{"id":669,"date":"2025-07-28T18:31:18","date_gmt":"2025-07-28T22:31:18","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=669"},"modified":"2025-10-10T18:00:05","modified_gmt":"2025-10-10T22:00:05","slug":"12-1","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/12-0\/12-1\/","title":{"rendered":"Cap\u00edtulo 12.1"},"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\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport numpy as np\r\n\r\nimport matplotlib\r\nmatplotlib.use('Agg')\r\n%matplotlib inline\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"teste-a-b\" style=\"text-align: center\">Teste A\/B<\/h1>\n<p style=\"text-align: justify\">Na an\u00e1lise de dados moderna, decidir se duas amostras num\u00e9ricas v\u00eam da mesma distribui\u00e7\u00e3o subjacente \u00e9 chamado de <em>teste A\/B<\/em>. O nome refere-se aos r\u00f3tulos das duas amostras, A e B.<\/p>\n<p style=\"text-align: justify\">Vamos desenvolver o m\u00e9todo no contexto de um exemplo. Os dados s\u00e3o provenientes de uma amostra de rec\u00e9m-nascidos em um grande sistema hospitalar. Trataremos como se fosse uma amostra aleat\u00f3ria simples, embora a amostragem tenha sido feita em m\u00faltiplos est\u00e1gios. <a href=\"https:\/\/www.stat.berkeley.edu\/~statlabs\/\">Stat Labs<\/a> por Deborah Nolan e Terry Speed cont\u00e9m detalhes sobre um conjunto de dados maior do qual este conjunto \u00e9 extra\u00eddo.<\/p>\n<h2 id=\"fumantes-e-n-o-fumantes\" style=\"text-align: justify\">Fumantes e N\u00e3o Fumantes<\/h2>\n<p style=\"text-align: justify\">A tabela <code>births<\/code> cont\u00e9m as seguintes vari\u00e1veis para 1.174 pares m\u00e3e-beb\u00ea: o peso ao nascer do beb\u00ea em on\u00e7as, o n\u00famero de dias gestacionais, a idade da m\u00e3e em anos completos, a altura da m\u00e3e em polegadas, o peso durante a gravidez em libras e se a m\u00e3e fumou ou n\u00e3o durante a gravidez.<\/p>\n<pre><code><span style=\"color: black\">births = Table.read_table(path_data + 'baby.csv')\r\nbirths<\/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\">Birth Weight<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Gestational Days<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Maternal Age<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Maternal Height<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Maternal Pregnancy Weight<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Maternal Smoker<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">284<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">27<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">62<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">100<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">113<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">282<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">33<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">64<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">135<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">128<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">279<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">28<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">64<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">115<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">108<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">282<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">23<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">67<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">125<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">136<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">286<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">25<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">62<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">93<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">138<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">244<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">33<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">62<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">178<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">132<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">245<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">23<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