Atividade 2- Consultoria Estatística
Mateus Peixoto
9 de março de 2019
Descrição do Banco de dados
O banco de dados para a análise estatística é referente a Hospitais do estado da Paraíba. São 919 observações de 4 variáveis, das quais abordam os pacientes que estão em um tratamento para detectar tumores nos Rins. As variáveis de estudo são: Médicos, lado do RIM, o tipo da IMAGEM, e o índice de qualidade da imagem para detectar tumores nos Rins (GSM). Sobre as variáveis, 5 médicos participaram da análise dos pacientes, nos quais eles realizaram um exame nos dois lados dos rins: Esquerdo e Direito. Além disso, a imagem foi categorizada em 4 tipos.
Inicialmente, será carregado o banco de dados deste estudo.
setwd("C:\\Users\\Mateus\\Desktop\\P7\\Consultoria\\Atividade 2")
dados<-read.table("Dados2.txt",h=T)
head(dados)## MÉDICO RIM IMAGEM GSM
## 1 1 D A 85
## 2 1 D P 124
## 3 1 D N 63
## 4 1 D M 92
## 5 1 E A 59
## 6 1 E P 130attach(dados)Em seguida, será carregado os pacotes utilizados para esta análise:
if(!require(psych)){install.packages("psych")}## Loading required package: psychif(!require(FSA)){install.packages("FSA")}## Loading required package: FSA## Warning: package 'FSA' was built under R version 3.5.3## ## FSA v0.8.22. See citation('FSA') if used in publication.
## ## Run fishR() for related website and fishR('IFAR') for related book.##
## Attaching package: 'FSA'## The following object is masked from 'package:psych':
##
## headtailif(!require(lattice)){install.packages("lattice")}## Loading required package: latticeif(!require(BSDA)){install.packages("BSDA")}## Loading required package: BSDA## Warning: package 'BSDA' was built under R version 3.5.3##
## Attaching package: 'BSDA'## The following object is masked from 'package:datasets':
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## Orangeif(!require(multcompView)){install.packages("multcompView")}## Loading required package: multcompView## Warning: package 'multcompView' was built under R version 3.5.3if(!require(PMCMR)){install.packages("PMCMR")}## Loading required package: PMCMR## Warning: package 'PMCMR' was built under R version 3.5.3## PMCMR is superseded by PMCMRplus and will be no longer maintained. You may wish to install PMCMRplus instead.if(!require(rcompanion)){install.packages("rcompanion")}## Loading required package: rcompanion## Warning: package 'rcompanion' was built under R version 3.5.3require(stats)
require(reshape2)## Loading required package: reshape2## Warning: package 'reshape2' was built under R version 3.5.3require(fBasics)## Loading required package: fBasics## Loading required package: timeDate## Loading required package: timeSeries##
## Attaching package: 'timeSeries'## The following object is masked from 'package:psych':
##
## outlier##
## Attaching package: 'fBasics'## The following object is masked from 'package:psych':
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## trrequire(ExpDes)## Loading required package: ExpDes##
## Attaching package: 'ExpDes'## The following object is masked from 'package:stats':
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## ccfrequire(nortest)## Loading required package: nortestrequire(agricolae)## Loading required package: agricolae## Warning: package 'agricolae' was built under R version 3.5.3##
## Attaching package: 'agricolae'## The following objects are masked from 'package:ExpDes':
##
## lastC, order.group, tapply.stat## The following objects are masked from 'package:timeDate':
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## kurtosis, skewness## The following object is masked from 'package:PMCMR':
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## durbin.testlado.rim<-as.factor(dados$RIM)
medico<-as.factor(dados$MÉDICO)
imagem<-as.factor(dados$IMAGEM)summary(factor(lado.rim))## D E
## 471 448summary(factor(medico))## 1 2 3 4 5
## 177 188 188 178 188summary(factor(imagem))## A M N P
## 230 229 231 229Para a variável resposta GSM:
round(basicStats(dados$GSM),3)## X..dados.GSM
## nobs 919.000
## NAs 0.000
## Minimum 25.000
## Maximum 180.000
## 1. Quartile 58.000
## 3. Quartile 97.000
## Mean 79.493
## Median 75.000
## Sum 73054.000
## SE Mean 0.904
## LCL Mean 77.720
## UCL Mean 81.266
## Variance 750.196
## Stdev 27.390
## Skewness 0.724
## Kurtosis 0.191Agora, vamos realizar o histograma da variável quantitativa GSM:
histPlot(as.timeSeries(dados$GSM))
Em seguida, será visualizado o histograma da variável versus a distribuição teórica:
densityPlot(as.timeSeries(dados$GSM))
Em seguida, os testes de normalidade:
qqnormPlot(as.timeSeries(dados$GSM))
Em seguida, o Boxplot da variável GSM:
boxplot(dados$GSM, las= 2)
Teste de normalidade
ad.test(dados$GSM)##
## Anderson-Darling normality test
##
## data: dados$GSM
## A = 9.9307, p-value < 2.2e-16De acordo com o teste de Anderson-Darling, os dados não são oriundos de uma distribuição normal.
