "majority" white

This statistic calculates the percentage of pupils that are in schools where at least 80% of the pupils are white British, reported separately for primary, middle and secondary schools. For minority ethnic groups, this implies that their group is in the minority in the school. The same statistic is also calculated for England as a whole for comparison. The sample is the number of pupils enrolled in state schools in England in a given year.

This statistic shows the percentage of pupils in schools in which white students are in the majority. The statistic is affected by the degree of segregation between white and non-white groups, but also the raw percentages of each group. For example, if an LA has a very high non-white percentage, then the percentage of pupils in schools which have a white 'majority' will be low. This may be the reverse in LAs with a lower percentage of non-white students.

An example is given below.

Statistic: Percentage of pupils in schools that are "majority" white

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
White 21.09% n/a 19.48% 80.17% 90.50% 82.36%
Black Caribbean n/a n/a 5.51% 6.78% 17.25% 10.97%
Black African n/a n/a n/a 8.79% 15.81% 13.94%
Indian 1.94% n/a 1.17% 15.17% 15.56% 16.96%
Pakistani n/a n/a n/a 6.25% 18.68% 13.33%
Bangladeshi n/a n/a n/a 7.74% 41.53% 14.60%
Chinese n/a n/a n/a 46.84% 60.42% 51.34%
Other 6.58% n/a 11.28% 30.47% 42.99% 36.94%
Missing n/a n/a n/a 48.67% 68.58% 54.17%

The percentages of each group for England as a whole are given for comparison. For example, 16.96% of Indian pupils in secondary schools in England in 2007 attend schools that are at least 80% White British. The corresponding percentage in the fictitious LA is 1.17%. This may reflect that Indian students in the fictitious LA are relatively less likely to attend white 'majority' schools, or that there is a relatively low percentage of White British pupils in the fictitious LA. Consulting the table for the percentage of each ethnic group in the fictitious LA, we see that 62.22% of pupils in secondary schools in the fictitious LA are White British. This may explain the lower percentage.

Note that some cells in the table are blank. This is because we report this statistic only where the percentage of the ethnic group is greater than 5%, and there are at least 100 students of that ethnicity, a minimum threshold for meaningful statistics. In this example, this condition is met for Black Caribbean pupils in secondary schools in the fictitious LA, but not in primary schools.

#### Mathematical notation

For each LA, the percentage of pupils in schools where are least 80% if pupils are White British is defined as the number of pupils in schools where at least 80% of the pupils are white British, divided by the total number of pupils in the LA. This number is then multiplied by 100 to give the percentage.

$percentage_{i80,l}=\left({\frac{n80_{il}}{N_l}}\right)\ast100$

Where n80il is the number of pupils of group i in LA l that attend schools where at least 80% of pupils are white British, and Sl is the total number of schools in LA l. Note that this statistic implicitly gives more weight to schools with larger numbers of the ethnic group in question.

### Percentage of pupils in schools that are "minority" white

This statistic calculates the percentage of pupils that are in schools where at most 20% of the pupils are white British, reported separately for primary, middle and secondary schools. For White British pupils, this implies that their group is in the minority in the school. The same statistic is also calculated for England as a whole for comparison. The sample is the number of pupils enrolled in state schools in England in a given year.

This statistic shows the percentage of pupils in schools in which white students are in the minority. The statistic is affected by the degree of segregation between white and non-white groups, but also the raw percentages of each group. For example, if an LA has a very low non-white percentage, then the percentage of pupils in schools which have a white 'minority' will be high. This may be the reverse in LAs with a higher percentage of non-white students.

An example is given below.

Statistic: Percentage of pupils in schools with at most 20% white students

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
White 2.85% n/a 1.46% 0.98% 0.58% 0.63%
Black Caribbean n/a n/a 7.68% 45.39% 31.02% 32.44%
Black African n/a n/a n/a 44.74% 42.44% 33.73%
Indian 27.95% n/a 19.87% 41.82% 36.47% 32.02%
Pakistani n/a n/a n/a 58.19% 32.53% 38.50%
Bangladeshi n/a n/a n/a 62.96% 21.45% 49.68%
Chinese n/a n/a n/a 11.10% 8.10% 6.44%
Other 18.09% n/a 5.98% 22.38% 20.00% 16.15%
Missing n/a n/a n/a 10.55% 7.30% 7.14%

The percentages of each group for England as a whole are given for comparison. For example, 32.02% of Indian pupils in secondary schools in England in 2007 attend schools that are at most 20% White British. The corresponding percentage in the fictitious LA is 19.87%. This may reflect that Indian students in the fictitious LA are relatively less likely than Indian students in England as a whole to attend white 'minority' schools, but it will also depend on relative populations.