">65<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">140<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">289<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">25<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">62<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">125<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">143<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">299<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">30<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">136<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">140<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">351<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">27<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Um dos objetivos do estudo era verificar se o tabagismo materno estava associado ao peso ao nascer. Vamos ver o que podemos dizer sobre as duas vari\u00e1veis.<\/p>\n<p style=\"text-align: justify\">Come\u00e7aremos selecionando apenas <code>Birth Weight<\/code> e <code>Maternal Smoker<\/code>. H\u00e1 715 n\u00e3o fumantes entre as mulheres da amostra e 459 fumantes.<\/p>\n<pre><code><span style=\"color: black\">smoking_and_birthweight = births.select('Maternal Smoker', 'Birth Weight')<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">smoking_and_birthweight.group('Maternal Smoker')<\/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\">Maternal Smoker<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">count<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">715<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">459<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Vejamos a distribui\u00e7\u00e3o dos pesos ao nascer dos beb\u00eas das m\u00e3es n\u00e3o fumantes em compara\u00e7\u00e3o com os das m\u00e3es fumantes. Para gerar dois histogramas sobrepostos, usaremos <code>hist<\/code> com o argumento opcional <code>group<\/code> que \u00e9 uma coluna r\u00f3tulo ou \u00edndice. As linhas da tabela s\u00e3o primeiro agrupadas por esta coluna e ent\u00e3o um histograma \u00e9 desenhado para cada uma.<\/p>\n<pre><code><span style=\"color: black\">smoking_and_birthweight.hist('Birth Weight', group = 'Maternal Smoker')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-671\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-1.png\" alt=\"\" width=\"680\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-1.png 680w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-1-300x125.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-1-555x233.png 555w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p style=\"text-align: justify\">A distribui\u00e7\u00e3o dos pesos dos beb\u00eas nascidos de m\u00e3es que fumaram parece estar ligeiramente deslocada para a esquerda da distribui\u00e7\u00e3o correspondente \u00e0s m\u00e3es n\u00e3o fumantes. Os pesos dos beb\u00eas das m\u00e3es que fumaram parecem ser menores em m\u00e9dia do que os pesos dos beb\u00eas das n\u00e3o fumantes.<\/p>\n<p style=\"text-align: justify\">Isso levanta a quest\u00e3o de saber se a diferen\u00e7a reflete apenas varia\u00e7\u00e3o ao acaso ou uma diferen\u00e7a nas distribui\u00e7\u00f5es na popula\u00e7\u00e3o maior. Poderia ser que n\u00e3o houvesse diferen\u00e7a entre as duas distribui\u00e7\u00f5es na popula\u00e7\u00e3o, mas estar\u00edamos vendo uma diferen\u00e7a nas amostras apenas por causa das m\u00e3es que foram selecionadas?<\/p>\n<h2 id=\"as-hip-teses\" style=\"text-align: justify\">As Hip\u00f3teses<\/h2>\n<p style=\"text-align: justify\">Podemos tentar responder a essa pergunta por meio de um teste de hip\u00f3teses. O modelo de chance que testaremos diz que n\u00e3o h\u00e1 diferen\u00e7a subjacente nas popula\u00e7\u00f5es; as distribui\u00e7\u00f5es nas amostras s\u00e3o diferentes apenas devido ao acaso.<\/p>\n<p style=\"text-align: justify\">Formalmente, esta \u00e9 a hip\u00f3tese nula. Precisaremos descobrir como simular uma estat\u00edstica \u00fatil sob esta hip\u00f3tese. Mas, para come\u00e7ar, vamos apenas declarar as duas hip\u00f3teses naturais.<\/p>\n<p style=\"text-align: justify\"><strong>Hip\u00f3tese nula:<\/strong> Na popula\u00e7\u00e3o, a distribui\u00e7\u00e3o dos pesos ao nascer dos beb\u00eas \u00e9 a mesma para m\u00e3es que n\u00e3o fumam e para m\u00e3es que fumam. A diferen\u00e7a na amostra \u00e9 devida ao acaso.