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{"id":6462,"date":"2020-03-31T13:00:49","date_gmt":"2020-03-31T16:00:49","guid":{"rendered":"https:\/\/site.statplace.com.br\/?p=6462"},"modified":"2024-10-02T14:43:42","modified_gmt":"2024-10-02T14:43:42","slug":"qual-o-melhor-teste-para-a-comparacao-de-medias","status":"publish","type":"post","link":"https:\/\/site.statplace.com.br\/blog\/qual-o-melhor-teste-para-a-comparacao-de-medias\/","title":{"rendered":"Qual o melhor teste para a compara\u00e7\u00e3o de m\u00e9dias?"},"content":{"rendered":"\n

Se voc\u00ea faz pesquisa cient\u00edfica ent\u00e3o com certeza j\u00e1 precisou comparar m\u00e9dias para analisar os resultados obtidos. O problema \u00e9 que existem muitos testes estat\u00edsticos poss\u00edveis e cada um deles \u00e9 aplicado para uma situa\u00e7\u00e3o diferente. <\/p>\n\n\n\n

Ent\u00e3o, como saber qual o melhor para os dados da sua pesquisa? Para responder essa pergunta \u00e9 preciso saber qual o tipo de dado que voc\u00ea tem em m\u00e3os. <\/p>\n\n\n\n

As vari\u00e1veis da sua pesquisa podem ser: quantitativas ou\nqualitativas, apresentar ou n\u00e3o distribui\u00e7\u00e3o normal, ser pareadas ou n\u00e3o e ter\nmais ou menos de dois n\u00edveis. Essas caracter\u00edsticas ser\u00e3o as respons\u00e1veis pela\nescolha dos testes.<\/p>\n\n\n\n

Continue lendo para saber mais sobre cada um dos testes e a sua aplicabilidade.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Quantitativa n\u00e3o apresenta distribui\u00e7\u00e3o normal<\/h2>\n\n\n\n

Teste de Wilcoxon\/ Mann-Whitney<\/h3>\n\n\n\n

Este \u00e9 um teste n\u00e3o param\u00e9trico baseado nos postos dos valores obtidos combinando 2 amostras, sendo que a utiliza\u00e7\u00e3o dele \u00e9 ideal para a compara\u00e7\u00e3o de 2 amostras n\u00e3o pareadas. Exemplo:<\/p>\n\n\n\n