cor.test(dados$GSM,dados$MÉDICO, method = "kendall")##
## Kendall's rank correlation tau
##
## data: dados$GSM and dados$MÉDICO
## z = 8.3345, p-value < 2.2e-16
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
## tau
## 0.2022142Portanto, rejeita-se a hipótese nula de que as variáveis não são correlacionadas ao nível de significância de 0,05. Ou seja as variavéis são correlacionadas.
Tabela de Frequência
tab<- xtabs( ~ medico + imagem,
data = dados)
tab## imagem
## medico A M N P
## 1 44 44 45 44
## 2 47 47 47 47
## 3 47 47 47 47
## 4 45 44 45 44
## 5 47 47 47 47Somatório
tabsum <- xtabs(GSM ~ medico+imagem,
data = dados)
tabsum## imagem
## medico A M N P
## 1 2895 3274 2523 4334
## 2 2774 3582 2502 4691
## 3 2650 3573 2466 4690
## 4 3268 3984 2709 5282
## 5 3952 4595 3117 6193Médias
tab.m<- tabsum/tab
tab.m## imagem
## medico A M N P
## 1 65.79545 74.40909 56.06667 98.50000
## 2 59.02128 76.21277 53.23404 99.80851
## 3 56.38298 76.02128 52.46809 99.78723
## 4 72.62222 90.54545 60.20000 120.04545
## 5 84.08511 97.76596 66.31915 131.76596O comando aggregate é uma função, como o nome sugere, agrega os dados, aplicando uma função especificada pelo parâmetro FUN.
dadosag<- aggregate(GSM, by = list(M= MÉDICO, I= IMAGEM), FUN = mean)
head(dadosag)## M I x
## 1 1 A 65.79545
## 2 2 A 59.02128
## 3 3 A 56.38298
## 4 4 A 72.62222
## 5 5 A 84.08511
## 6 1 M 74.40909Aplicando o teste de Friedman
friedman.test(dadosag$x, dadosag$M, dadosag$I)##
## Friedman rank sum test
##
## data: dadosag$x, dadosag$M and dadosag$I
## Friedman chi-squared = 13.6, df = 4, p-value = 0.008687Como o P-value é menor que o nivel de significância, há indicios para rejeitarmos H0.
Em seguida, pode-se visualizar a saída do teste de Friedman, para a variável Médico
out<-with(dadosag,friedman(I,M, x,alpha=0.05, group=TRUE,console=TRUE,main="Dados dos rins"))##
## Study: Dados dos rins
##
## M, Sum of the ranks
##
## x r
## 1 8 4
## 2 10 4
## 3 6 4
## 4 16 4
## 5 20 4
##
## Friedman's Test
## ===============
## Adjusted for ties
## Critical Value: 13.6
## P.Value Chisq: 0.008687446
## F Value: 17
## P.Value F: 6.948281e-05
##
## Post Hoc Analysis
##
## Alpha: 0.05 ; DF Error: 12
## t-Student: 2.178813
## LSD: 4.357626
##
## Treatments with the same letter are not significantly different.
##
## Sum of ranks groups
## 5 20 a
## 4 16 a
## 2 10 b
## 1 8 b
## 3 6 bpode-se perceber que os medicos 5 e 4 não diferem significativamente entre si, enquanto os medicos 1, 2 e 3 diferem significativamente dos medicos 5 e 4 .
