{"id":420,"date":"2023-07-30T01:30:00","date_gmt":"2023-07-30T01:30:00","guid":{"rendered":"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa\/"},"modified":"2023-07-30T01:30:00","modified_gmt":"2023-07-30T01:30:00","slug":"mann-whitney-voce-testa","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa\/","title":{"rendered":"Teste u de mann-whitney"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Um <strong>teste U de Mann-Whitney<\/strong> (\u00e0s vezes chamado de teste de soma de postos de Wilcoxon) \u00e9 usado para comparar diferen\u00e7as entre duas amostras independentes quando as distribui\u00e7\u00f5es amostrais n\u00e3o s\u00e3o normalmente distribu\u00eddas e os tamanhos das amostras s\u00e3o pequenos (n &lt;30).<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c9 considerado o equivalente n\u00e3o param\u00e9trico do <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener\">teste t independente para duas amostras<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aqui est\u00e3o alguns exemplos de quando voc\u00ea pode usar um teste U de Mann-Whitney:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Voc\u00ea deseja comparar os sal\u00e1rios de cinco graduados da universidade A com os sal\u00e1rios de cinco graduados da universidade B. Os sal\u00e1rios n\u00e3o s\u00e3o distribu\u00eddos normalmente.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Voc\u00ea quer saber se a perda de peso varia para dois grupos: 12 pessoas que usam a dieta A e 10 pessoas que usam a dieta B. A perda de peso n\u00e3o \u00e9 normalmente distribu\u00edda.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Voc\u00ea quer saber se as notas de 8 alunos da turma A diferem daquelas de 7 alunos da turma B. As notas n\u00e3o s\u00e3o distribu\u00eddas normalmente.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Em cada exemplo, voc\u00ea deseja comparar dois grupos, as distribui\u00e7\u00f5es amostrais n\u00e3o s\u00e3o normais e os tamanhos amostrais s\u00e3o pequenos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Assim, um teste U de Mann-Whitney \u00e9 apropriado desde que as seguintes suposi\u00e7\u00f5es sejam atendidas.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Suposi\u00e7\u00f5es do teste Mann-Whitney U<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Antes de realizar um teste U de Mann-Whitney, voc\u00ea deve garantir que as quatro suposi\u00e7\u00f5es a seguir sejam atendidas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ordin\u00e1ria ou cont\u00ednua:<\/strong> A vari\u00e1vel que voc\u00ea est\u00e1 analisando \u00e9 ordinal ou cont\u00ednua. Exemplos de vari\u00e1veis ordinais incluem itens Likert (por exemplo, uma escala de 5 pontos que varia de \u201cdiscordo totalmente\u201d a \u201cconcordo totalmente\u201d). Exemplos de vari\u00e1veis cont\u00ednuas incluem altura (medida em polegadas), peso (medido em libras) ou pontua\u00e7\u00f5es em testes (medidos de 0 a 100).<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Independ\u00eancia:<\/strong> Todas as observa\u00e7\u00f5es de ambos os grupos s\u00e3o independentes umas das outras.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Forma:<\/strong> As formas das distribui\u00e7\u00f5es para os dois grupos s\u00e3o aproximadamente as mesmas.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Se essas suposi\u00e7\u00f5es forem atendidas, voc\u00ea poder\u00e1 realizar um teste U de Mann-Whitney.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Como realizar um teste U de Mann-Whitney<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Para realizar um teste U de Mann-Whitney, seguimos o <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener\">procedimento padr\u00e3o de teste de hip\u00f3tese de cinco etapas<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Indique as suposi\u00e7\u00f5es.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Na maioria dos casos, o teste U de Mann-Whitney \u00e9 realizado como um teste bicaudal. As hip\u00f3teses nula e alternativa s\u00e3o escritas na forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> As duas popula\u00e7\u00f5es s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> As duas popula\u00e7\u00f5es n\u00e3o s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Determine um n\u00edvel de signific\u00e2ncia a ser usado para a hip\u00f3tese.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Decida um n\u00edvel de signific\u00e2ncia. As escolhas comuns s\u00e3o 0,01, 0,05 e 0,1.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Encontre a estat\u00edstica de teste.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A estat\u00edstica de teste \u00e9 denotada por U e \u00e9 a menor entre U <sub>1<\/sub> e U <sub>2<\/sub> , conforme definido abaixo:<\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde n <sub>1<\/sub> e n <sub>2<\/sub> s\u00e3o os tamanhos das amostras para as amostras 1 e 2, respectivamente, e R <sub>1<\/sub> e R <sub>2<\/sub> s\u00e3o a soma das classifica\u00e7\u00f5es para as amostras 1 e 2, respectivamente.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">Os exemplos abaixo mostrar\u00e3o como encontrar essa estat\u00edstica de teste em detalhes.<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. Rejeite ou n\u00e3o rejeite a hip\u00f3tese nula.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Usando as estat\u00edsticas de teste, determine se voc\u00ea pode ou n\u00e3o rejeitar a hip\u00f3tese nula com base no n\u00edvel de signific\u00e2ncia e no valor cr\u00edtico encontrados na tabela U de Mann-Whitney.