<\/p>\n<p style=\"text-align: justify\"><strong>Hip\u00f3tese alternativa:<\/strong> Na popula\u00e7\u00e3o, os beb\u00eas das m\u00e3es que fumam t\u00eam um peso ao nascer menor, em m\u00e9dia, do que os beb\u00eas das n\u00e3o fumantes.<\/p>\n<h2 id=\"estat-stica-do-teste\" style=\"text-align: justify\">Estat\u00edstica do Teste<\/h2>\n<p style=\"text-align: justify\">A hip\u00f3tese alternativa compara os pesos m\u00e9dios ao nascer dos dois grupos e diz que a m\u00e9dia para as m\u00e3es que fumam \u00e9 menor. Portanto, \u00e9 razo\u00e1vel usarmos a diferen\u00e7a entre as m\u00e9dias dos dois grupos como nossa estat\u00edstica.<\/p>\n<p style=\"text-align: justify\">Faremos a subtra\u00e7\u00e3o na ordem &#8220;peso m\u00e9dio do grupo que fuma &#8211; peso m\u00e9dio do grupo que n\u00e3o fuma&#8221;. Valores pequenos (ou seja, grandes valores negativos) dessa estat\u00edstica favorecer\u00e3o a hip\u00f3tese alternativa.<\/p>\n<p style=\"text-align: justify\">O valor observado da estat\u00edstica do teste \u00e9 cerca de -9,27 on\u00e7as.<\/p>\n<pre><code><span style=\"color: black\">means_table = smoking_and_birthweight.group('Maternal Smoker', np.average)\r\nmeans_table<\/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\">Maternal Smoker<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Birth Weight average<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">123.085<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">113.819<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">means = means_table.column(1)\r\nobserved_difference = means.item(1) - 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[1]:<\/td>\n<td style=\"text-align: left\">-9.266142572024918<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Vamos calcular tais diferen\u00e7as repetidamente em nossas simula\u00e7\u00f5es abaixo, ent\u00e3o vamos definir uma fun\u00e7\u00e3o para fazer o trabalho. A fun\u00e7\u00e3o recebe 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 a vari\u00e1vel booleana para agrupamento<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Ela retorna a diferen\u00e7a entre as m\u00e9dias do grupo <code>True<\/code> e do grupo <code>False<\/code>.<\/p>\n<p style=\"text-align: justify\">Voc\u00ea logo ver\u00e1 por que estamos especificando os dois argumentos. Por enquanto, verifique se a fun\u00e7\u00e3o retorna o que deve.<\/p>\n<pre><code><span style=\"color: black\">def difference_of_means(table, group_label):\r\n    \"\"\"Leva: nome da tabela,\r\n    r\u00f3tulo da coluna que indica o grupo ao qual a linha pertence\r\n    Retorna: Diferen\u00e7a dos pesos m\u00e9dios ao nascer dos dois grupos\"\"\"\r\n    reduced = table.select('Birth Weight', 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<p style=\"text-align: justify\">Para verificar se a fun\u00e7\u00e3o est\u00e1 funcionando, vamos us\u00e1-la para calcular a diferen\u00e7a observada entre as m\u00e9dias dos pesos ao nascer dos dois grupos na amostra.<\/p>\n<pre><code><span style=\"color: black\">difference_of_means(births, 'Maternal Smoker')<\/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\">-9.266142572024918<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">\u00c9 o mesmo que o valor de <code>observed_difference<\/code> calculado anteriormente.<\/p>\n<h2 id=\"previs-o-da-estat-stica-sob-a-hip-tese-nula\" style=\"text-align: justify\">Previs\u00e3o da Estat\u00edstica Sob a Hip\u00f3tese Nula<\/h2>\n<p style=\"text-align: justify\">Para ver como a estat\u00edstica deve variar sob a hip\u00f3tese nula, temos que descobrir como simular a estat\u00edstica sob essa hip\u00f3tese. Um m\u00e9todo inteligente baseado em <em>permuta\u00e7\u00f5es aleat\u00f3rias<\/em> faz exatamente isso.<\/p>\n<p style=\"text-align: justify\">Se n\u00e3o houvesse diferen\u00e7a entre as duas distribui\u00e7\u00f5es na popula\u00e7\u00e3o subjacente, ent\u00e3o o fato de um peso ao nascer ter o r\u00f3tulo <code>True<\/code> ou <code>False<\/code> em rela\u00e7\u00e3o ao tabagismo materno n\u00e3o deveria fazer diferen\u00e7a na m\u00e9dia. A ideia, ent\u00e3o, \u00e9 embaralhar todos os r\u00f3tulos aleatoriamente entre as m\u00e3es. Isso \u00e9 chamado de <em>permuta\u00e7\u00e3o aleat\u00f3ria<\/em>.