{"id":677,"date":"2025-07-28T18:34:16","date_gmt":"2025-07-28T22:34:16","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=677"},"modified":"2025-10-11T02:22:38","modified_gmt":"2025-10-11T06:22:38","slug":"12-2","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/12-0\/12-2\/","title":{"rendered":"Cap\u00edtulo 12.2"},"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=\"causalidade\" style=\"text-align: center\">Causalidade<\/h1>\n<p style=\"text-align: justify\">Nossos m\u00e9todos para comparar duas amostras t\u00eam um uso poderoso na an\u00e1lise de experimentos controlados randomizados. Como os grupos de tratamento e controle s\u00e3o designados aleatoriamente em tais experimentos, as diferen\u00e7as em seus resultados podem ser comparadas com o que aconteceria apenas por acaso, se o tratamento n\u00e3o tivesse efeito algum. Se as diferen\u00e7as observadas forem mais marcantes do que o que prever\u00edamos como puramente devido ao acaso, teremos evid\u00eancias de<em> causalidade<\/em>. Devido \u00e0 designa\u00e7\u00e3o imparcial de indiv\u00edduos para os grupos de tratamento e controle, as diferen\u00e7as nos resultados dos dois grupos podem ser atribu\u00eddas ao tratamento.<\/p>\n<p style=\"text-align: justify\">A chave para a an\u00e1lise de experimentos controlados randomizados \u00e9 entender exatamente como o acaso entra em cena. Isso nos ajuda a estabelecer hip\u00f3teses nulas e alternativas claras. Uma vez feito isso, podemos simplesmente usar os m\u00e9todos das se\u00e7\u00f5es anteriores para completar a an\u00e1lise.<\/p>\n<p style=\"text-align: justify\">Vamos ver como fazer isso em um exemplo.<\/p>\n<h2 id=\"tratando-dor-cr-nica-nas-costas-um-ensaio-cl-nico-randomizado\" style=\"text-align: justify\">Tratando Dor Cr\u00f4nica nas Costas: Um Ensaio Cl\u00ednico Randomizado<\/h2>\n<p style=\"text-align: justify\">A dor lombar em adultos pode ser muito persistente e dif\u00edcil de tratar. M\u00e9todos comuns variam de corticosteroides a acupuntura. Um <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/11376175\">ensaio cl\u00ednico randomizado (RCT)<\/a> examinou o efeito do uso da Toxina Botul\u00ednica A (BTA) como tratamento. A toxina botul\u00ednica \u00e9 uma prote\u00edna neurot\u00f3xica que causa a doen\u00e7a botulismo; <a href=\"https:\/\/en.wikipedia.org\/wiki\/Botulinum_toxin\">Wikipedia<\/a> diz que a botulina &#8220;\u00e9 a toxina mais letal conhecida.&#8221; Existem sete tipos de toxina botul\u00ednica. A Toxina Botul\u00ednica A \u00e9 um dos tipos que pode causar doen\u00e7as em humanos, mas tamb\u00e9m \u00e9 usada na medicina para tratar v\u00e1rias doen\u00e7as envolvendo m\u00fasculos. O RCT analisado por Foster, Clapp e Jabbari em 2001 examinou-a como tratamento para dor lombar.<\/p>\n<p style=\"text-align: justify\">Trinta e um pacientes com dor lombar foram randomizados em grupos de tratamento e controle, com 15 no grupo de tratamento e 16 no controle. O grupo controle recebeu solu\u00e7\u00e3o salina normal, e os ensaios foram duplo-cego, de modo que nem os m\u00e9dicos nem os pacientes sabiam em que grupo estavam.<\/p>\n<p style=\"text-align: justify\">Oito semanas ap\u00f3s o in\u00edcio do estudo, nove dos 15 no grupo de tratamento e dois dos 16 no grupo de controle tiveram al\u00edvio da dor (de acordo com uma defini\u00e7\u00e3o precisa usada pelos pesquisadores). Esses dados est\u00e3o na tabela <code>bta<\/code> e parecem mostrar que o tratamento tem um benef\u00edcio claro.<\/p>\n<pre><code><span style=\"color: black\">bta = Table.read_table(path_data + 'bta.csv')\r\nbta.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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Vamos ver quantos pacientes se recuperaram em cada grupo. Lembre-se que contar \u00e9 o mesmo que somar zeros e uns. A soma de 1 no grupo controle \u00e9 o n\u00famero de pacientes do grupo controle que tiveram al\u00edvio da dor.