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. Interprete os resultados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Interprete os resultados do teste no contexto da pergunta feita.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Exemplos de realiza\u00e7\u00e3o de um teste U de Mann-Whitney<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Os exemplos a seguir mostram como realizar um teste U de Mann-Whitney.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 1<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Queremos saber se um novo medicamento \u00e9 eficaz ou n\u00e3o na preven\u00e7\u00e3o de ataques de p\u00e2nico. Um total de 12 pacientes s\u00e3o divididos aleatoriamente em dois grupos de 6 e designados para receber o novo medicamento ou o placebo. Os pacientes ent\u00e3o registram o n\u00famero de ataques de p\u00e2nico que sofreram ao longo de um m\u00eas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os resultados s\u00e3o mostrados abaixo:<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">NOVA DROGA<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">PLACEBO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><em><strong>Realize um teste U de Mann-Whitney para ver se h\u00e1 uma diferen\u00e7a no n\u00famero de ataques de p\u00e2nico entre os pacientes do grupo placebo em compara\u00e7\u00e3o com o grupo do novo medicamento. Use um n\u00edvel de signific\u00e2ncia de 0,05.<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Indique as suposi\u00e7\u00f5es.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> As duas popula\u00e7\u00f5es s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> As duas popula\u00e7\u00f5es n\u00e3o s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Determine um n\u00edvel de signific\u00e2ncia a ser usado para a hip\u00f3tese.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">O problema nos diz que devemos usar um n\u00edvel de signific\u00e2ncia de 0,05.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Encontre a estat\u00edstica de teste.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Lembre-se de que a estat\u00edstica de teste \u00e9 denotada como U e \u00e9 a menor entre U <sub>1<\/sub> e U <sub>2<\/sub> , conforme definido abaixo:<\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde n <sub>1<\/sub> e n <sub>2<\/sub> s\u00e3o os tamanhos das amostras para as amostras 1 e 2, respectivamente, e R <sub>1<\/sub> e R <sub>2<\/sub> s\u00e3o a soma das classifica\u00e7\u00f5es para as amostras 1 e 2, respectivamente.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Para encontrar<\/span> <span style=\"color: #000000;\">R <sub>1<\/sub> e R <sub>2<\/sub> , precisamos combinar as observa\u00e7\u00f5es de ambos os grupos e orden\u00e1-las do menor para o maior:<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #008080;\">NOVA DROGA<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #ff0000;\">PLACEBO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>3<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>4<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>5<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>8<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>1<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>6<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>4<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>3<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>1<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>5<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>9<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong>Amostra total: <span style=\"color: #008080;\">1<\/span> , <span style=\"color: #ff0000;\">1<\/span> , <span style=\"color: #ff0000;\">2<\/span> , <span style=\"color: #008080;\">3<\/span> , <span style=\"color: #008080;\">3<\/span> , <span style=\"color: #ff0000;\">4<\/span> , <span style=\"color: #008080;\">4<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #ff0000;\">6<\/span> , <span style=\"color: #ff0000;\">8<\/span> , <span style=\"color: #ff0000;\">9<\/span><\/strong><\/span><\/p>\n<div>\n<p> <span style=\"color: #000000;\"><strong>Classifica\u00e7\u00f5es: <span style=\"color: #008080;\">1,5<\/span> , <span style=\"color: #ff0000;\">1,5<\/span> , <span style=\"color: #ff0000;\">3<\/span> , <span style=\"color: #008080;\">4,5<\/span> , <span style=\"color: #008080;\">4,5<\/span> , <span style=\"color: #ff0000;\">6,5<\/span> , <span style=\"color: #008080;\">6,5<\/span> , <span style=\"color: #008080;\">8,5<\/span> , <span style=\"color: #008080;\">8,5<\/span> , <span style=\"color: #ff0000;\">10<\/span> , <span style=\"color: #ff0000;\">11<\/span> , <span style=\"color: #ff0000;\">12<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= soma das classifica\u00e7\u00f5es da amostra 1 = 1,5+4,5+4,5+6,5+8,5+8,5 = 34<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= soma das classifica\u00e7\u00f5es da amostra 2 = 1,5+3+6,5+10+11+12 = 44<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em seguida, usamos nossos tamanhos de amostra n <sub>1<\/sub> e n <sub>2<\/sub> , bem como nossa soma de classifica\u00e7\u00e3o R <sub>1<\/sub> e R <sub>2<\/sub> para encontrar U <sub>1<\/sub> e U <sub>2<\/sub> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 6(6) + 6(6+1)\/2 \u2013 34 = 23<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 6(6) + 6(6+1)\/2 \u2013 44 = 13<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nossas estat\u00edsticas de teste s\u00e3o as menores entre <sub>U1<\/sub> e <sub>U2<\/sub> , que s\u00e3o U=13.