{"id":684,"date":"2025-07-28T18:38:20","date_gmt":"2025-07-28T22:38:20","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=684"},"modified":"2025-10-11T02:24:04","modified_gmt":"2025-10-11T06:24:04","slug":"12-3","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/12-0\/12-3\/","title":{"rendered":"Cap\u00edtulo 12.3"},"content":{"rendered":"<div style=\"position: relative\">\n<div style=\"float: left;width: 300px;background-color: #f5f5f5;border: 1px solid #ddd;border-radius: 5px;padding: 15px;margin-right: 20px;margin-bottom: 5px;overflow: hidden\">\n<h3 style=\"margin: 0 0 10px 0;padding-bottom: 8px;border-bottom: 1px solid #ddd\">\u00cdndice<\/h3>\n<ol style=\"margin: 0;padding-left: 0;list-style-type: none\">\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/\">1. O que \u00e9 Ci\u00eancia de Dados?<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/\">1.1. Introdu\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-1\/\">1.1.1. Ferramentas Computacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-2\/\">1.1.2. T\u00e9cnicas Estat\u00edsticas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-2\/\">1.2. Por que Ci\u00eancia de Dados?<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/\">1.3. Tra\u00e7ando os Cl\u00e1ssicos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-1\/\">1.3.1. Personagens Liter\u00e1rios<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-2\/\">1.3.2. Outro Tipo de Personagem<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/\">2. Causalidade e Experimentos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-1\/\">2.1. John Snow e a Bomba da Broad Street<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-2\/\">2.2. O &#8220;Grande Experimento&#8221; de Snow<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-3\/\">2.3. Estabelecendo Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-4\/\">2.4. Randomiza\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-5\/\">2.5. Notas Finais<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/\">3. Progamando em Python<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-1\/\">3.1. Express\u00f5es<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/\">3.2. Nomes<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/2-1\/\">3.2.1. Exemplo: Taxas de Crescimento<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-3\/\">3.3. Chamadas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-4\/\">3.4. Introdu\u00e7\u00e3o \u00e0s Tabelas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/\">4. Tipos de Dados<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-1\/\">4.1. N\u00fameros<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/\">4.2. Strings<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/2-1\/\">4.2.1. M\u00e9todos de Strings<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-3\/\">4.3. Compara\u00e7\u00f5es<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/\">5. Sequ\u00eancias<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-1\/\">5.1. Arrays<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-2\/\">5.2. Ranges<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-3\/\">5.3. Mais sobre Arrays<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/\">6. Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-1\/\">6.1. Ordenando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-2\/\">6.2. Selecionando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-3\/\">6.3. Exemplo: Tend\u00eancias Populacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-4\/\">6.4. Examplo: Propor\u00e7\u00f5es de Sexos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/\">7. Visualiza\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-1\/\">7.1. Visualizando Distribui\u00e7\u00f5es<br \/>\nCateg\u00f3ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-2\/\">7.2. Visualizando Distribui\u00e7\u00f5es Num\u00e9ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-3\/\">7.3. Gr\u00e1ficos Sobrepostos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/\">8. Fun\u00e7\u00f5es e Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-1\/\">8.1. Aplicando Fun\u00e7\u00e3o a uma Coluna<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-2\/\">8.2. Classificando por uma Vari\u00e1vel<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-3\/\">8.3. Classifica\u00e7\u00e3o Cruzada<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-4\/\">8.4. Unindo Tabelas por Colunas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-5\/\">8.5. Compartilhamento de Bicicletas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/\">9. Aleatoriedade<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-1\/\">9.1. Declara\u00e7\u00f5es Condicionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-2\/\">9.2. Itera\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-3\/\">9.3. Simula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-4\/\">9.4. O Problema de Monty Hall<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-5\/\">9.5. Encontrando Probabilidades<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/\">10. Amostragem e Distribui\u00e7\u00f5es Emp\u00edricas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-1\/\">10.1. Distribui\u00e7\u00f5es Emp\u00edricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-2\/\">10.2. Amostragem de uma Popula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-3\/\">10.3. Distribui\u00e7\u00e3o Emp\u00edrica de uma<br \/>\nEstat\u00edstica<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-4\/\">10.4. Amostragem Aleat\u00f3ria em Python <\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/\">11. Testando Hip\u00f3teses<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-1\/\">11.1. Avaliando um Modelo<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-2\/\">11.2. M\u00faltiplas Categorias<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-3\/\">11.3. Decis\u00f5es e Incertezas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-4\/\">11.4. Probabilidades de Erro<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/\">12. Comparando Duas Amostras<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-1\/\">12.1. Teste A\/B<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">12.2. Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-3\/\">12.3. Esvaziar<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/\">13. Estima\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-1\/\">13.1. Percentis<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-2\/\">13.2. O Bootstrap<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-3\/\">13.3. Intervalos de Confian\u00e7a<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-4\/\">13.4. Usando Intervalos de Confian\u00e7a<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/\">14. Por que a M\u00e9dia \u00e9 Importante<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-1\/\">14.1. Propriedades da M\u00e9dia<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-2\/\">14.2. Variabilidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-3\/\">14.3. O DP e a Curva Normal<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-4\/\">14.4. Teorema Central do Limite<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-5\/\">14.5. Variabilidade da M\u00e9dia da Amostra<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-6\/\">14.6. Escolhendo um Tamanho de Amostra<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/\">15. Previs\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-1\/\">15.1. Correla\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-2\/\">15.2. Linha de Regress\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-3\/\">15.3. M\u00e9todo dos M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-4\/\">15.4. Regress\u00e3o de M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-5\/\">15.5. Diagn\u00f3sticos Visuais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-6\/\">15.6. Diagn\u00f3stico Num\u00e9rico<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<p><!-- Main Content --><\/p>\n<div style=\"overflow: hidden\">\n<p><!--###########################################################################################################################################################--><\/p>\n<pre><code><span style=\"color: black\">from datascience import *\r\n%matplotlib inline\r\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')\r\nimport numpy as np<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"esvaziar\" style=\"text-align: center\">Esvaziar<\/h1>\n<p style=\"text-align: justify\">Em 18 de janeiro de 2015, os Indianapolis Colts e os New England Patriots jogaram o jogo do campeonato da American Football Conference (AFC) para determinar qual dessas equipes jogaria no Super Bowl. Ap\u00f3s o jogo, surgiram alega\u00e7\u00f5es de que as bolas dos Patriots n\u00e3o haviam sido infladas conforme exigido pelos regulamentos; elas estavam mais macias. Isso poderia ser uma vantagem, j\u00e1 que bolas mais macias podem ser mais f\u00e1ceis de segurar.<\/p>\n<p style=\"text-align: justify\">Por v\u00e1rias semanas, o mundo do futebol americano foi consumido por acusa\u00e7\u00f5es, nega\u00e7\u00f5es, teorias e suspeitas: a imprensa rotulou o t\u00f3pico como Deflategate, em refer\u00eancia ao esc\u00e2ndalo pol\u00edtico Watergate dos anos 1970. A National Football League (NFL) encomendou uma an\u00e1lise independente. Neste exemplo, faremos nossa pr\u00f3pria an\u00e1lise dos dados.