<\/p>\n<pre><code><span style=\"color: black\">bta.group('Group', sum)<\/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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Result sum<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Como a contagem \u00e9 igual \u00e0 <em>soma<\/em> de zeros e uns, a <em>propor\u00e7\u00e3o<\/em> de pacientes que tiveram al\u00edvio da dor \u00e9 a <em>m\u00e9dia<\/em> de zeros e uns.<\/p>\n<pre><code><span style=\"color: black\">bta.group('Group', 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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Result average<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.125<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">No grupo de tratamento, 60% dos pacientes tiveram al\u00edvio da dor, em compara\u00e7\u00e3o com apenas 12,5% no grupo de controle. Nenhum dos pacientes sofreu efeitos colaterais.<\/p>\n<p style=\"text-align: justify\">Assim, as indica\u00e7\u00f5es s\u00e3o de que a toxina botul\u00ednica A foi melhor do que o soro fisiol\u00f3gico. Mas a conclus\u00e3o ainda n\u00e3o \u00e9 definitiva. Os pacientes foram designados aleatoriamente para os dois grupos, ent\u00e3o talvez a diferen\u00e7a possa ser apenas devido ao acaso?<\/p>\n<p style=\"text-align: justify\">Para entender o que isso significa, precisamos considerar a possibilidade de que, entre os 31 pacientes do estudo, alguns foram simplesmente mais capazes de se recuperar do que outros, mesmo sem qualquer ajuda do tratamento. E se uma propor\u00e7\u00e3o incomumente grande desses pacientes fosse designada para o grupo de tratamento, apenas por acaso? Ent\u00e3o, mesmo que o tratamento n\u00e3o fizesse nada al\u00e9m do soro fisiol\u00f3gico no grupo de controle, os resultados do grupo de tratamento poderiam parecer melhores do que os do grupo de controle.<\/p>\n<p style=\"text-align: justify\">Para considerar essa possibilidade, vamos come\u00e7ar definindo cuidadosamente o modelo de chance.<\/p>\n<h2 id=\"resultados-potenciais\" style=\"text-align: justify\">Resultados Potenciais<\/h2>\n<p style=\"text-align: justify\">Antes que os pacientes sejam randomizados nos dois grupos, nossas mentes instintivamente imaginam dois resultados poss\u00edveis para cada paciente: o resultado que o paciente teria se fosse designado para o grupo de tratamento e o resultado que o mesmo paciente teria se fosse designado para o grupo de controle. Esses s\u00e3o chamados de dois <em>resultados potenciais<\/em> do paciente.<\/p>\n<p style=\"text-align: justify\">Assim, existem 31 resultados potenciais de tratamento e 31 resultados potenciais de controle. A quest\u00e3o \u00e9 sobre as distribui\u00e7\u00f5es desses dois conjuntos de 31 resultados cada. Eles s\u00e3o iguais ou diferentes?<\/p>\n<p style=\"text-align: justify\">Ainda n\u00e3o podemos responder a isso, porque n\u00e3o podemos ver todos os 31 valores em cada grupo. Podemos ver apenas uma sele\u00e7\u00e3o aleat\u00f3ria de 16 dos resultados potenciais de controle e os resultados de tratamento dos <em>outros<\/em> 15 pacientes.<\/p>\n<p style=\"text-align: justify\">Aqui est\u00e1 uma boa maneira de visualizar o cen\u00e1rio. Cada paciente tem um ingresso de dois lados:<\/p>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-679\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-1.png\" alt=\"\" width=\"960\" height=\"540\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-1.png 960w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-1-300x169.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-1-768x432.png 768w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-1-569x320.png 569w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<p style=\"text-align: justify\">Ap\u00f3s a randomiza\u00e7\u00e3o, podemos ver a metade direita de um conjunto aleat\u00f3rio de ingressos e a metade esquerda do grupo restante.<\/p>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-680\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-2.png\" alt=\"\" width=\"960\" height=\"540\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-2.png 960w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-2-300x169.