{"id":781,"date":"2025-07-29T16:41:13","date_gmt":"2025-07-29T20:41:13","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=781"},"modified":"2025-10-11T16:10:22","modified_gmt":"2025-10-11T20:10:22","slug":"14-6","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/14-0\/14-6\/","title":{"rendered":"Cap\u00edtulo 14.6"},"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\nimport numpy as np\r\npath_data = '..\/..\/..\/..\/data\/'\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=\"escolhendo-um-tamanho-de-amostra\" style=\"text-align: center\">Escolhendo um Tamanho de Amostra<\/h1>\n<p style=\"text-align: justify\">A candidata A est\u00e1 disputando uma elei\u00e7\u00e3o. Uma organiza\u00e7\u00e3o de pesquisa deseja estimar a propor\u00e7\u00e3o de eleitores que votar\u00e3o nela. Vamos supor que eles planejam tirar uma amostra aleat\u00f3ria simples de eleitores, embora na realidade seu m\u00e9todo de amostragem seja mais complexo. Como eles podem decidir qual deve ser o tamanho da amostra para obter um n\u00edvel desejado de precis\u00e3o?<\/p>\n<p style=\"text-align: justify\">Agora estamos em posi\u00e7\u00e3o de responder a essa pergunta, depois de fazer algumas suposi\u00e7\u00f5es:<\/p>\n<ul style=\"text-align: justify\">\n<li>A popula\u00e7\u00e3o de eleitores \u00e9 muito grande e, portanto, podemos supor que a amostra aleat\u00f3ria ser\u00e1 retirada com reposi\u00e7\u00e3o.<\/li>\n<li>A organiza\u00e7\u00e3o de pesquisa far\u00e1 sua estimativa construindo um intervalo de confian\u00e7a aproximado de 95% para a percentagem de eleitores que votar\u00e3o na candidata A.<\/li>\n<li>O n\u00edvel desejado de precis\u00e3o \u00e9 que a largura do intervalo n\u00e3o deve ser superior a 1%. Isso \u00e9 bastante preciso! Por exemplo, o intervalo de confian\u00e7a (33,2%, 34%) seria aceit\u00e1vel, mas (33,2%, 35%) n\u00e3o seria.<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Vamos trabalhar com a propor\u00e7\u00e3o amostral de eleitores para a candidata A. Lembre-se de que uma propor\u00e7\u00e3o \u00e9 uma m\u00e9dia, quando os valores na popula\u00e7\u00e3o s\u00e3o apenas 0 (o tipo de indiv\u00edduo que voc\u00ea n\u00e3o est\u00e1 contando) ou 1 (o tipo de indiv\u00edduo que voc\u00ea est\u00e1 contando).<\/p>\n<h2 id=\"largura-do-intervalo-de-confian-a\" style=\"text-align: justify\">Largura do Intervalo de Confian\u00e7a<\/h2>\n<p style=\"text-align: justify\">Se tiv\u00e9ssemos uma amostra aleat\u00f3ria, poder\u00edamos usar a t\u00e9cnica de bootstrap para construir um intervalo de confian\u00e7a para a percentagem de eleitores para a candidata A. Mas ainda n\u00e3o temos uma amostra &#8211; estamos tentando descobrir o qu\u00e3o grande a amostra deve ser para que nosso intervalo de confian\u00e7a seja t\u00e3o estreito quanto queremos.<\/p>\n<p style=\"text-align: justify\">Em situa\u00e7\u00f5es como esta, \u00e9 \u00fatil ver o que a teoria prev\u00ea.<\/p>\n<p style=\"text-align: justify\">O Teorema do Limite Central diz que as probabilidades para a propor\u00e7\u00e3o da amostra s\u00e3o aproximadamente normalmente distribu\u00eddas, centradas na propor\u00e7\u00e3o populacional de 1&#8217;s, com um desvio padr\u00e3o igual ao desvio padr\u00e3o da popula\u00e7\u00e3o de 0&#8217;s e 1&#8217;s dividido pela raiz quadrada do tamanho da amostra.<\/p>\n<p style=\"text-align: justify\">Portanto, o intervalo de confian\u00e7a ainda ser\u00e1 o &#8220;meio 95%&#8221; de uma distribui\u00e7\u00e3o normal, mesmo que n\u00e3o possamos pegar as extremidades como o 2,5\u00ba e o 97,5\u00ba percentis das propor\u00e7\u00f5es bootstrapadas.<\/p>\n<p style=\"text-align: justify\">Existe outra maneira de encontrar a largura do intervalo? Sim, porque sabemos que, para vari\u00e1veis normalmente distribu\u00eddas, o intervalo &#8220;centro \u00b1 2 desvios padr\u00e3o&#8221; cont\u00e9m 95% dos dados.<\/p>\n<p style=\"text-align: justify\">O intervalo de confian\u00e7a se estender\u00e1 por 2 desvios padr\u00e3o da propor\u00e7\u00e3o da amostra, de cada lado do centro. Portanto, a largura do intervalo ser\u00e1 de 4 desvios padr\u00e3o da propor\u00e7\u00e3o da amostra.