E para a variavel Imagem
out<-with(dadosag,friedman(M,I, x,alpha=0.05, group=TRUE,console=TRUE,main="Dados sobre exame visual de rins"))##
## Study: Dados sobre exame visual de rins
##
## I, Sum of the ranks
##
## x r
## A 10 5
## M 15 5
## N 5 5
## P 20 5
##
## Friedman's Test
## ===============
## Adjusted for ties
## Critical Value: 15
## P.Value Chisq: 0.001816649
## F Value: Inf
## P.Value F: 0
##
## Post Hoc Analysis
##
## Alpha: 0.05 ; DF Error: 12
## t-Student: 2.178813
## LSD: 0
##
## Treatments with the same letter are not significantly different.
##
## Sum of ranks groups
## P 20 a
## M 15 b
## A 10 c
## N 5 dTodas as imagens diferem significativamente entre si.
imagem_A=dados[dados$IMAGEM=="A",c(1,4)]
dim(imagem_A)## [1] 230 2headtail(imagem_A)## MÉDICO GSM
## 1 1 85
## 5 1 59
## 9 2 106
## 905 4 70
## 912 5 70
## 913 5 68imagem_P=dados[dados$IMAGEM=="P",c(1,4)]
dim(imagem_P)## [1] 229 2headtail(imagem_P)## MÉDICO GSM
## 2 1 124
## 6 1 130
## 11 2 113
## 907 4 117
## 914 5 123
## 915 5 127imagem_M=dados[dados$IMAGEM=="M",c(1,4)]
dim(imagem_M)## [1] 229 2headtail(imagem_M)## MÉDICO GSM
## 4 1 92
## 8 1 98
## 15 2 111
## 911 4 87
## 918 5 92
## 919 5 94imagem_N=dados[dados$IMAGEM=="N",c(1,4)]
dim(imagem_N)## [1] 231 2headtail(imagem_N)## MÉDICO GSM
## 3 1 63
## 7 1 51
## 13 2 104
## 909 4 53
## 916 5 52
## 917 5 51Teste para a imagem A
kruskal.test(imagem_A$GSM~factor(imagem_A$MÉDICO))##
## Kruskal-Wallis rank sum test
##
## data: imagem_A$GSM by factor(imagem_A$MÉDICO)
## Kruskal-Wallis chi-squared = 70.798, df = 4, p-value = 1.54e-14Teste para a imagem P
kruskal.test(imagem_P$GSM~factor(imagem_P$MÉDICO))##
## Kruskal-Wallis rank sum test
##
## data: imagem_P$GSM by factor(imagem_P$MÉDICO)
## Kruskal-Wallis chi-squared = 66.634, df = 4, p-value = 1.165e-13Teste para a imagem N
kruskal.test(imagem_N$GSM~factor(imagem_N$MÉDICO))##
## Kruskal-Wallis rank sum test
##
## data: imagem_N$GSM by factor(imagem_N$MÉDICO)
## Kruskal-Wallis chi-squared = 43.922, df = 4, p-value = 6.658e-09Teste para a imagem M
kruskal.test(imagem_M$GSM~factor(imagem_M$MÉDICO))##
## Kruskal-Wallis rank sum test
##
## data: imagem_M$GSM by factor(imagem_M$MÉDICO)
## Kruskal-Wallis chi-squared = 60.894, df = 4, p-value = 1.882e-12Como o p-value é menor que o nível de significância de 0,05, pode-se concluir que existem diferenças significativas, ou seja a hipótese nula é rejeitada, temos que, ao menos um dos grupos é diferente dos demais.