<\/p>\n<p style=\"text-align: justify\">A press\u00e3o \u00e9 frequentemente medida em libras por polegada quadrada (psi). As regras da NFL estipulam que as bolas de jogo devem ser infladas para ter press\u00f5es na faixa de 12,5 psi a 13,5 psi. Cada equipe joga com 12 bolas. As equipes s\u00e3o respons\u00e1veis por manter a press\u00e3o em suas pr\u00f3prias bolas, mas os oficiais do jogo inspecionam as bolas. Antes do in\u00edcio do jogo da AFC, todas as bolas dos Patriots estavam com cerca de 12,5 psi. A maioria das bolas dos Colts estava com cerca de 13,0 psi. No entanto, esses dados pr\u00e9-jogo n\u00e3o foram registrados.<\/p>\n<p style=\"text-align: justify\">Durante o segundo quarto, os Colts interceptaram uma bola dos Patriots. Nas laterais, eles mediram a press\u00e3o da bola e determinaram que estava abaixo do limite de 12,5 psi. Imediatamente, informaram aos oficiais.<\/p>\n<p style=\"text-align: justify\">No intervalo, todas as bolas do jogo foram coletadas para inspe\u00e7\u00e3o. Dois oficiais, Clete Blakeman e Dyrol Prioleau, mediram a press\u00e3o em cada uma das bolas.<\/p>\n<p style=\"text-align: justify\">Aqui est\u00e3o os dados. Cada linha corresponde a uma bola de futebol. A press\u00e3o \u00e9 medida em psi. A bola dos Patriots que havia sido interceptada pelos Colts n\u00e3o foi inspecionada no intervalo. A maioria das bolas dos Colts tamb\u00e9m n\u00e3o foi inspecionada &#8211; os oficiais simplesmente ficaram sem tempo e tiveram que devolver as bolas para o in\u00edcio do segundo tempo.<\/p>\n<pre><code><span style=\"color: black\">football = Table.read_table(path_data + 'deflategate.csv')\r\nfootball.show()<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Team<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Blakeman<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Prioleau<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.8<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.85<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.2<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.15<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.5<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.45<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.95<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.85<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.3<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.55<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.95<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.35<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.9<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.9<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.35<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.35<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.75<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.3<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.95<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.55<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.15<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Para cada uma das 15 bolas inspecionadas, os dois \u00e1rbitros obtiveram resultados diferentes. N\u00e3o \u00e9 incomum que medi\u00e7\u00f5es repetidas no mesmo objeto produzam resultados diferentes, especialmente quando as medi\u00e7\u00f5es s\u00e3o realizadas por pessoas diferentes. Ent\u00e3o, atribuiremos a cada bola a m\u00e9dia das duas medi\u00e7\u00f5es feitas naquela bola.<\/p>\n<pre><code><span style=\"color: black\">football = football.with_column(\r\n    'Combined', (football.column(1)+football.column(2))\/2\r\n    ).drop(1, 2)\r\nfootball.show()<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Team<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Combined<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.65<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.025<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.325<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.85<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.275<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.775<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.075<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.325<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.15<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.7<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.125<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.525<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.525<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.725<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">\u00c0 primeira vista, parece evidente que as bolas de futebol dos Patriots estavam sob press\u00e3o mais baixa do que as bolas dos Colts. Como alguma defla\u00e7\u00e3o \u00e9 normal durante o jogo, os analistas independentes decidiram calcular a queda na press\u00e3o desde o in\u00edcio do jogo. Lembre-se de que todas as bolas dos Patriots come\u00e7aram em cerca de 12,5 psi, e as bolas dos Colts em cerca de 13,0 psi. Portanto, a queda na press\u00e3o das bolas dos Patriots foi calculada como 12,5 menos a press\u00e3o no intervalo, e a queda na press\u00e3o das bolas dos Colts foi de 13,0 menos a press\u00e3o no intervalo.