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-2-768x432.png 768w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-2-569x320.png 569w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<p style=\"text-align: justify\">A tabela <code>observed_outcomes<\/code> coleta as informa\u00e7\u00f5es sobre os resultados potenciais de cada paciente, deixando a metade n\u00e3o observada de cada &#8220;ingresso&#8221; em branco. (\u00c9 apenas outra maneira de pensar na tabela <code>bta<\/code>, contendo as mesmas informa\u00e7\u00f5es.)<\/p>\n<pre><code><span style=\"color: black\">observed_outcomes = Table.read_table(path_data + \"observed_outcomes.csv\")\r\nobserved_outcomes.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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Outcome if assigned treatment<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Outcome if assigned control<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Unknown<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"as-hip-teses\" style=\"text-align: justify\">As Hip\u00f3teses<\/h2>\n<p style=\"text-align: justify\">A quest\u00e3o \u00e9 se o tratamento faz alguma diferen\u00e7a. Em termos da tabela <code>observed_outcomes<\/code>, a quest\u00e3o \u00e9 se a distribui\u00e7\u00e3o dos 31 valores de &#8220;treatment&#8221; na Coluna 1 (incluindo os desconhecidos) \u00e9 diferente da distribui\u00e7\u00e3o dos 31 valores de &#8220;control&#8221; na Coluna 2 (tamb\u00e9m incluindo os desconhecidos).<\/p>\n<p style=\"text-align: justify\"><strong>Hip\u00f3tese Nula:<\/strong> A distribui\u00e7\u00e3o de todos os 31 resultados potenciais de &#8220;treatment&#8221; \u00e9 a mesma que a de todos os 31 resultados potenciais de &#8220;control&#8221;. A toxina botul\u00ednica A n\u00e3o faz nada diferente do soro fisiol\u00f3gico; a diferen\u00e7a nas duas amostras \u00e9 apenas devido ao acaso.<\/p>\n<p style=\"text-align: justify\"><strong>Hip\u00f3tese Alternativa:<\/strong> A distribui\u00e7\u00e3o dos 31 resultados potenciais de &#8220;treatment&#8221; \u00e9 diferente da dos 31 resultados de controle. O tratamento faz algo diferente do controle.<\/p>\n<p style=\"text-align: justify\">Observe que a alternativa n\u00e3o especifica que o tratamento ajuda \u2013 apenas que \u00e9 diferente do controle. Isso \u00e9 padr\u00e3o em estudos m\u00e9dicos porque n\u00e3o pr\u00e9-julga qual ser\u00e1 o resultado. Mas voc\u00ea pode realizar um teste para saber se o tratamento \u00e9 melhor que o controle. Basta ajustar sua estat\u00edstica de teste de acordo.<\/p>\n<p style=\"text-align: justify\">Existem 31 resultados observados conjuntamente nos dois grupos. Se a hip\u00f3tese nula fosse verdadeira, n\u00e3o importaria quais desses 31 resultados seriam rotulados como &#8220;treatment&#8221; e quais como &#8220;control&#8221;. Qualquer subconjunto aleat\u00f3rio de 16 dos 31 valores poderia ser chamado de &#8220;control&#8221; e os 15 restantes de &#8220;treatment&#8221;.<\/p>\n<p style=\"text-align: justify\">Podemos simular isso. Podemos permutar aleatoriamente os 31 valores, dividi-los em dois grupos de 16 e 15, e ver qu\u00e3o diferentes s\u00e3o as distribui\u00e7\u00f5es nos dois grupos. Como os dados s\u00e3o zeros e uns, podemos ver apenas qu\u00e3o diferentes s\u00e3o as duas propor\u00e7\u00f5es.<\/p>\n<p style=\"text-align: justify\">Foi exatamente isso que fizemos para o teste A\/B na se\u00e7\u00e3o anterior. A Amostra A \u00e9 agora o grupo de controle e a Amostra B o grupo de tratamento. Realizaremos o teste abaixo mostrando os detalhes de todas as etapas. Voc\u00ea deve confirmar que s\u00e3o as mesmas etapas realizadas para o teste A\/B.<\/p>\n<h2 id=\"a-estat-stica-do-teste\" style=\"text-align: justify\">A Estat\u00edstica do Teste<\/h2>\n<p style=\"text-align: justify\">Se as propor\u00e7\u00f5es dos dois grupos forem muito diferentes entre si, inclinaremos para a hip\u00f3tese alternativa de que as duas distribui\u00e7\u00f5es subjacentes s\u00e3o diferentes. Ent\u00e3o, nossa estat\u00edstica de teste ser\u00e1 a dist\u00e2ncia entre as propor\u00e7\u00f5es dos dois grupos, ou seja, o valor absoluto da diferen\u00e7a entre elas.