GrupoA1 <- c(1, 2, 3, 2, 3, 4, 5, 4, 3, 2, 2, 2, 3, 2, 3, 2)\nGrupoA2 <- c(3, 4, 4, 4, 5, 5, 3, 3, 2, 3, 3, 4, 2, 4)\n\nMedidasA <- c(GrupoA1, GrupoA2)\n\nMedidasA %>% \n  shapiro.test()# N\u00e3o segue distribui\u00e7\u00e3o normal\n## \n##  Shapiro-Wilk normality test\n## \n## data:  .\n## W = 0.90592, p-value = 0.01176\nGruposA <- c(rep(\"G1\", length(GrupoA1)), \n             rep(\"G2\", length(GrupoA2))) %>% \n  as.factor()\n\nwilcox.test(MedidasA ~ GruposA, exact = FALSE)# exact: quando n\u00e3o tem empate nos postos\n## \n##  Wilcoxon rank sum test with continuity correction\n## \n## data:  MedidasA by GruposA\n## W = 61.5, p-value = 0.03053\n## alternative hypothesis: true location shift is not equal to 0\nwhitney.abg(MedidasA, GruposA)\n##     N  M\u00e9dia      E.P. 1\u00ba Q. 2\u00ba Q. 3\u00ba Q.    Valor-p\n## G1 16 2.6875 0.2536196     2   2.5     3 0.03052584\n## G2 14 3.5000 0.2513699     3   3.5     4 0.03052584<\/code><\/pre>\n\n\n\n
Teste de Kruskall-Wallis<\/h3>\n\n\n\n
O teste de Kruskal-Wallis <\/a>\u00e9 uma extens\u00e3o do de Wilcoxon\/Mann-Whitney. \u00c9 um teste n\u00e3o param\u00e9trico utilizado para comparar 3 ou mais amostras n\u00e3o pareadas. Ele \u00e9 usado para testar a hip\u00f3tese nula de que todas as popula\u00e7\u00f5es possuem m\u00e9dias iguais contra a hip\u00f3tese alternativa de que ao menos duas das popula\u00e7\u00f5es possuem m\u00e9dias diferentes quanto \u00e0 uma vari\u00e1vel quantitativa. Exemplo:<\/p>\n\n\n\n
GrupoB1 <- c(1, 1, 3, 2, 2, 4, 4, 4, 2, 2, 3, 2, 1, 2, 3, 2)\nGrupoB2 <- c(4, 5, 4, 4, 5, 5, 3, 3, 2, 5, 3, 4)\nGrupoB3 <- c(5, 4, 4, 4, 3, 5, 4, 4, 5, 5, 3, 3, 2, 3, 3, 4, 2, 4)\n\nMedidasB <- c(GrupoB1, GrupoB2, GrupoB3)\n\nMedidasB %>% \n  shapiro.test()# N\u00e3o segue distribui\u00e7\u00e3o normal\n## \n##  Shapiro-Wilk normality test\n## \n## data:  .\n## W = 0.90793, p-value = 0.001482\nGruposB <- c(rep(\"G1\", length(GrupoB1)), \n             rep(\"G2\", length(GrupoB2)), \n             rep(\"G3\", length(GrupoB3))) %>% \n  as.factor()\n\nkruskal.test(MedidasB ~ GruposB)\n## \n##  Kruskal-Wallis rank sum test\n## \n## data:  MedidasB by GruposB\n## Kruskal-Wallis chi-squared = 14.47, df = 2, p-value = 0.0007208\nkruskal.abg(MedidasB, GruposB)$tabela\n##     N    M\u00e9dia      E.P. 1\u00ba Q. 2\u00ba Q. 3\u00ba Q.      Valor-p\n## G1 16 2.375000 0.2561738     2     2     3 0.0007207691\n## G2 12 3.916667 0.2875796     3     4     5 0.0007207691\n## G3 18 3.722222 0.2258688     3     4     4 0.0007207691<\/code><\/pre>\n\n\n\n
Quando o teste de Kruskall-Wallis verifica diferen\u00e7a significativa, utiliza-se o de Nemenyi, que \u00e9 um post-hoc, para a verifica\u00e7\u00e3o de diferen\u00e7as par-a-par (compara\u00e7\u00f5es m\u00faltiplas). Exemplo:<\/p>\n\n\n\n
if(!require(PMCMR)){ install.packages(\"PMCMR\"); require(PMCMR) }\n\nposthoc.kruskal.nemenyi.test(MedidasB ~ GruposB, dist = \"Chisq\")# M\u00e9todo para determinar o valor-p (defaut tukey)\n## \n##  Pairwise comparisons using Nemenyi-test with Chi-squared    \n##                        approximation for independent samples \n## \n## data:  MedidasB by GruposB \n## \n##    G1     G2    \n## G2 0.0039 -     \n## G3 0.0059 0.9018\n## \n## P value adjustment method: none\nkruskal.abg(MedidasB, GruposB)$C.Multiplas\n##             G1        G2\n## G2 0.003937787        NA\n## G3 0.005871800 0.9018024<\/code><\/pre>\n\n\n\n
Teste de Wilcoxon pareado<\/h3>\n\n\n\n
O teste de Wilcoxon pareado \u00e9 utilizado para comparar se as medidas de posi\u00e7\u00e3o de 2 amostras s\u00e3o iguais no caso em que as amostras s\u00e3o dependentes (pareadas)<\/a>. Exemplo:<\/p>\n\n\n\n
GrupoC1 <- c(2, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 3, 2, 1, 1, 2, 4, 2)\nGrupoC2 <- c(3, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 2, 4, 2)\n\nMedidasC <- c(GrupoC1, GrupoC2)\n\nMedidasC %>% \n  shapiro.test()# N\u00e3o segue distribui\u00e7\u00e3o normal\n## \n##  Shapiro-Wilk normality test\n## \n## data:  .\n## W = 0.87325, p-value = 0.0006849\nGruposC <- c(rep(\"G1\", length(GrupoC1)), \n             rep(\"G2\", length(GrupoC2))) %>% \n  as.factor()\n\nwilcox.test(MedidasC ~ GruposC, exact = FALSE, paired = TRUE)\n## \n##  Wilcoxon signed rank test with continuity correction\n## \n## data:  MedidasC by GruposC\n## V = 0, p-value = 0.007745\n## alternative hypothesis: true location shift is not equal to 0\nwilcox.abg(GrupoC1, GrupoC2)\n##           N_validos      M\u00e9dia       E.P 1\u00baQ  2\u00baQ 3\u00baQ     Valor-P\n## diferen\u00e7a        18 -0.7777778 0.2222222  -1 -0.5   0 0.007744715<\/code><\/pre>\n\n\n\n
Teste de Friedman<\/h3>\n\n\n\n
Esse \u00e9 um teste  n\u00e3o-param\u00e9trico utilizado para comparar 3 ou mais amostras pareadas quanto \u00e0 uma vari\u00e1vel quantitativa. Exemplo:<\/p>\n\n\n\n
GrupoD1 <- c(2, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 3, 2, 1, 1, 2, 4, 2)\nGrupoD2 <- c(3, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 2, 4, 2)\nGrupoD3 <- c(2, 5, 4, 4, 3, 4, 4, 5, 4, 4, 2, 4, 2, 5, 3, 3, 4, 2)\n\nMedidasD <- c(GrupoD1, GrupoD2, GrupoD3)\n\nMedidasD %>%\n  shapiro.test()# N\u00e3o segue distribui\u00e7\u00e3o normal\n## \n##  Shapiro-Wilk normality test\n## \n## data:  .\n## W = 0.91304, p-value = 0.0008227\nMatriz <- cbind(GrupoD1, GrupoD2, GrupoD3)\n\nMatriz %>%\n  friedman.test()\n## \n##  Friedman rank sum test\n## \n## data:  .\n## Friedman chi-squared = 16.836, df = 2, p-value = 0.0002208<\/code><\/pre>\n\n\n\n
Quando o teste de Friedman verifica diferen\u00e7a significativa, utiliza-se o de Nemenyi, que \u00e9 um post-hoc, para a verifica\u00e7\u00e3o de diferen\u00e7as par-a-par (compara\u00e7\u00f5es m\u00faltiplas). Exemplo:<\/p>\n\n\n\n
Matriz %>% \n  posthoc.friedman.nemenyi.test()# Pacote PMCMR\n## \n##  Pairwise comparisons using Nemenyi multiple comparison test \n##              with q approximation for unreplicated blocked data \n## \n## data:  . \n## \n##         GrupoD1 GrupoD2\n## GrupoD2 0.21810 -      \n## GrupoD3 0.00099 0.13394\n## \n## P value adjustment method: none<\/code><\/pre>\n\n\n\n
Quantitativa apresenta distribui\u00e7\u00e3o normal<\/h2>\n\n\n\n
Teste t<\/h3>\n\n\n\n
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