<\/p>\n<p style=\"text-align: justify\">Estamos dispostos a tolerar uma largura de 1% = 0,01. Portanto, usando a f\u00f3rmula desenvolvida na \u00faltima se\u00e7\u00e3o,<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">4 \u00d7 <sup>SD da popula\u00e7\u00e3o de 0-1<\/sup>\u2044<sub>\u221atamanho da amostra<\/sub> \u2264 0,01<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Assim,<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">\u221atamanho da amostra \u2265 4 \u00d7 <sup>SD da popula\u00e7\u00e3o de 0-1<\/sup>\u2044<sub>0,01<\/sub><\/div>\n<p>&nbsp;<\/p>\n<h2 id=\"o-desvio-padr-o-de-uma-cole-o-de-0-s-e-1-s\" style=\"text-align: justify\">O Desvio Padr\u00e3o de uma cole\u00e7\u00e3o de 0&#8217;s e 1&#8217;s<\/h2>\n<p style=\"text-align: justify\">Se soub\u00e9ssemos o desvio padr\u00e3o da popula\u00e7\u00e3o, estar\u00edamos prontos. Poder\u00edamos calcular a raiz quadrada do tamanho da amostra e depois elevar ao quadrado para obter o tamanho da amostra. Mas n\u00e3o sabemos o desvio padr\u00e3o da popula\u00e7\u00e3o. A popula\u00e7\u00e3o consiste em 1 para cada eleitor para a candidata A e 0 para todos os outros eleitores, e <em>n\u00e3o sabemos qual propor\u00e7\u00e3o de cada tipo existe.<\/em> \u00c9 isso que estamos tentando estimar.<\/p>\n<p style=\"text-align: justify\">Ent\u00e3o, estamos presos? N\u00e3o, porque podemos <em>limitar<\/em> o desvio padr\u00e3o da popula\u00e7\u00e3o. Aqui est\u00e3o histogramas de duas dessas distribui\u00e7\u00f5es, uma para uma propor\u00e7\u00e3o igual de 1&#8217;s e 0&#8217;s, e outra com 90% de 1&#8217;s e 10% de 0&#8217;s. Qual delas tem o maior desvio padr\u00e3o?<\/p>\n<pre><code><span style=\"color: black\">pop_50 = make_array(1, 1, 1, 1, 1, 0, 0, 0, 0, 0)\r\npop_90 = make_array(1, 1, 1, 1, 1, 1, 1, 1, 1, 0)\r\n\r\ncoins = Table().with_columns(\r\n   \"Proportion of 1's: 0.5\", pop_50,\r\n   \"Proportion of 1's: 0.9\", pop_90,\r\n)\r\ncoins.hist(bins=np.arange(-0.5, 1.6, 1))\r\nplots.scatter(0.5, -0.02, marker='^', color='darkblue', s=60)\r\nplots.scatter(0.9, -0.02, marker='^', color='gold', s=60)\r\nplots.ylim(-0.05, 1);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-783\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-1.png\" alt=\"\" width=\"665\" height=\"270\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-1.png 665w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-1-300x122.png 300w\" sizes=\"(max-width: 665px) 100vw, 665px\" \/><\/p>\n<p style=\"text-align: justify\">Lembre-se de que os poss\u00edveis valores na popula\u00e7\u00e3o s\u00e3o apenas 0 e 1.<\/p>\n<p style=\"text-align: justify\">O histograma azul (50% 1&#8217;s e 50% 0&#8217;s) tem mais dispers\u00e3o do que o dourado. A m\u00e9dia \u00e9 0.5. Metade das desvios da m\u00e9dia \u00e9 igual a 0.5 e a outra metade \u00e9 igual a -0.5, ent\u00e3o o desvio padr\u00e3o \u00e9 0.5.<\/p>\n<p style=\"text-align: justify\">No histograma dourado, toda a \u00e1rea est\u00e1 concentrada em torno de 1, resultando em menos dispers\u00e3o. 90% dos desvios s\u00e3o pequenos: 0.1. Os outros 10% s\u00e3o -0.9, que \u00e9 grande, mas no geral a dispers\u00e3o \u00e9 menor do que no histograma azul.<\/p>\n<p style=\"text-align: justify\">A mesma observa\u00e7\u00e3o seria v\u00e1lida se vari\u00e1ssemos a propor\u00e7\u00e3o de 1&#8217;s ou deix\u00e1ssemos a propor\u00e7\u00e3o de 0&#8217;s maior do que a propor\u00e7\u00e3o de 1&#8217;s. Vamos verificar isso calculando os desvios padr\u00e3o de popula\u00e7\u00f5es de 10 elementos que consistem apenas em 0&#8217;s e 1&#8217;s, em propor\u00e7\u00f5es variadas. A fun\u00e7\u00e3o <code>np.ones<\/code> \u00e9 \u00fatil para isso. Ela recebe um n\u00famero inteiro positivo como argumento e retorna um array consistindo desse n\u00famero de 1&#8217;s.