<\/p>\n<p style=\"text-align: justify\">Valores grandes da estat\u00edstica do teste favorecer\u00e3o a hip\u00f3tese alternativa em detrimento da nula.<\/p>\n<p style=\"text-align: justify\">Como as propor\u00e7\u00f5es dos dois grupos foram 0.6 e 0.125, o valor observado da estat\u00edstica do teste \u00e9 | 0.6 &#8211; 0.125 | = 0.475.<\/p>\n<pre><code><span style=\"color: black\">bta.group('Group', 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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Result average<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.125<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">observed_proportions = bta.group('Group', np.average).column(1)\r\nobserved_distance = abs(observed_proportions.item(0) - observed_proportions.item(1))\r\nobserved_distance<\/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\">0.475<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Como fizemos antes, definiremos uma fun\u00e7\u00e3o que recebe os dois argumentos a seguir:<\/p>\n<ul style=\"text-align: justify\">\n<li>o nome da tabela de dados<\/li>\n<li>o r\u00f3tulo da coluna dos r\u00f3tulos do grupo<\/li>\n<\/ul>\n<p style=\"text-align: justify\">e retorna a dist\u00e2ncia entre as duas propor\u00e7\u00f5es do grupo<\/p>\n<pre><code><span style=\"color: black\">def distance(table, group_label):\r\n    reduced = table.select('Result', group_label)\r\n    proportions = reduced.group(group_label, np.average).column(1)\r\n    return abs(proportions.item(1) - proportions.item(0))<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">distance(bta, 'Group')<\/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\">0.475<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"prevendo-a-estat-stica-sob-a-hip-tese-nula\" style=\"text-align: justify\">Prevendo a Estat\u00edstica Sob a Hip\u00f3tese Nula<\/h2>\n<p style=\"text-align: justify\">Podemos simular resultados sob a hip\u00f3tese nula para ver como nossa estat\u00edstica de teste deve sair se a hip\u00f3tese nula for verdadeira.<\/p>\n<h3 id=\"gerando-um-valor-da-estat-stica\" style=\"text-align: justify\">Gerando Um Valor da Estat\u00edstica<\/h3>\n<p style=\"text-align: justify\">A simula\u00e7\u00e3o segue exatamente o mesmo processo que usamos na se\u00e7\u00e3o anterior. Come\u00e7amos permutando aleatoriamente todas as etiquetas dos grupos e, em seguida, atribu\u00edmos as etiquetas embaralhadas aos resultados 0\/1.<\/p>\n<pre><code><span style=\"color: black\">shuffled_labels = bta.sample(with_replacement=False).column(0)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">bta_with_shuffled_labels = bta.with_column('Shuffled Label', shuffled_labels)\r\nbta_with_shuffled_labels.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\">Group<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Result<\/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\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Control<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Treatment<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Agora podemos encontrar a dist\u00e2ncia entre as duas propor\u00e7\u00f5es depois que os r\u00f3tulos dos grupos foram embaralhados.<\/p>\n<pre><code><span style=\"color: black\">distance(bta_with_shuffled_labels, '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\">0.08750000000000002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Isso \u00e9 bem diferente da dist\u00e2ncia entre as duas propor\u00e7\u00f5es originais.<\/p>\n<pre><code><span style=\"color: black\">distance(bta_with_shuffled_labels, 'Group')<\/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\">0.475<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 id=\"teste-de-permuta-o\" style=\"text-align: justify\">Teste de Permuta\u00e7\u00e3o<\/h3>\n<p style=\"text-align: justify\">Se embaralh\u00e1ssemos as etiquetas novamente, qu\u00e3o diferente seria a nova dist\u00e2ncia? Para responder a isso, definiremos uma fun\u00e7\u00e3o que simula um valor simulado da dist\u00e2ncia sob a hip\u00f3tese de sorteios aleat\u00f3rios da mesma distribui\u00e7\u00e3o subjacente. E ent\u00e3o coletaremos 20.000 desses valores simulados em um array.