Note that some cells in the table are blank. This is because we report this statistic only where the percentage of the ethnic group is greater than 5%, and there are at least 100 students of that ethnicity, a minimum threshold for meaningful statistics. In this example, this condition is met for Black Caribbean pupils in secondary schools in the fictitious LA, but not in primary schools.

#### Mathematical notation

For each LA, the percentage of pupils in schools where are most 20% if pupils are White British is defined as the number of pupils in schools where at most 20% of the pupils are white British, divided by the total number of pupils in the LA. This number is then multiplied by 100 to give the percentage.

$percentage_{i20,l}=\left({\frac{n20_{il}}{N_l}}\right)\ast100$

Where n20il is the number of pupils of group i in LA l that attend schools where at most 20% of pupils are white British, and Sl is the total number of schools in LA l. Note that this statistic implicitly gives more weight to schools with larger numbers of the ethnic group in question.

### Dissimilarity Index

The dissimilarity index (D) is a measure of segregation designed to capture the degree of "unevenness" between two groups. That is, how much does the school population reflect the wider population at the LA level? Schools would be perfectly integrated if each school's population reflected the LA population.

In our context we measure unevenness between pupils of a specific ethnic group and other all pupils. For example, we measure unevenness for Black Caribbean and non Black Caribbean pupils, and between Chinese and non Chinese pupils. The D index is calculated separately for each ethnic group and phase of education (primary, middle and secondary schools). The D index is also calculated for England as a whole for comparison; we present the value of D at the 25th, 50th, and 75th percentile to give a meaningful comparison.

We do not present statistics in cases where an ethnic group forms less than 5% of an LA and phase of education or where there are less than 100, as below this minimum threshold, the dissimilarity index is likely to be biased. We advise caution when looking at statistics for groups just above this threshold.

The dissimilarity index is the most widely used index for looking at the degree of evenness between two populations. The dissimilarity index (D) varies between 0 and 1, where 0 represents perfect integration and 1 represents perfect segregation. The value of D represents the proportion of the minority group population that would have to change schools to achieve the same distribution of that of the LA. An example is given below:

Statistic: Dissimilarity Index for each ethnic group

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
p25 p50 p75 p25 p50 p75 p25 p50 p75
White 0.40 n/a 0.27 0.28 0.34 0.42 0.24 0.32 0.33 0.24 0.28 0.38
Black Caribbean n/a n/a 0.27 0.29 0.36 0.54 0.18 0.18 0.49 0.24 0.40 0.44
Black African n/a n/a n/a 0.29 0.38 0.49 0.29 0.29 0.29 0.26 0.35 0.46
Indian 0.40 n/a 0.36 0.44 0.55 0.60 0.31 0.31 0.52 0.39 0.49 0.56
Pakistani n/a n/a n/a 0.64 0.64 0.73 0.23 0.23 0.70 0.58 0.63 0.63
Bangladeshi n/a n/a n/a 0.47 0.60 0.64 0.32 0.75 0.82 0.46 0.51 0.61
Chinese n/a n/a n/a 0.49 0.57 0.63 0.38 0.38 0.50 0.36 0.39 0.45
Other 0.24 n/a 0.15 0.22 0.26 0.32 0.16 0.16 0.31 0.18 0.22 0.25
Missing n/a n/a n/a 0.53 0.55 0.59 0.31 0.40 0.43 0.40 0.49 0.50

In this case Indian students in secondary education in the fictitious LA have a value of D of 0.36. The interpretation for this number is that 36% of Indian students would have to change schools in order for the school population to reflect the LA population. Compared to the D index for secondary education in England, the value for Indians in the fictitious LA is very close to the 25th percentile for England as a whole. This suggests that the fictitious LA has low unevenness relative to England as a whole. In general, a dissimilarity index of less than 0.3 is considered low, between 0.3 and 0.6 as moderate and above 0.6 as high (Massey and Denton, 1993).

#### Mathematical notation

For each LA l and ethnic group i, the dissimilarity index is given by:

$D=\frac{1}{2}\sum\limits_{s=1}^S{\left|{\frac{n_{is}}{n_{il}}-\frac{\left({N-n}\right)_{is}}{\left({N-n}\right)_{il}}}\right|}$

Where nis represents the number of ethnic group i in school s, and nil represents the number of ethnic group i in LA l. The ratio of these two values therefore gives the proportion of ethnic group i in school s relative to the total LA population; a greater proportion indicates more members of group i in school s. (N - n)is represents the number of students in the school not in ethnic group i in school s, and (N - n)il for LA l. Note that the calculation therefore measures the segregation of ethnic group i relative to all other ethnic groups. The ratio of these numbers gives the proportion of students that are not in ethnic group i in the school relative to the LA.