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">Nota: Tamb\u00e9m poder\u00edamos usar a <a href=\"https:\/\/statorials.org\/pt\/calculadora-de-teste-de-mann-whitney\/\" target=\"_blank\" rel=\"noopener\">calculadora do teste U de Mann-Whitney<\/a> para determinar que U = 13.<\/span><\/em><\/p>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong>4. Rejeite ou n\u00e3o rejeite a hip\u00f3tese nula.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Usando n <sub>1<\/sub> = 6 e n <sub>2<\/sub> = 6 com um n\u00edvel de signific\u00e2ncia de 0,05, a tabela U de Mann-Whitney nos diz que o valor cr\u00edtico \u00e9 5:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1381 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex1.png\" alt=\"Tabela de valores cr\u00edticos do teste Mann Whitney U\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Como nossa estat\u00edstica de teste (13) \u00e9 maior que nosso valor cr\u00edtico (5), n\u00e3o conseguimos rejeitar a hip\u00f3tese nula.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. Interprete os resultados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Como n\u00e3o conseguimos rejeitar a hip\u00f3tese nula, n\u00e3o temos evid\u00eancias suficientes para dizer que o n\u00famero de ataques de p\u00e2nico sofridos pelos pacientes do grupo placebo seja diferente daquele do grupo do novo medicamento.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 2<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Queremos saber se estudar 30 minutos por dia durante uma semana ajuda os alunos a terem um melhor desempenho em uma prova. Um total de 15 pacientes s\u00e3o designados aleatoriamente para estudar ou nenhum grupo de estudo. Depois de uma semana, todos os alunos fazem o mesmo teste.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os resultados dos testes para ambos os grupos s\u00e3o mostrados abaixo:<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">ESTUDAR<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">NENHUM ESTUDO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">89<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">88<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">92<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">93<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">94<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">95<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">75<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">91<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">72<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">99<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">80<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">84<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">81<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">90<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><em><strong>Realize um teste U de Mann-Whitney para ver se h\u00e1 uma diferen\u00e7a nas pontua\u00e7\u00f5es dos testes para o grupo de estudo em compara\u00e7\u00e3o com o grupo sem estudo. Use um n\u00edvel de signific\u00e2ncia de 0,01.<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Indique as suposi\u00e7\u00f5es.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> As duas popula\u00e7\u00f5es s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> As duas popula\u00e7\u00f5es n\u00e3o s\u00e3o iguais<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Determine um n\u00edvel de signific\u00e2ncia a ser usado para a hip\u00f3tese.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">O problema nos diz que devemos usar um n\u00edvel de signific\u00e2ncia de 0,01.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Encontre a estat\u00edstica de teste.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Lembre-se de que a estat\u00edstica de teste \u00e9 denotada como U e \u00e9 a menor entre U <sub>1<\/sub> e U <sub>2<\/sub> , conforme definido abaixo:<\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">voc\u00ea <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde n <sub>1<\/sub> e n <sub>2<\/sub> s\u00e3o os tamanhos das amostras para as amostras 1 e 2, respectivamente, e R <sub>1<\/sub> e R <sub>2<\/sub> s\u00e3o a soma das classifica\u00e7\u00f5es para as amostras 1 e 2, respectivamente.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Para encontrar<\/span> <span style=\"color: #000000;\">R <sub>1<\/sub> e R <sub>2<\/sub> , precisamos combinar as observa\u00e7\u00f5es de ambos os grupos e orden\u00e1-las do menor para o maior:<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">ESTUDAR<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #ff0000;\">NENHUM ESTUDO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>89<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">88<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">92<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">93<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">94<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">95<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">96<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">75<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">91<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">72<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">99<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">80<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">84<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">81<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">90<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Amostra