<\/p>\n<p style=\"text-align: justify\">Voc\u00ea pode ver que estamos fazendo exatamente o que fizemos em nossos exemplos anteriores do teste de permuta\u00e7\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def one_simulated_distance():\r\n    shuffled_labels = bta.sample(with_replacement = False\r\n                                                    ).column('Group')\r\n    shuffled_table = bta.select('Result').with_column(\r\n        'Shuffled Label', shuffled_labels)\r\n    return distance(shuffled_table, 'Shuffled Label') <\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">distances = make_array()\r\n\r\nrepetitions = 20000\r\nfor i in np.arange(repetitions):\r\n    new_distance = one_simulated_distance()\r\n    distances = np.append(distances, new_distance)<\/span><\/code><\/pre>\n<h2 id=\"conclus-o-do-teste\" style=\"text-align: justify\">Conclus\u00e3o do Teste<\/h2>\n<p style=\"text-align: justify\">O array <code>distances<\/code> cont\u00e9m 20.000 valores de nossa estat\u00edstica de teste simulada sob a hip\u00f3tese nula. Aqui est\u00e1 seu histograma emp\u00edrico junto com o valor observado da estat\u00edstica. Para encontrar o P-valor do teste, lembre-se de que valores grandes da dist\u00e2ncia favorecer a hip\u00f3tese alternativa.<\/p>\n<pre><code><span style=\"color: black\">Table().with_column('Distance', distances).hist(\r\n    bins = np.arange(0, 0.7, 0.1), left_end = observed_distance)\r\n# Par\u00e2metros de plotagem; voc\u00ea pode ignorar o c\u00f3digo abaixo\r\nplots.ylim(-0.1, 5.5)\r\nplots.scatter(observed_distance, 0, color='red', s=40, zorder=3)\r\nplots.title('Prediction Under the Null Hypothesis')\r\nprint('Observed Distance', observed_distance)<\/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\">Observed Distance 0.475<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-682\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-3.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-3.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/12-2-3-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p style=\"text-align: justify\">Para encontrar numericamente o p-valor emp\u00edrico, devemos encontrar a propor\u00e7\u00e3o de estat\u00edsticas simuladas que foram iguais ou maiores que a estat\u00edstica observada.<\/p>\n<pre><code><span style=\"color: black\">empirical_p = np.count_nonzero(distances &gt;= observed_distance) \/ 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\">0.00875<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Este \u00e9 um pequeno p-valor. A estat\u00edstica observada est\u00e1 na cauda do histograma emp\u00edrico da estat\u00edstica de teste gerada sob a hip\u00f3tese nula.<\/p>\n<p style=\"text-align: justify\">O resultado \u00e9 estatisticamente significativo. O teste favorece a hip\u00f3tese alternativa em rela\u00e7\u00e3o \u00e0 nula. As evid\u00eancias apoiam a hip\u00f3tese de que o tratamento est\u00e1 fazendo alguma diferen\u00e7a.<\/p>\n<p style=\"text-align: justify\">O estudo relata um P-valor de 0,009, ou 0,9%, que n\u00e3o est\u00e1 muito longe do nosso valor emp\u00edrico.<\/p>\n<h2 id=\"causalidade2\" style=\"text-align: justify\">Causalidade<\/h2>\n<p style=\"text-align: justify\">Como os ensaios foram randomizados, o teste \u00e9 evid\u00eancia de que o tratamento <em>causa<\/em> a diferen\u00e7a. A atribui\u00e7\u00e3o aleat\u00f3ria de pacientes aos dois grupos garante que n\u00e3o h\u00e1 uma vari\u00e1vel de confus\u00e3o que possa afetar a conclus\u00e3o de causalidade.