```The 2014 World Cup – a nearest neighbour analysis
The 20th FIFA football World Cup took place in Brazil from
12 June to 13 July 2014. The national teams of 31
countries and Brazil played 64 matches in 12 stadiums
across the country.
Brazil, the largest country in both South America and Latin
America is the world’s fifth largest country in terms of
population and size. In 2010, the population of Brazil was
190,732,694, although this number has grown considerably
since then.
The average population density, in number of people per
square kilometre was 23.28 in 2011, according to the World
Bank. However, the distribution of people is very uneven in
Brazil.
World cup 2014 poster
Image courtesy of http://www.copa2014.gov.br/en/noticia/2014-fifa-world-cup-ambassadors-unveil-officialposter under the Licença Creative Commons Atribuição 3.0 Brasil
The stadiums are located in 12 state capitals and cover all the main regions of Brazil.
The Nearest Neighbour Analysis is a statistical tool for examining a geographical
distribution of locations to determine whether the pattern to be considered is regular,
random or clustered.
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The 2014 World Cup – a nearest neighbour analysis
Regular
Random
Clustered
The technique is best applied to a sample size of 30 or more locations – however, a
Nearest Neighbour Analysis can be used to consider the locations of the 12 World Cup
2014 stadiums if a suitable warning as to the validity and interpretation of the result is
given.
Nearest Neighbour Analysis
The Nearest Neighbour Analysis statistic is calculated from the formula:
Rn = 2đ √
n
A
đ is the mean of the distance observed between each location and its nearest neighbour,
n is the number of sampled locations – for this analysis, n = 12
and A is the area under consideration.
 Distances need to be measured accurately, as straight-line measurements in
kilometres.
 The area must also be measured in square kilometres. Brazil occupies
approximately half of South America, with a total area of 8,514,215 km2. This
includes 8,456,510 km2 of land and 55,455 km2 of water.
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The 2014 World Cup – a nearest neighbour analysis
Using the map of the World Cup 2014 stadiums and Google Earth, complete the
table below to calculate the nearest neighbour analysis value.
To nearest
Distance (km)
Belo Horizonte
Rio de Janeiro
346
Brasília
Belo Horizonte
614
Cuiabá
Curitiba
Fortaleza
Manaus
Natal
Porto Alegre
Recife
Rio de Janeiro
São Paulo
Total distance
Mean distance
Rn = 2đ √
n
A
The Nearest Neighbour Analysis will always generate a result between 0 and 2.15. Values
of 2.15 indicate a regular pattern of the distribution, values close to a value of one indicate
a random distribution and values of zero indicate a clustered distribution.
What does the calculated value tell you about the distribution of stadiums for the 2014
World Cup in Brazil?
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The 2014 World Cup – a nearest neighbour analysis
Calculate the Nearest Neighbour Analysis value using the distribution of the World Cup
2014 teams’ training camps.
Team
City
Team
City
Algeria
Sorocaba
Greece
Aracaju
Argentina
Vespasiano
Honduras
Porto Feliz
Australia
Vitória
Iran
Guarulhos
Belgium
Mogi das
Cruzes
Italy
Mangaratiba
Bosnia and
Herzegovina
Guarujá
Ivory Coast
Águas de
Lindoia
Brazil
Teresópolis
Japan
Itu
Cameroon
Vitória
Mexico
Santos
Chile
Belo
Horizonte
Netherlands
Rio de
Janeiro
Colombia
Cotia
Nigeria
Campinas
Costa Rica
Santos
Portugal
Campinas
Croatia
Mata de São
João
Russia
Itu
Viamão
South Korea
Foz do Iguaçu
England
Rio de
Janeiro
Spain
Curitiba
France
Ribeirão Preto
Switzerland
Porto Seguro
Germany
Santa Cruz
Cabrália
United States
São Paulo
Ghana
Maceió
Uruguay
Sete Lagoas
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The 2014 World Cup – a nearest neighbour analysis
From training
camp
To nearest training
camp
Águas de Lindoia
Ivory Coast
Aracaju
Greece
Belo Horizonte
Chile
Campinas
Nigeria
Campinas
Portugal
Cotia
Colombia
Curitiba
Spain
Foz do Iguaçu
South Korea
Guarujá
Bosnia and
Herzegovina
Guarulhos
Iran
Itu
Japan
Itu
Russia
Maceió
Ghana
Mangaratiba
Italy
Mata de São João
Croatia
Mogi das Cruzes
Belgium
Porto Feliz
Honduras
Porto Seguro
Switzerland
Ribeirão Preto
France
Rio de Janeiro
England
Rio de Janeiro
Netherlands
Santa Cruz Cabrália
Germany
Santos
Costa Rica
Santos
Mexico
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Distance (km)
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The 2014 World Cup – a nearest neighbour analysis
São Paulo
United States
Sete Lagoas
Uruguay
Sorocaba
Algeria
Teresópolis
Brazil
Vespasiano
Argentina
Viamão
Vitória
Australia
Vitória
Cameroon
Total distance
Mean distance
N = 32
Area = 8,456,510 km2
Rn = 2đ √
n
A
What does the calculated value tell you about the distribution of training camps for the
teams of the 2014 World Cup in Brazil? Why do you think this is?
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The 2014 World Cup – a nearest neighbour analysis
Rn = 2đ √
To nearest
Distance (km)
Belo Horizonte
Rio de Janeiro
346
Brasília
Belo Horizonte
614
Cuiabá
Brasília
882
Curitiba
São Paulo
354
Fortaleza
Natal
430
Manaus
Cuiabá
1453
Natal
Recife
244
Porto Alegre
Cuiabá
546
Recife
Natal
244
Rio de Janeiro
Belo Horizonte
346
Recife
661
São Paulo
Cuiabá
354
Total distance
6474
Mean distance
539.5
n
A
Rn
= 1079
√
Rn
= 1079
x 0.001191228 = 1.29 (to 2dp)
12
= 1079√0.00000141902
8,456,510
This value suggests a random distribution for the 12 stadiums.
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