<\/p>\n<p style=\"text-align: justify\">O embaralhamento garante que a contagem dos r\u00f3tulos <code>True<\/code> n\u00e3o mude, nem a contagem dos r\u00f3tulos <code>False<\/code>. Isso \u00e9 importante para a comparabilidade das diferen\u00e7as simuladas de m\u00e9dias e a diferen\u00e7a original das m\u00e9dias. Veremos mais tarde no curso que o tamanho da amostra afeta a variabilidade de uma m\u00e9dia amostral.<\/p>\n<p style=\"text-align: justify\">Calcule a diferen\u00e7a entre as duas novas m\u00e9dias de grupo: a m\u00e9dia do peso dos beb\u00eas cujas m\u00e3es foram rotuladas aleatoriamente como fumantes e a m\u00e9dia do peso dos beb\u00eas das m\u00e3es restantes que foram rotuladas aleatoriamente como n\u00e3o fumantes. Este \u00e9 um valor simulado da estat\u00edstica do teste sob a hip\u00f3tese nula.<\/p>\n<p style=\"text-align: justify\">Vamos ver como fazer isso. \u00c9 sempre uma boa ideia come\u00e7ar com os dados. Reduzimos a tabela para ter apenas as colunas que precisamos.<\/p>\n<pre><code><span style=\"color: black\">smoking_and_birthweight<\/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\">Maternal Smoker<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Birth Weight<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">113<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">128<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">108<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">136<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">138<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">132<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">143<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">140<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Existem 1.174 linhas na tabela. Para embaralhar todos os r\u00f3tulos, sortearemos uma amostra aleat\u00f3ria de 1.174 linhas sem reposi\u00e7\u00e3o. Em seguida, a amostra incluir\u00e1 todas as linhas da tabela, em ordem aleat\u00f3ria.<\/p>\n<p style=\"text-align: justify\">Podemos usar o m\u00e9todo de tabela <code>sample<\/code> com o argumento opcional <code>with_replacement=False<\/code>. N\u00e3o precisamos especificar um tamanho de amostra, porque por padr\u00e3o, <code>sample<\/code> desenha tantas vezes quantas linhas houver na tabela.<\/p>\n<pre><code><span style=\"color: black\">shuffled_labels = smoking_and_birthweight.sample(with_replacement = False).column(0)\r\noriginal_and_shuffled = smoking_and_birthweight.with_column('Shuffled Label', shuffled_labels)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">original_and_shuffled<\/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\">Maternal Smoker<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Birth Weight<\/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\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">113<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">128<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">108<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">136<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">138<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">132<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">120<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">143<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">140<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">A m\u00e3e de cada beb\u00ea agora tem um r\u00f3tulo aleat\u00f3rio de fumante\/n\u00e3o fumante na coluna <code>Shuffled Label<\/code>, enquanto seu r\u00f3tulo original est\u00e1 em <code>Maternal Smoker<\/code>. Se a hip\u00f3tese nula for verdadeira, todos os rearranjos aleat\u00f3rios dos r\u00f3tulos dever\u00e3o ser igualmente prov\u00e1veis.<\/p>\n<p style=\"text-align: justify\">Vamos ver qu\u00e3o diferentes s\u00e3o os pesos m\u00e9dios nos dois grupos rotulados aleatoriamente.<\/p>\n<pre><code><span style=\"color: black\">shuffled_only = original_and_shuffled.select('Birth Weight','Shuffled Label')\r\nshuffled_group_means = shuffled_only.group('Shuffled Label', np.average)\r\nshuffled_group_means<\/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\">Shuffled Label<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Birth Weight average<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">False<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">119.277<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">True<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">119.752<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">As m\u00e9dias dos dois grupos selecionados aleatoriamente est\u00e3o um pouco mais pr\u00f3ximas do que as m\u00e9dias dos dois grupos originais. Podemos usar nossa fun\u00e7\u00e3o <code>difference_of_means<\/code> para encontrar as duas diferen\u00e7as.