<\/p>\n<p style=\"text-align: justify\">Podemos calcular a queda de press\u00e3o para cada bola de futebol, definindo primeiro uma matriz de valores iniciais. Para isso, precisaremos de uma matriz composta por 11 valores, cada um dos quais \u00e9 12,5, e outro composto por quatro valores, cada um dos quais \u00e9 todos os 13. Usaremos a fun\u00e7\u00e3o NumPy <code>np.ones<\/code>, que recebe uma contagem como argumento e retorna uma matriz com tantos elementos, cada um dos quais \u00e9 1.<\/p>\n<pre><code><span style=\"color: black\">np.ones(11)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[1]:<\/td>\n<td style=\"text-align: left\">array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">patriots_start = 12.5 * np.ones(11)\r\ncolts_start = 13 * np.ones(4)\r\nstart = np.append(patriots_start, colts_start)\r\nstart<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[2]:<\/td>\n<td style=\"text-align: left\">array([12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,<br \/>\n13. , 13. , 13. , 13. ])<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">A queda de press\u00e3o para cada bola de futebol \u00e9 a diferen\u00e7a entre a press\u00e3o inicial e a medi\u00e7\u00e3o de press\u00e3o combinada.<\/p>\n<pre><code><span style=\"color: black\">drop = start - football.column('Combined')\r\nfootball = football.with_column('Pressure Drop', drop)\r\nfootball.show()<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Team<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Combined<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Pressure Drop<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.65<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.85<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.025<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.475<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.325<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.175<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.85<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.65<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.275<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.225<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.775<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.725<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.075<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.425<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.325<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.175<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.15<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.35<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">10.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.8<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">11.125<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.375<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.525<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.475<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.525<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.475<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.725<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.275<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">12.35<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.65<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Parece que as quedas dos Patriots foram maiores que as dos Colts. Vejamos a queda m\u00e9dia em cada um dos dois grupos. N\u00e3o precisamos mais das pontua\u00e7\u00f5es combinadas.<\/p>\n<pre><code><span style=\"color: black\">football = football.drop('Combined')\r\nfootball.group('Team', np.average)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Team<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Pressure Drop average<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.46875<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.20227<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">A queda m\u00e9dia para os Patriots foi de cerca de 1,2 psi, em compara\u00e7\u00e3o com cerca de 0,47 psi para os Colts.