imagem_A$MEDICO <-as.factor(imagem_A$MÉDICO)
MED1_A<-imagem_A[imagem_A$MÉDICO == "1",2]
MED2_A<-imagem_A[imagem_A$MÉDICO == "2",2]
MED3_A<-imagem_A[imagem_A$MÉDICO == "3",2]
MED4_A<-imagem_A[imagem_A$MEDICO == "4",2]
MED5_A<-imagem_A[imagem_A$MEDICO == "5",2]
wilcox.test(MED1_A,MED2_A, paired = FALSE)## Warning in wilcox.test.default(MED1_A, MED2_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_A and MED2_A
## W = 1366, p-value = 0.008428
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_A,MED3_A, paired = FALSE)## Warning in wilcox.test.default(MED1_A, MED3_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_A and MED3_A
## W = 1400.5, p-value = 0.003636
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_A,MED4_A, paired = FALSE)## Warning in wilcox.test.default(MED1_A, MED4_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_A and MED4_A
## W = 747, p-value = 0.04646
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_A,MED5_A, paired = FALSE)## Warning in wilcox.test.default(MED1_A, MED5_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_A and MED5_A
## W = 393.5, p-value = 3.661e-07
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_A,MED3_A, paired = FALSE)## Warning in wilcox.test.default(MED2_A, MED3_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_A and MED3_A
## W = 1103, p-value = 0.994
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_A,MED4_A, paired = FALSE)## Warning in wilcox.test.default(MED2_A, MED4_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_A and MED4_A
## W = 516, p-value = 2.359e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_A,MED5_A, paired = FALSE)## Warning in wilcox.test.default(MED2_A, MED5_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_A and MED5_A
## W = 331, p-value = 4.986e-09
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_A,MED4_A, paired = FALSE)## Warning in wilcox.test.default(MED3_A, MED4_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_A and MED4_A
## W = 450, p-value = 2.102e-06
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_A,MED5_A, paired = FALSE)## Warning in wilcox.test.default(MED3_A, MED5_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_A and MED5_A
## W = 208, p-value = 1.219e-11
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED4_A,MED5_A, paired = FALSE)## Warning in wilcox.test.default(MED4_A, MED5_A, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED4_A and MED5_A
## W = 627.5, p-value = 0.0007879
## alternative hypothesis: true location shift is not equal to 0MEDICO 2 E 4, diferem significativamente
imagem_M$MEDICO<-as.factor(imagem_M$MÉDICO)
MED1_M<-imagem_M[imagem_M$MÉDICO == "1",2]
MED2_M<-imagem_M[imagem_M$MÉDICO == "2",2]
MED3_M<-imagem_M[imagem_M$MÉDICO == "3",2]
MED4_M<-imagem_M[imagem_M$MÉDICO == "4",2]
MED5_M<-imagem_M[imagem_M$MÉDICO == "5",2]
wilcox.test(MED1_M,MED2_M, paired = FALSE)## Warning in wilcox.test.default(MED1_M, MED2_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_M and MED2_M
## W = 961, p-value = 0.5645
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_M,MED3_M, paired = FALSE)## Warning in wilcox.test.default(MED1_M, MED3_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_M and MED3_M
## W = 934.5, p-value = 0.4314
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_M,MED4_M, paired = FALSE)## Warning in wilcox.test.default(MED1_M, MED4_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_M and MED4_M
## W = 416.5, p-value = 4.213e-06
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_M,MED5_M, paired = FALSE)## Warning in wilcox.test.default(MED1_M, MED5_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_M and MED5_M
## W = 293.5, p-value = 4.127e-09
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_M,MED3_M, paired = FALSE)## Warning in wilcox.test.default(MED2_M, MED3_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_M and MED3_M
## W = 1108, p-value = 0.9819
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_M,MED4_M, paired = FALSE)## Warning in wilcox.test.default(MED2_M, MED4_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_M and MED4_M
## W = 536, p-value = 7.719e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_M,MED5_M, paired = FALSE)## Warning in wilcox.test.default(MED2_M, MED5_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_M and MED5_M
## W = 390, p-value = 6.627e-08
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_M,MED4_M, paired = FALSE)## Warning in wilcox.test.default(MED3_M, MED4_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_M and MED4_M
## W = 531, p-value = 6.543e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_M,MED5_M, paired = FALSE)## Warning in wilcox.test.default(MED3_M, MED5_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_M and MED5_M
## W = 386, p-value = 5.597e-08
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED4_M,MED5_M, paired = FALSE)## Warning in wilcox.test.default(MED4_M, MED5_M, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED4_M and MED5_M
## W = 774, p-value = 0.0392
## alternative hypothesis: true location shift is not equal to 0Medicos 1 e 2, 1 e 3, 2 e 3, diferem significativamente
imagem_N$MEDICO<-as.factor(imagem_N$MÉDICO)