<\/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[3]:<\/td>\n<td style=\"text-align: left\">0.4747109100050153<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">difference_of_means(original_and_shuffled, 'Maternal Smoker')<\/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\">-9.266142572024918<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Mas ser\u00e1 que uma mistura diferente poderia resultar em uma diferen\u00e7a maior entre as m\u00e9dias dos grupos? Para ter uma ideia da variabilidade, precisamos simular a diferen\u00e7a muitas vezes.<\/p>\n<p style=\"text-align: justify\">Como sempre, vamos come\u00e7ar definindo uma fun\u00e7\u00e3o que simula um valor da estat\u00edstica de teste sob a hip\u00f3tese nula. Isso se resume a coletar o c\u00f3digo que escrevemos acima.<\/p>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o \u00e9 chamada <code>one_simulated_difference_of_means<\/code>. Ela n\u00e3o recebe argumentos e retorna a diferen\u00e7a entre as m\u00e9dias dos pesos ao nascer de dois grupos formados pela mistura aleat\u00f3ria de todos os r\u00f3tulos.<\/p>\n<pre><code><span style=\"color: black\">def one_simulated_difference_of_means():\r\n    \"\"\"Retorna: Diferen\u00e7a entre pesos m\u00e9dios ao nascer\r\n    de beb\u00eas de fumantes e n\u00e3o fumantes ap\u00f3s embaralhar r\u00f3tulos\"\"\"\r\n\r\n    # array de shuffed labels\r\n    shuffled_labels = births.sample(with_replacement=False).column('Maternal Smoker')\r\n\r\n    # tabela de birth weights e shuffled labels\r\n    shuffled_table = births.select('Birth Weight').with_column(\r\n        'Shuffled Label', shuffled_labels)\r\n\r\n    return difference_of_means(shuffled_table, 'Shuffled Label')   <\/span><\/code><\/pre>\n<p style=\"text-align: justify\">Execute a c\u00e9lula abaixo algumas vezes para ver como a sa\u00edda muda.<\/p>\n<pre><code><span style=\"color: black\">one_simulated_difference_of_means()<\/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\">-0.058299434770034964<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"teste-de-permuta-o\" style=\"text-align: justify\">Teste de Permuta\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">Os testes baseados em permuta\u00e7\u00f5es aleat\u00f3rias dos dados s\u00e3o chamados de <em>testes de permuta\u00e7\u00e3o<\/em>. Estamos realizando um neste exemplo. Na c\u00e9lula abaixo, simularemos nossa estat\u00edstica de teste \u2013 a diferen\u00e7a entre o peso m\u00e9dio ao nascer dos dois grupos formados aleatoriamente \u2013 muitas vezes e colete as diferen\u00e7as em uma matriz.<\/p>\n<pre><code><span style=\"color: black\">differences = make_array()\r\n\r\nrepetitions = 5000\r\nfor i in np.arange(repetitions):\r\n    new_difference = one_simulated_difference_of_means()\r\n    differences = np.append(differences, new_difference)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">O array <code>differences<\/code> cont\u00e9m 5.000 valores simulados de nossa estat\u00edstica de teste: a diferen\u00e7a entre o peso m\u00e9dio no grupo de fumantes e o peso m\u00e9dio no grupo de n\u00e3o fumantes, quando os r\u00f3tulos s\u00e3o atribu\u00eddos aleatoriamente.<\/p>\n<h2 id=\"conclus-o-do-teste\" style=\"text-align: justify\">Conclus\u00e3o do Teste<\/h2>\n<p style=\"text-align: justify\">O histograma abaixo mostra a distribui\u00e7\u00e3o desses 5.000 valores. \u00c9 a distribui\u00e7\u00e3o emp\u00edrica da estat\u00edstica de teste simulada sob a hip\u00f3tese nula. Isso \u00e9 uma previs\u00e3o sobre a estat\u00edstica de teste, baseada na hip\u00f3tese nula.<\/p>\n<pre><code><span style=\"color: black\">Table().with_column('Difference Between Group Means', differences).hist()\r\nprint('Observed Difference:', observed_difference)\r\nplots.title('Prediction Under the Null Hypothesis');<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-672\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-2.png\" alt=\"\" width=\"433\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-2.