<\/p>\n<p style=\"text-align: justify\">A quest\u00e3o agora \u00e9 por que as bolas dos Patriots tiveram uma queda maior na press\u00e3o, em m\u00e9dia, do que as bolas dos Colts. Poderia ser devido ao acaso?<\/p>\n<h2 id=\"as-hip\u00f3teses\" style=\"text-align: justify\">As Hip\u00f3teses<\/h2>\n<p style=\"text-align: justify\">Como o acaso entra aqui? Nada estava sendo selecionado aleatoriamente. Mas podemos criar um modelo de acaso hipotetizando que as 11 quedas dos Patriots parecem uma amostra aleat\u00f3ria de 11 de todas as 15 quedas, com as quedas dos Colts sendo as quatro restantes. Esse \u00e9 um modelo de acaso completamente especificado sob o qual podemos simular dados. Portanto, essa \u00e9 a <strong>hip\u00f3tese nula<\/strong>.<\/p>\n<p style=\"text-align: justify\">Para a alternativa, podemos considerar que as quedas dos Patriots s\u00e3o grandes demais, em m\u00e9dia, para se assemelhar a uma amostra aleat\u00f3ria extra\u00edda de todas as quedas.<\/p>\n<h2 id=\"estat\u00edstica-de-teste\" style=\"text-align: justify\">Estat\u00edstica de Teste<\/h2>\n<p style=\"text-align: justify\">Uma estat\u00edstica natural \u00e9 a diferen\u00e7a entre as duas quedas m\u00e9dias, que iremos calcular como &#8220;queda m\u00e9dia para Patriots &#8211; queda m\u00e9dia para Colts&#8221;. Valores altos dessa estat\u00edstica favorecer\u00e3o a hip\u00f3tese alternativa.<\/p>\n<pre><code><span style=\"color: black\">observed_means = football.group('Team', np.average).column(1)\r\n\r\nobserved_difference = observed_means.item(1) - observed_means.item(0)\r\nobserved_difference<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[3]:<\/td>\n<td style=\"text-align: left\">0.733522727272728<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Essa diferen\u00e7a positiva reflete o fato de que a queda m\u00e9dia na press\u00e3o das bolas de futebol dos Patriots foi maior do que a dos Colts.<\/p>\n<p style=\"text-align: justify\">Assim como fizemos na se\u00e7\u00e3o anterior, escreveremos uma fun\u00e7\u00e3o para calcular a diferen\u00e7a entre as quedas m\u00e9dias nos dois grupos. A fun\u00e7\u00e3o <code>difference_of_means<\/code> leva dois argumentos:<\/p>\n<ul style=\"text-align: justify\">\n<li>o nome da tabela de dados<\/li>\n<li>o r\u00f3tulo da coluna que cont\u00e9m os dois r\u00f3tulos de grupo<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Ele retorna a diferen\u00e7a entre as quedas m\u00e9dias dos dois grupos. Calcularemos a diferen\u00e7a como as quedas dos Patriots menos as quedas dos Colts, como antes.<\/p>\n<pre><code><span style=\"color: black\">def difference_of_means(table, group_label):\r\n    reduced = table.select('Pressure Drop', group_label)\r\n    means_table = reduced.group(group_label, np.average)\r\n    means = means_table.column(1)\r\n    return means.item(1) - means.item(0)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">difference_of_means(football, 'Team')<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[4]:<\/td>\n<td style=\"text-align: left\">0.733522727272728<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Este \u00e9 o mesmo valor que encontramos anteriormente como <code>observed_difference<\/code>.<\/p>\n<h2 id=\"prevendo-a-estat\u00edstica-sob-a-hip\u00f3tese-nula\" style=\"text-align: justify\">Prevendo a Estat\u00edstica sob a Hip\u00f3tese Nula<\/h2>\n<p style=\"text-align: justify\">Se a hip\u00f3tese nula fosse verdadeira, ent\u00e3o n\u00e3o deveria importar quais bolas de futebol s\u00e3o rotuladas como Patriots e quais s\u00e3o rotuladas como Colts. As distribui\u00e7\u00f5es dos dois conjuntos de quedas seriam as mesmas. Podemos simular isso embaralhando aleatoriamente os r\u00f3tulos dos times.<\/p>\n<pre><code><span style=\"color: black\">shuffled_labels = football.sample(with_replacement=False).column(0)\r\noriginal_and_shuffled = football.with_column('Shuffled Label', shuffled_labels)\r\noriginal_and_shuffled.show()<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Team<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Pressure Drop<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Shuffled Label<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.85<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.475<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.175<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.65<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.225<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.725<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.425<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.175<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.35<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.375<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.475<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.475<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.275<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colts<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.65<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Patriots<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Como as m\u00e9dias de todos os grupos se comparam?