total: <span style=\"color: #ff0000;\">72<\/span> , <span style=\"color: #ff0000;\">75<\/span> <span style=\"color: #008080;\">,<\/span> <span style=\"color: #ff0000;\">80<\/span> , 81, 84, <span style=\"color: #ff0000;\">88<\/span> , <span style=\"color: #008080;\">89<\/span> , <span style=\"color: #ff0000;\">90<\/span> , <span style=\"color: #008080;\">91<\/span> , <span style=\"color: #008080;\">92<\/span> , <span style=\"color: #008080;\">93<\/span> , <span style=\"color: #008080;\">94<\/span> , <span style=\"color: #ff0000;\">95<\/span> , <span style=\"color: #008080;\">96<\/span> <span style=\"color: #008080;\">,<\/span> <span style=\"color: #ff0000;\">99<\/span><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Linhas: <span style=\"color: #ff0000;\">1<\/span> , <span style=\"color: #ff0000;\">2<\/span> , <span style=\"color: #ff0000;\">3<\/span> , <span style=\"color: #ff0000;\">4<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #ff0000;\">6<\/span> , <span style=\"color: #008080;\">7<\/span> , <span style=\"color: #008080;\">8<\/span> , <span style=\"color: #008080;\">9<\/span> , <span style=\"color: #008080;\">10<\/span> , <span style=\"color: #ff0000;\">11<\/span> , <span style=\"color: #008080;\">12<\/span> , <span style=\"color: #ff0000;\">13<\/span> , <span style=\"color: #008080;\">14<\/span> , <span style=\"color: #008080;\">15<\/span><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= soma das classifica\u00e7\u00f5es da amostra 1 = 5+7+8+9+10+12+14+15 = 80<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= soma das classifica\u00e7\u00f5es da amostra 2 = 1+2+3+4+6+11+13 = 40<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em seguida, usamos nossos tamanhos de amostra n <sub>1<\/sub> e n <sub>2<\/sub> , bem como nossa soma de classifica\u00e7\u00e3o R <sub>1<\/sub> e R <sub>2<\/sub> para encontrar U <sub>1<\/sub> e U <sub>2<\/sub> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 8(7) + 8(8+1)\/2 \u2013 80 = 12<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 8(7) + 7(7+1)\/2 \u2013 40 = 44<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nossas estat\u00edsticas de teste s\u00e3o as menores entre <sub>U1<\/sub> e <sub>U2<\/sub> , que s\u00e3o U=12.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">Nota: Tamb\u00e9m poder\u00edamos usar a <a href=\"https:\/\/statorials.org\/pt\/calculadora-de-teste-de-mann-whitney\/\" target=\"_blank\" rel=\"noopener\">calculadora do teste U de Mann-Whitney<\/a> para determinar que U = 12.<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. Rejeite ou n\u00e3o rejeite a hip\u00f3tese nula.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Usando n <sub>1<\/sub> = 8 e n <sub>2<\/sub> = 7 com um n\u00edvel de signific\u00e2ncia de 0,01, a tabela U de Mann-Whitney nos diz que o valor cr\u00edtico \u00e9 6:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1383 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex2.png\" alt=\"Tabela de valores cr\u00edticos do teste Mann Whitney U\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Como nossa estat\u00edstica de teste (12) \u00e9 maior que nosso valor cr\u00edtico (6), n\u00e3o conseguimos rejeitar a hip\u00f3tese nula.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. Interprete os resultados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Como n\u00e3o conseguimos rejeitar a hip\u00f3tese nula, n\u00e3o temos evid\u00eancias suficientes para dizer que os resultados dos testes dos alunos que estudaram s\u00e3o diferentes daqueles dos alunos que n\u00e3o estudaram.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <a href=\"https:\/\/statorials.org\/pt\/calculadora-de-teste-de-mann-whitney\/\" target=\"_blank\" rel=\"noopener\">Calculadora de teste Mann-Whitney U<\/a><br \/> Mesa U Mann-Whitney<br \/> <a href=\"https:\/\/statorials.org\/pt\/como-realizar-um-teste-mann-whitney-u-no-excel\/\" target=\"_blank\" rel=\"noopener\">Como realizar um teste U de Mann-Whitney no Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa-r\/\" target=\"_blank\" rel=\"noopener\">Como realizar um teste U de Mann-Whitney em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa-python\/\">Como realizar um teste U de Mann-Whitney em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa-spss\/\" target=\"_blank\" rel=\"noopener\">Como realizar um teste U de Mann-Whitney no SPSS<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/mann-whitney-voce-testa-estatisticas\/\" target=\"_blank\" rel=\"noopener\">Como realizar um teste U de Mann-Whitney no Stata<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um teste U de Mann-Whitney (\u00e0s vezes chamado de teste de soma de postos de Wilcoxon) \u00e9 usado para comparar diferen\u00e7as entre duas amostras independentes quando as distribui\u00e7\u00f5es amostrais n\u00e3o s\u00e3o normalmente distribu\u00eddas e os tamanhos das amostras s\u00e3o pequenos (n &lt;30). \u00c9 considerado o equivalente n\u00e3o param\u00e9trico do teste t independente para duas amostras [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-420","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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