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-2-300x211.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p style=\"text-align: justify\">Observe como a distribui\u00e7\u00e3o est\u00e1 centrada aproximadamente em torno de 0. Isso faz sentido, porque sob a hip\u00f3tese nula, os dois grupos devem ter m\u00e9dias aproximadamente iguais. Portanto, a diferen\u00e7a entre as m\u00e9dias dos grupos deve estar em torno de 0.<\/p>\n<p style=\"text-align: justify\">A diferen\u00e7a observada na amostra original \u00e9 de cerca de -9,27 on\u00e7as, o que nem mesmo aparece na escala horizontal do histograma. O valor observado da estat\u00edstica e o comportamento previsto da estat\u00edstica sob a hip\u00f3tese nula s\u00e3o inconsistentes.<\/p>\n<p style=\"text-align: justify\">A conclus\u00e3o do teste \u00e9 que os dados favorecem a hip\u00f3tese alternativa em rela\u00e7\u00e3o \u00e0 hip\u00f3tese nula. Isso suporta a hip\u00f3tese de que o peso m\u00e9dio ao nascer de beb\u00eas nascidos de m\u00e3es que fumam \u00e9 menor do que o peso m\u00e9dio ao nascer de beb\u00eas de m\u00e3es n\u00e3o fumantes.<\/p>\n<p style=\"text-align: justify\">Se voc\u00ea deseja calcular um p-valor emp\u00edrico, lembre-se de que valores baixos da estat\u00edstica favorecem a hip\u00f3tese alternativa.<\/p>\n<pre><code><span style=\"color: black\">empirical_p = np.count_nonzero(differences &lt;= observed_difference) \/ repetitions\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[6]:<\/td>\n<td style=\"text-align: left\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">O p-valor emp\u00edrico \u00e9 0, o que significa que nenhuma das 5.000 amostras permutadas resultou em uma diferen\u00e7a de -9,27 ou menos. Esta \u00e9 apenas uma aproxima\u00e7\u00e3o. A chance exata de obter uma diferen\u00e7a nesse intervalo n\u00e3o \u00e9 0. Mas \u00e9 extremamente pequeno, de acordo com a nossa simula\u00e7\u00e3o, e portanto podemos rejeitar a hip\u00f3tese nula.<\/p>\n<h2 id=\"outro-teste-de-permuta-o\" style=\"text-align: justify\">Outro Teste de Permuta\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">Podemos usar o mesmo m\u00e9todo para comparar outros atributos dos fumantes e dos n\u00e3o fumantes, como a idade. Os histogramas das idades dos dois grupos mostram que, na amostra, as m\u00e3es que fumavam tendiam a ser mais jovens.<\/p>\n<pre><code><span style=\"color: black\">smoking_and_age = births.select('Maternal Smoker', 'Maternal Age')\r\nsmoking_and_age.hist('Maternal Age', group = 'Maternal Smoker')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-673\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-3.png\" alt=\"\" width=\"669\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-3.png 669w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-3-300x127.png 300w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/p>\n<p style=\"text-align: justify\">A diferen\u00e7a observada entre as idades m\u00e9dias \u00e9 de cerca de -0.8 anos.<\/p>\n<p style=\"text-align: justify\">Vamos reescrever o c\u00f3digo que comparou o peso ao nascer para que agora compare as idades dos fumantes e dos n\u00e3o fumantes.<\/p>\n<pre><code><span style=\"color: black\">def difference_of_means(table, group_label):\r\n    \"\"\"Leva: nome da tabela,\r\n    r\u00f3tulo da coluna que indica o grupo ao qual a linha pertence\r\n    Retorna: Diferen\u00e7a das idades m\u00e9dias dos dois grupos\"\"\"\r\n    reduced = table.select('Maternal Age', 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\">observed_age_difference = difference_of_means(births, 'Maternal Smoker')\r\nobserved_age_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\">-0.8076725017901509<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Lembre-se de que a diferen\u00e7a \u00e9 calculada como a m\u00e9dia da idade dos fumantes menos a m\u00e9dia da idade dos n\u00e3o fumantes. O sinal negativo indica que os fumantes s\u00e3o mais jovens em m\u00e9dia.<\/p>\n<p style=\"text-align: justify\">Essa diferen\u00e7a \u00e9 devida ao acaso, ou reflete uma diferen\u00e7a subjacente na popula\u00e7\u00e3o?