<\/p>\n<pre><code><span style=\"color: black\">difference_of_means(original_and_shuffled, 'Shuffled Label')<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[5]:<\/td>\n<td style=\"text-align: left\">-0.5619318181818183<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">difference_of_means(original_and_shuffled, 'Team')<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[6]:<\/td>\n<td style=\"text-align: left\">0.733522727272728<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Os valores m\u00e9dios de queda das duas equipes est\u00e3o mais pr\u00f3ximos quando os r\u00f3tulos das equipes s\u00e3o atribu\u00eddos aleatoriamente \u00e0s bolas do que estavam para os dois grupos realmente usados no jogo.<\/p>\n<h2 id=\"teste-de-permuta\u00e7\u00e3o\" style=\"text-align: justify\">Teste de Permuta\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">\u00c9 hora de um passo que agora \u00e9 familiar. Vamos simular repetidamente a estat\u00edstica de teste sob a hip\u00f3tese nula.<\/p>\n<p style=\"text-align: justify\">permuta\u00e7\u00f5es repetidas das bolas e atribuindo conjuntos aleat\u00f3rios \u00e0s duas equipes.<\/p>\n<p style=\"text-align: justify\">Como de costume, come\u00e7aremos escrevendo uma fun\u00e7\u00e3o <code>one_simulated_difference<\/code> que retorna um valor simulado da diferen\u00e7a entre as quedas m\u00e9dias de press\u00e3o dos grupos rotulados como Patriots e Colts ap\u00f3s permutar aleatoriamente os r\u00f3tulos das equipes das bolas.<\/p>\n<pre><code><span style=\"color: black\">def one_simulated_difference():\r\n    shuffled_labels = football.sample(with_replacement = False\r\n                                                    ).column('Team')\r\n    shuffled_table = football.select('Pressure Drop').with_column(\r\n        'Shuffled Label', shuffled_labels)\r\n    return difference_of_means(shuffled_table, 'Shuffled Label')   <\/span><\/code><\/pre>\n<p style=\"text-align: justify\">Agora podemos usar um loop <code>for<\/code> e esta fun\u00e7\u00e3o para criar um array <code>differences<\/code> que cont\u00e9m 10.000 valores da estat\u00edstica de teste simulada sob a hip\u00f3tese nula.<\/p>\n<pre><code><span style=\"color: black\">differences = make_array()\r\n\r\nrepetitions = 10000\r\nfor i in np.arange(repetitions):\r\n    new_difference = one_simulated_difference()\r\n    differences = np.append(differences, new_difference)<\/span><\/code><\/pre>\n<h2 id=\"conclus\u00e3o-do-teste\" style=\"text-align: justify\">Conclus\u00e3o do Teste<\/h2>\n<p style=\"text-align: justify\">Para calcular o p-valor emp\u00edrico, \u00e9 importante lembrar da hip\u00f3tese alternativa, que \u00e9 que as quedas dos Patriots s\u00e3o grandes demais para serem resultado apenas da varia\u00e7\u00e3o ao acaso.<\/p>\n<p style=\"text-align: justify\">Quedas maiores para os Patriots favorecem a hip\u00f3tese alternativa. Portanto, o p-valor \u00e9 a probabilidade (calculada sob a hip\u00f3tese nula) de obter uma estat\u00edstica de teste igual ao nosso valor observado de 0,733522727272728 ou maior.<\/p>\n<p style=\"text-align: justify\">A figura abaixo visualiza esse c\u00e1lculo. Ela consiste na distribui\u00e7\u00e3o emp\u00edrica da estat\u00edstica de teste sob a hip\u00f3tese nula, com a estat\u00edstica observada marcada em vermelho no eixo horizontal e a \u00e1rea correspondente ao valor p sombreada em dourado.<\/p>\n<pre><code><span style=\"color: black\">Table().with_column(\r\n    'Difference Between Group Averages', differences).hist(\r\n    left_end = observed_difference\r\n)\r\nplots.ylim(-0.1, 1.4)\r\nplots.scatter(observed_difference, 0, color='red', s=30, zorder=3)\r\nplots.title('Prediction Under the Null Hypothesis')\r\nprint('Observed Difference:', observed_difference)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[7]:<\/td>\n<td style=\"text-align: left\">Observed Difference: 0.733522727272728<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-685\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-3-1.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-3-1.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-3-1-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p style=\"text-align: justify\">A olho nu, o valor p parece bem pequeno. Podemos confirmar isso por meio de um c\u00e1lculo.