In summary, the two terms represent the proportion of group i in school s and the proportion of all those not in group i in school s. After taking the difference between the two terms, a larger number represents a larger proportion of group i in school s. A higher absolute value (note the modulus in the equation) gives the level of dissimilarity, or unevenness in the population of group i and not i. The value of dissimilarity for the fictitious LA as a whole is the summation of values for all schools in the fictitious LA.

### Index of Isolation

The index of isolation (I) is a measure of segregation designed to capture the measure of "exposure" between two groups. In our context we measure exposure between pupils of a specific ethnic group and other all pupils. For example, we measure exposure between Black Caribbean and non Black Caribbean pupils, and between Chinese and non Chinese pupils. The statistic is calculated separately for each ethnic group and for primary, middle and secondary schools. The I index is also calculated for England as a whole for comparison; we present the value of I at the 25th, 50th, and 75th percentile to give a meaningful comparison. We do not present statistics in cases where an ethnic group forms less than 5% of an LA and phase of education, or where there are less than 100. This is because below this minimum threshold, the index of isolation is likely to be biased. We advise caution when looking at statistics for groups just above this minimum threshold.

The I index relates to the degree of exposure within the school population; how likely is it that minority group members of a certain group come into contact with members of the same group, rather than other ethnic groups? Like the D index, the I index ranges between 0 and 1. A value of 0 reflects perfect integration, and a value of 1 reflects perfect segregation.

Despite any geographical clustering that may occur, very small minority groups tend to have a high degree of exposure to members of other groups. Very large minority groups may experience much lower levels of exposure to members of other groups. To account for the effect of group size within the LA, we follow an adjustment used by Cutler, Glaeser and Vigdor (1998).

An example is given below:

Statistic: Index of Isolation for each ethnic group

LA 2007 England 2007
Group Primary Middle Secondary Primary Middle Secondary
p25 p50 p75 p25 p50 p75 p25 p50 p75
White 0.23 n/a 0.12 0.05 0.10 0.18 0.02 0.02 0.08 0.04 0.05 0.09
Black Caribbean n/a n/a 0.02 0.04 0.06 0.13 0.01 0.01 0.02 0.02 0.04 0.07
Black African n/a n/a n/a 0.05 0.07 0.09 0.04 0.04 0.04 0.02 0.04 0.06
Indian 0.17 n/a 0.14 0.05 0.15 0.20 0.10 0.10 0.10 0.05 0.11 0.16
Pakistani n/a n/a n/a 0.33 0.41 0.45 0.01 0.01 0.09 0.12 0.36 0.36
Bangladeshi n/a n/a n/a 0.06 0.18 0.33 0.01 0.14 0.17 0.05 0.15 0.18
Chinese n/a n/a n/a 0.01 0.01 0.01 0.01 0.02 0.03 0.01 0.01 0.02
Other 0.04 n/a 0.01 0.03 0.04 0.06 0.02 0.04 0.04 0.02 0.02 0.03
Missing n/a n/a n/a 0.05 0.07 0.10 0.03 0.03 0.05 0.04 0.05 0.09

In this case Indian students in secondary education in the fictitious LA have an I value of 0.14. Compared to the I index for secondary education in England, the value for Indians in the fictitious LA is very close to the 75th percentile for England as a whole. This suggests that Indian pupils in the fictitious LA have a high exposure to other Indian students relative to England as a whole.

#### Mathematical notation

For each LA l and ethnic group i, the basic Index of Isolation is given by:

$I=\sum\limits_{s=1}^S{\frac{n_{is}}{n_{il}}}.\frac{n_{is}}{N_l}$

Where nis represents the number of ethnic group i in school s, nil represents the number of ethnic group i in LA l, and Nl is the total number of students in LA l. The Index of Isolation is interpreted as the likelihood of coming into contact with another member of your ethnic group. As $\frac{n_{is}}{n_{il}}$ or $\frac{n_{is}}{N_l}$ increases, the likelihood of coming into contact with a pupil of your ethnic group increases.

The calculation above does not take account of the size of ethnic group i in LA l, which will have a positive effect on the I index. To eliminate this effect, Cutler, Glaeser and Vigdor (1998) suggest the following adjustment:

$I=\frac{\sum\limits_{s=1}^S{\left({\frac{n_{is}}{n_{il}}.\frac{n_{is}}{N_l}}\right)}-\left({\frac{n_{il}}{N_l}}\right)}{\min\left({\frac{n_{il}}{N_l},1}\right)-\left({\frac{n_{il}}{N_l}}\right)}$

The share of the LA population that is of ethnic group i, $\left({\frac{n_{il}}{N_l}}\right)$ is subtracted from the original summation to take account of the relative size of the ethnic group. So that the index remains in the range 0 to 1, this value is divided by the maximum value of this measure $\min\left({\frac{n_{il}}{N_l},1}\right)-\left({\frac{n_{il}}{N_l}}\right)$ .