<\/p>\n<pre><code><span style=\"color: black\">sd = make_array()\r\nfor i in np.arange(1, 10, 1):\r\n    # Cria um array de i 1's e (10-i) 0's\r\n    population = np.append(np.ones(i), 1-np.ones(10-i))\r\n    sd = np.append(sd, np.std(population))\r\n\r\nzero_one_sds = Table().with_columns(\r\n    \"Population Proportion of 1's\", np.arange(0.1, 1, 0.1),\r\n    \"Population SD\", sd\r\n)\r\n\r\nzero_one_sds<\/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\">Population Proportion of 1&#8217;s<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Population SD<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.3<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.4<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.458258<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.489898<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.5<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.489898<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.458258<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.4<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.9<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">N\u00e3o \u00e9 de surpreender que o SD de uma popula\u00e7\u00e3o com 10% de 1 e 90% de 0 seja o mesmo que o de uma popula\u00e7\u00e3o com 90% de 1 e 10% de 0. Isso ocorre porque voc\u00ea troca as barras de um histograma para obter o outro; h\u00e1 nenhuma mudan\u00e7a na dispers\u00e3o.<\/p>\n<p style=\"text-align: justify\">Mais importante para nossos prop\u00f3sitos, o SD aumenta \u00e0 medida que a propor\u00e7\u00e3o de 1 aumenta, at\u00e9 que a propor\u00e7\u00e3o de 1 seja 0,5; ent\u00e3o come\u00e7a a diminuir simetricamente.<\/p>\n<pre><code><span style=\"color: black\">zero_one_sds.scatter(\"Population Proportion of 1's\")<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-784\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-2.png\" alt=\"\" width=\"381\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-2.png 381w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-2-300x269.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-6-2-356x320.png 356w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p style=\"text-align: justify\"><strong>Resumo:<\/strong> O SD de uma popula\u00e7\u00e3o de 1 e 0 \u00e9 no m\u00e1ximo 0,5. Esse \u00e9 o valor do SD quando 50% da popula\u00e7\u00e3o \u00e9 codificada como 1 e os outros 50% s\u00e3o codificados como 0.<\/p>\n<h2 id=\"o-tamanho-da-amostra\" style=\"text-align: justify\">O Tamanho da Amostra<\/h2>\n<p style=\"text-align: justify\">Sabemos que<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">\u221atamanho da amostra \u2265 4 \u00d7 <sup>SD da popula\u00e7\u00e3o 0-1<\/sup>\u2044<sub>0.01<\/sub><\/div>\n<p>&nbsp;<\/p>\n<p>e que o SD da popula\u00e7\u00e3o 0-1 \u00e9 no m\u00e1ximo 0.5, independentemente da propor\u00e7\u00e3o de 1&#8217;s na popula\u00e7\u00e3o. Portanto, \u00e9 seguro tomar<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\">\u221atamanho da amostra \u2265 4 \u00d7 <sup>0.5<\/sup>\u2044<sub>0.01<\/sub> = 200<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Portanto, o tamanho da amostra deve ser pelo menos 200^2 = 40,000. \u00c9 uma amostra enorme! Mas \u00e9 isso que voc\u00ea precisa se deseja garantir uma grande precis\u00e3o com alta confian\u00e7a, n\u00e3o importa como seja a popula\u00e7\u00e3o.<\/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\/14-0\/14-4\/\">\u2190 Cap\u00edtulo 14.5 &#8211; Variabilidade da M\u00e9dia da Amostra<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/\">Cap\u00edtulo 15 &#8211; Previs\u00e3o \u2192<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><!--###########################################################################################################################################################--><\/p>\n<\/div>\n<\/div>\n<div style=\"clear: both;height: 1px;margin-top: -1px\"><\/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":722,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-781","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/781","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=781"}],"version-history":[{"count":4,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/781\/revisions"}],"predecessor-version":[{"id":1070,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/781\/revisions\/1070"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/722"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=781"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}