<\/p>\n<p style=\"text-align: justify\">Se o tratamento n\u00e3o tivesse sido atribu\u00eddo aleatoriamente, nosso teste ainda apontaria para uma <em>associa\u00e7\u00e3o<\/em> entre o tratamento e os resultados da dor nas costas entre nossos 31 pacientes. Mas cuidado: sem randomiza\u00e7\u00e3o, essa associa\u00e7\u00e3o n\u00e3o implicaria que o tratamento causou uma mudan\u00e7a nos resultados da dor nas costas. Por exemplo, se os pr\u00f3prios pacientes tivessem escolhido se iriam administrar o tratamento, talvez os pacientes que experimentassem mais dor seriam mais propensos a escolher o tratamento <em>e<\/em> mais propensos a experimentar alguma redu\u00e7\u00e3o da dor mesmo sem medica\u00e7\u00e3o. A dor pr\u00e9-existente seria ent\u00e3o um <em>fator de confus\u00e3o<\/em> na an\u00e1lise.<\/p>\n<h2 id=\"uma-meta-an-lise\" style=\"text-align: justify\">Uma Meta-An\u00e1lise<\/h2>\n<p style=\"text-align: justify\">Embora o ECR forne\u00e7a evid\u00eancias de que o tratamento com toxina botul\u00ednica A ajudou os pacientes, um estudo com 31 pacientes n\u00e3o \u00e9 suficiente para estabelecer a efic\u00e1cia de um tratamento m\u00e9dico. Isso n\u00e3o \u00e9 apenas por causa do pequeno tamanho da amostra. Nossos resultados nesta se\u00e7\u00e3o s\u00e3o v\u00e1lidos para os 31 pacientes do estudo, mas estamos realmente interessados na popula\u00e7\u00e3o de <em>todos os pacientes poss\u00edveis<\/em>.<\/p>\n<p style=\"text-align: justify\">Em 2011, um grupo de pesquisadores realizou uma <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/21249702\">meta-an\u00e1lise<\/a> dos estudos sobre o tratamento. Ou seja, eles identificaram todos os estudos dispon\u00edveis sobre tais tratamentos para dor lombar e resumiram os resultados compilados.<\/p>\n<p style=\"text-align: justify\">Havia v\u00e1rios estudos, mas poucos puderam ser inclu\u00eddos de maneira cientificamente s\u00f3lida: &#8220;Exclu\u00edmos evid\u00eancias de dezenove estudos devido \u00e0 n\u00e3o randomiza\u00e7\u00e3o, dados incompletos ou n\u00e3o publicados.&#8221; Apenas tr\u00eas ensaios controlados randomizados permaneceram, um dos quais \u00e9 o que estudamos nesta se\u00e7\u00e3o. A meta-an\u00e1lise deu a ele a maior avalia\u00e7\u00e3o entre todos os estudos (LBP significa dor lombar): &#8220;Identificamos tr\u00eas estudos que investigaram os m\u00e9ritos do BoNT para LBP, mas apenas um tinha baixo risco de vi\u00e9s e avaliou pacientes com LBP n\u00e3o espec\u00edfica (N = 31).&#8221;<\/p>\n<p style=\"text-align: justify\">Resumindo, a meta-an\u00e1lise concluiu: &#8220;H\u00e1 evid\u00eancias de baixa qualidade de que as inje\u00e7\u00f5es de BoNT melhoraram a dor, a fun\u00e7\u00e3o ou ambos melhor do que as inje\u00e7\u00f5es de solu\u00e7\u00e3o salina e evid\u00eancias de qualidade muito baixa de que foram melhores do que as inje\u00e7\u00f5es de acupuntura ou esteroides. &#8230; Mais pesquisas provavelmente ter\u00e3o um impacto importante na estimativa do efeito e em nossa confian\u00e7a nele. Ensaios futuros devem padronizar popula\u00e7\u00f5es de pacientes, protocolos de tratamento e grupos de compara\u00e7\u00e3o, alistar mais participantes e incluir resultados de longo prazo, an\u00e1lise de custo-benef\u00edcio e relev\u00e2ncia cl\u00ednica dos achados.&#8221;<\/p>\n<p style=\"text-align: justify\">\u00c9 necess\u00e1rio muito trabalho cuidadoso para estabelecer que um tratamento m\u00e9dico tem um efeito ben\u00e9fico. Saber como analisar ensaios controlados randomizados \u00e9 uma parte crucial desse trabalho. Agora que voc\u00ea sabe como fazer isso, est\u00e1 bem posicionado para ajudar as profiss\u00f5es m\u00e9dicas e outras a estabelecer rela\u00e7\u00f5es de causa e efeito.<\/p>\n<p>&nbsp;<\/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\/12-1\/\">\u2190 Cap\u00edtulo 12.1 &#8211; Teste A\/B<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-3\/\">Cap\u00edtulo 12.3 &#8211; Esvaziar \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-677","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/677","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=677"}],"version-history":[{"count":9,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/677\/revisions"}],"predecessor-version":[{"id":1039,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/677\/revisions\/1039"}],"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=677"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}