<\/p>\n<pre><code><span style=\"color: black\">empirical_p = np.count_nonzero(differences &gt;= observed_difference) \/ 10000\r\nempirical_p<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[8]:<\/td>\n<td style=\"text-align: left\">0.0026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Como em exemplos anteriores deste teste, a maior parte da distribui\u00e7\u00e3o est\u00e1 centrada em torno de 0. Sob a hip\u00f3tese nula, as defla\u00e7\u00f5es dos Patriots s\u00e3o uma amostra aleat\u00f3ria das 15 defla\u00e7\u00f5es, e portanto, as dos Colts tamb\u00e9m s\u00e3o. Portanto, os dois conjuntos de defla\u00e7\u00f5es devem ser aproximadamente iguais em m\u00e9dia, e, portanto, sua diferen\u00e7a deve ser em torno de 0.<\/p>\n<p style=\"text-align: justify\">Mas o valor observado da estat\u00edstica de teste est\u00e1 bastante distante do centro da distribui\u00e7\u00e3o. Por qualquer crit\u00e9rio razo\u00e1vel para o que \u00e9 &#8220;pequeno&#8221;, o p-valor emp\u00edrico \u00e9 pequeno. Portanto, acabamos rejeitando a hip\u00f3tese nula de aleatoriedade e conclu\u00edmos que as defla\u00e7\u00f5es dos Patriots foram grandes demais para refletir apenas varia\u00e7\u00e3o ao acaso.<\/p>\n<p style=\"text-align: justify\">A equipe investigativa independente analisou os dados de v\u00e1rias maneiras diferentes, levando em considera\u00e7\u00e3o as leis da f\u00edsica. O relat\u00f3rio final disse,<\/p>\n<blockquote><p>&#8220;[A] queda m\u00e9dia de press\u00e3o das bolas do jogo dos Patriots excedeu a queda m\u00e9dia de press\u00e3o das bolas dos Colts em 0,45 a 1,02 psi, dependendo de v\u00e1rios pressupostos poss\u00edveis sobre os calibradores usados, e assumindo uma press\u00e3o inicial de 12,5 psi para as bolas dos Patriots e 13,0 para as bolas dos Colts.&#8221;<\/p>\n<p>&#8212; <em>Relat\u00f3rio investigativo encomendado pela NFL referente ao jogo do campeonato da AFC em 18 de janeiro de 2015<\/em><\/p><\/blockquote>\n<p style=\"text-align: justify\">Nossa an\u00e1lise mostra uma queda m\u00e9dia de press\u00e3o de cerca de 0,73 psi, o que est\u00e1 pr\u00f3ximo do centro do intervalo &#8220;0,45 a 1,02 psi&#8221; e, portanto, consistente com a an\u00e1lise oficial.<\/p>\n<p style=\"text-align: justify\">Lembre-se de que nosso teste de hip\u00f3teses n\u00e3o estabelece a raz\u00e3o <em>por que<\/em> a diferen\u00e7a n\u00e3o se deve ao acaso. Estabelecer causalidade geralmente \u00e9 mais complexo do que realizar um teste de hip\u00f3teses.<\/p>\n<p style=\"text-align: justify\">Mas a pergunta mais importante no mundo do futebol era sobre a causalidade: a quest\u00e3o era se a queda excessiva de press\u00e3o nas bolas dos Patriots foi deliberada. Se voc\u00ea estiver curioso sobre a resposta dada pelos investigadores, aqui est\u00e1 o <a href=\"https:\/\/nfllabor.files.wordpress.com\/2015\/05\/investigative-and-expert-reports-re-footballs-used-during-afc-championsh.pdf\">relat\u00f3rio completo<\/a>.<\/p>\n<p><!--###########################################################################################################################################################--><\/p>\n<table width=\"100%\">\n<tbody>\n<tr>\n<td align=\"left\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">\u2190 Cap\u00edtulo 12.2 &#8211; Causalidade<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/\">Cap\u00edtulo 13 &#8211; Estima\u00e7\u00e3o \u2192<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><!--###########################################################################################################################################################--><\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u00cdndice 1. O que \u00e9 Ci\u00eancia de Dados? 1.1. Introdu\u00e7\u00e3o 1.1.1. Ferramentas Computacionais 1.1.2. T\u00e9cnicas Estat\u00edsticas 1.2. Por que Ci\u00eancia de Dados? 1.3. Tra\u00e7ando os Cl\u00e1ssicos 1.3.1. Personagens Liter\u00e1rios 1.3.2. Outro Tipo de Personagem 2. Causalidade e Experimentos 2.1. John Snow e a Bomba da Broad Street 2.2. O &#8220;Grande Experimento&#8221; de Snow 2.3. Estabelecendo [&hellip;]<\/p>\n","protected":false},"author":21894,"featured_media":0,"parent":665,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-684","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/users\/21894"}],"replies":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/comments?post=684"}],"version-history":[{"count":2,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/684\/revisions"}],"predecessor-version":[{"id":1040,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/684\/revisions\/1040"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/665"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=684"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}