<\/p>\n<p style=\"text-align: justify\">Como antes, podemos usar um teste de permuta\u00e7\u00e3o para responder a essa pergunta. Se as distribui\u00e7\u00f5es subjacentes das idades nos dois grupos forem iguais, ent\u00e3o a distribui\u00e7\u00e3o emp\u00edrica da diferen\u00e7a com base em amostras permutadas prever\u00e1 como a estat\u00edstica deve variar devido ao acaso.<\/p>\n<p style=\"text-align: justify\">Vamos seguir o mesmo processo que em qualquer simula\u00e7\u00e3o. Come\u00e7aremos escrevendo uma fun\u00e7\u00e3o que retorna um valor simulado da diferen\u00e7a entre m\u00e9dias, e ent\u00e3o escreveremos um <code>for<\/code> loop para simular numerosos valores assim e colet\u00e1-los em uma matriz.<\/p>\n<pre><code><span style=\"color: black\">def one_simulated_difference_of_means():\r\n    \"\"\"Retorna: Diferen\u00e7a entre idades m\u00e9dias\r\n    de fumantes e n\u00e3o fumantes ap\u00f3s embaralhar os r\u00f3tulos\"\"\"\r\n\r\n    # array de r\u00f3tulos embaralhados\r\n    shuffled_labels = births.sample(with_replacement=False).column('Maternal Smoker')\r\n\r\n    # tabela de idades e r\u00f3tulos embaralhados\r\n    shuffled_table = births.select('Maternal Age').with_column(\r\n        'Shuffled Label', shuffled_labels)\r\n\r\n    return difference_of_means(shuffled_table, 'Shuffled Label')   <\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">age_differences = make_array()\r\n\r\nrepetitions = 5000\r\nfor i in np.arange(repetitions):\r\n    new_difference = one_simulated_difference_of_means()\r\n    age_differences = np.append(age_differences, new_difference)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">A diferen\u00e7a observada est\u00e1 na cauda da distribui\u00e7\u00e3o emp\u00edrica das diferen\u00e7as simuladas sob a hip\u00f3tese nula.<\/p>\n<pre><code><span style=\"color: black\">Table().with_column(\r\n    'Difference Between Group Means', age_differences).hist(\r\n    right_end = observed_age_difference)\r\n# Plotting parameters; you can ignore the code below\r\nplots.ylim(-0.1, 1.2)\r\nplots.scatter(observed_age_difference, 0, color='red', s=40, zorder=3)\r\nplots.title('Prediction Under the Null Hypothesis')\r\nprint('Observed Difference:', observed_age_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[8]:<\/td>\n<td style=\"text-align: left\">Observed Difference: -0.8076725017901509<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-674\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-4.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-4.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-1-4-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p style=\"text-align: justify\">Mais uma vez, a distribui\u00e7\u00e3o emp\u00edrica das diferen\u00e7as simuladas est\u00e1 centrada aproximadamente em torno de 0, porque a simula\u00e7\u00e3o est\u00e1 sob a hip\u00f3tese nula de que n\u00e3o h\u00e1 diferen\u00e7a entre as distribui\u00e7\u00f5es dos dois grupos.<\/p>\n<p style=\"text-align: justify\">O p-valor emp\u00edrico do teste \u00e9 a propor\u00e7\u00e3o de diferen\u00e7as simuladas que foram iguais ou menores que a diferen\u00e7a observada. Isso ocorre porque valores baixos da diferen\u00e7a favorecem a hip\u00f3tese alternativa de que os fumantes eram, em m\u00e9dia, mais jovens.<\/p>\n<pre><code><span style=\"color: black\">empirical_p = np.count_nonzero(age_differences &lt;= observed_age_difference) \/ 5000\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[9]:<\/td>\n<td style=\"text-align: left\">0.0108<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">O p-valor emp\u00edrico est\u00e1 em torno de 1% e, portanto, o resultado \u00e9 estatisticamente significativo. O teste apoia a hip\u00f3tese de que os fumantes eram, em m\u00e9dia, mais jovens.<\/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\/\">\u2190 Cap\u00edtulo 12 &#8211; Comparando Duas Amostras<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">Cap\u00edtulo 12.2 &#8211; Causalidade \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-669","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/669","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=669"}],"version-history":[{"count":4,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/669\/revisions"}],"predecessor-version":[{"id":1033,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/669\/revisions\/1033"}],"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=669"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}