The 2014 World Cup a nearest neighbour analysis

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Ivan Godoi Ferreira
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1 World cup 2014 poster The 2014 World Cup a earest eighbour aalysis The 20th FIFA football World Cup took place i Brazil from 12 Jue to 13 July The atioal teams of 31 coutries ad Brazil played 64 matches i 12 stadiums across the coutry. Brazil, the largest coutry i both South America ad Lati America is the world s fifth largest coutry i terms of populatio ad size. I 2010, the populatio of Brazil was 190,732,694, although this umber has grow cosiderably sice the. The average populatio desity, i umber of people per square kilometre was i 2011, accordig to the World Bak. However, the distributio of people is very ueve i Brazil. Image courtesy of uder the Liceça Creative Commos Atribuição 3.0 Brasil The stadiums are located i 12 state capitals ad cover all the mai regios of Brazil. Map adapted from The Nearest Neighbour Aalysis is a statistical tool for examiig a geographical distributio of locatios to determie whether the patter to be cosidered is regular, radom or clustered Page 1 of 7

Brazil, the largest coutry i both South America ad Lati America is the world s fifth largest coutry i terms of populatio ad size.

2 Regular Radom Clustered The techique is best applied to a sample size of 30 or more locatios however, a Nearest Neighbour Aalysis ca be used to cosider the locatios of the 12 World Cup 2014 stadiums if a suitable warig as to the validity ad iterpretatio of the result is give. Nearest Neighbour Aalysis The Nearest Neighbour Aalysis statistic is calculated from the formula: R = 2đ A đ is the mea of the distace observed betwee each locatio ad its earest eighbour, is the umber of sampled locatios for this aalysis, = 12 ad A is the area uder cosideratio. Distaces eed to be measured accurately, as straight-lie measuremets i kilometres. The area must also be measured i square kilometres. Brazil occupies approximately half of South America, with a total area of 8,514,215 km 2. This icludes 8,456,510 km 2 of lad ad 55,455 km 2 of water Page 2 of 7

Nearest Neighbour Aalysis The Nearest Neighbour Aalysis statistic is calculated from the formula: R = 2đ A đ is the mea of the distace observed betwee each locatio ad its earest eighbour, is the

3 Studet tasks Usig the map of the World Cup 2014 stadiums ad Google Earth, complete the table below to calculate the earest eighbour aalysis value. From stadium To earest stadium Distace (km) Belo Horizote Rio de Jaeiro 346 Brasília Belo Horizote 614 Cuiabá Curitiba Fortaleza Maaus Natal Porto Alegre Recife Rio de Jaeiro Salvador São Paulo Total distace Mea distace R = 2đ A The Nearest Neighbour Aalysis will always geerate a result betwee 0 ad Values of 2.15 idicate a regular patter of the distributio, values close to a value of oe idicate a radom distributio ad values of zero idicate a clustered distributio. What does the calculated value tell you about the distributio of stadiums for the 2014 World Cup i Brazil? Page 3 of 7

Total distace Mea distace R = 2đ A The Nearest Neighbour Aalysis will always geerate a result betwee 0 ad 2.15. Values of 2.

4 Extesio task Calculate the Nearest Neighbour Aalysis value usig the distributio of the World Cup 2014 teams traiig camps. Team City Team City Algeria Sorocaba Greece Aracaju Argetia Vespasiao Hoduras Porto Feliz Australia Vitória Ira Guarulhos Belgium Mogi das Cruzes Italy Magaratiba Bosia ad Herzegovia Guarujá Ivory Coast Águas de Lidoia Brazil Teresópolis Japa Itu Cameroo Vitória Mexico Satos Chile Belo Horizote Netherlads Rio de Jaeiro Colombia Cotia Nigeria Campias Costa Rica Satos Portugal Campias Croatia Mata de São João Russia Itu Ecuador Viamão South Korea Foz do Iguaçu Eglad Rio de Jaeiro Spai Curitiba Frace Ribeirão Preto Switzerlad Porto Seguro Germay Sata Cruz Cabrália Uited States São Paulo Ghaa Maceió Uruguay Sete Lagoas Page 4 of 7

Coast Águas de Lidoia Brazil Teresópolis Japa Itu Cameroo Vitória Mexico Satos Chile Belo Horizote Netherlads Rio de Jaeiro Colombia Cotia Nigeria Campias Costa Rica Satos Portugal Campias Croatia

5 From traiig camp Águas de Lidoia Aracaju Belo Horizote Campias Campias Cotia Curitiba Foz do Iguaçu Guarujá Guarulhos Itu Itu Maceió Magaratiba Mata de São João Mogi das Cruzes Porto Feliz Porto Seguro Ribeirão Preto Rio de Jaeiro Rio de Jaeiro Sata Cruz Cabrália Satos Satos To earest traiig camp Ivory Coast Greece Chile Nigeria Portugal Colombia Spai South Korea Bosia ad Herzegovia Ira Japa Russia Ghaa Italy Croatia Belgium Hoduras Switzerlad Frace Eglad Netherlads Germay Costa Rica Mexico Distace (km) Page 5 of 7

Satos To earest traiig camp Ivory Coast Greece Chile Nigeria Portugal Colombia Spai South Korea Bosia ad Herzegovia Ira Japa Russia Ghaa

6 São Paulo Sete Lagoas Sorocaba Teresópolis Vespasiao Viamão Vitória Vitória Uited States Uruguay Algeria Brazil Argetia Ecuador Australia Cameroo Total distace Mea distace N = 32 Area = 8,456,510 km 2 R = 2đ A What does the calculated value tell you about the distributio of traiig camps for the teams of the 2014 World Cup i Brazil? Why do you thik this is? Page 6 of 7

2 R = 2đ A What does the calculated value tell you about the distributio of traiig camps for the

7 Suggested aswer Usig Google Earth to measure the distaces betwee the stadiums: From stadium To earest stadium Distace (km) Belo Horizote Rio de Jaeiro 346 Brasília Belo Horizote 614 Cuiabá Brasília 882 Curitiba São Paulo 354 Fortaleza Natal 430 Maaus Cuiabá 1453 Natal Recife 244 Porto Alegre Cuiabá 546 Recife Natal 244 Rio de Jaeiro Belo Horizote 346 Salvador Recife 661 São Paulo Cuiabá 354 Total distace 6474 R = 2đ A Mea distace R = ,456,510 = R = 1079 x = 1.29 (to 2dp) This value suggests a radom distributio for the 12 stadiums Page 7 of 7

Natal 244 Rio de Jaeiro Belo Horizote 346 Salvador Recife 661 São Paulo Cuiabá 354 Total distace 6474 R = 2đ A Mea distace 539.

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