MED1_N<-imagem_N[imagem_N$MÉDICO == "1",2]
MED2_N<-imagem_N[imagem_N$MÉDICO == "2",2]
MED3_N<-imagem_N[imagem_N$MÉDICO == "3",2]
MED4_N<-imagem_N[imagem_N$MÉDICO == "4",2]
MED5_N<-imagem_N[imagem_N$MÉDICO == "5",2]
wilcox.test(MED1_N,MED2_N, paired = FALSE)## Warning in wilcox.test.default(MED1_N, MED2_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_N and MED2_N
## W = 1345.5, p-value = 0.02458
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_N,MED3_N, paired = FALSE)## Warning in wilcox.test.default(MED1_N, MED3_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_N and MED3_N
## W = 1251, p-value = 0.1313
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_N,MED4_N, paired = FALSE)## Warning in wilcox.test.default(MED1_N, MED4_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_N and MED4_N
## W = 843.5, p-value = 0.1736
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_N,MED5_N, paired = FALSE)## Warning in wilcox.test.default(MED1_N, MED5_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_N and MED5_N
## W = 506.5, p-value = 1.692e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_N,MED3_N, paired = FALSE)## Warning in wilcox.test.default(MED2_N, MED3_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_N and MED3_N
## W = 1042, p-value = 0.6388
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_N,MED4_N, paired = FALSE)## Warning in wilcox.test.default(MED2_N, MED4_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_N and MED4_N
## W = 670.5, p-value = 0.002518
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_N,MED5_N, paired = FALSE)## Warning in wilcox.test.default(MED2_N, MED5_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_N and MED5_N
## W = 408.5, p-value = 1.425e-07
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_N,MED4_N, paired = FALSE)## Warning in wilcox.test.default(MED3_N, MED4_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_N and MED4_N
## W = 708, p-value = 0.006369
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_N,MED5_N, paired = FALSE)## Warning in wilcox.test.default(MED3_N, MED5_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_N and MED5_N
## W = 383, p-value = 4.859e-08
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED4_N,MED5_N, paired = FALSE)## Warning in wilcox.test.default(MED4_N, MED5_N, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED4_N and MED5_N
## W = 721, p-value = 0.008639
## alternative hypothesis: true location shift is not equal to 01 e 3, 1 e 4, 1 e 5, 2 e 3, diferem significativamente
imagem_P$MEDICO<-as.factor(imagem_P$MÉDICO)
MED1_P<-imagem_P[imagem_P$MÉDICO == "1",2]
MED2_P<-imagem_P[imagem_P$MÉDICO == "2",2]
MED3_P<-imagem_P[imagem_P$MÉDICO == "3",2]
MED4_P<-imagem_P[imagem_P$MÉDICO == "4",2]
MED5_P<-imagem_P[imagem_P$MÉDICO == "5",2]
wilcox.test(MED1_P,MED2_P, paired = FALSE)## Warning in wilcox.test.default(MED1_P, MED2_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_P and MED2_P
## W = 1003.5, p-value = 0.8116
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_P,MED3_P, paired = FALSE)## Warning in wilcox.test.default(MED1_P, MED3_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_P and MED3_P
## W = 992.5, p-value = 0.7446
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_P,MED4_P, paired = FALSE)## Warning in wilcox.test.default(MED1_P, MED4_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_P and MED4_P
## W = 441.5, p-value = 1.126e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED1_P,MED5_P, paired = FALSE)## Warning in wilcox.test.default(MED1_P, MED5_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED1_P and MED5_P
## W = 275, p-value = 1.689e-09
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_P,MED3_P, paired = FALSE)## Warning in wilcox.test.default(MED2_P, MED3_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_P and MED3_P
## W = 1112, p-value = 0.9578
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_P,MED4_P, paired = FALSE)## Warning in wilcox.test.default(MED2_P, MED4_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_P and MED4_P
## W = 520.5, p-value = 4.589e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED2_P,MED5_P, paired = FALSE)## Warning in wilcox.test.default(MED2_P, MED5_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED2_P and MED5_P
## W = 335.5, p-value = 6.152e-09
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_P,MED4_P, paired = FALSE)## Warning in wilcox.test.default(MED3_P, MED4_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_P and MED4_P
## W = 506.5, p-value = 2.822e-05
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED3_P,MED5_P, paired = FALSE)## Warning in wilcox.test.default(MED3_P, MED5_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED3_P and MED5_P
## W = 319.5, p-value = 2.964e-09
## alternative hypothesis: true location shift is not equal to 0wilcox.test(MED4_P,MED5_P, paired = FALSE)## Warning in wilcox.test.default(MED4_P, MED5_P, paired = FALSE): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: MED4_P and MED5_P
## W = 716.5, p-value = 0.01178
## alternative hypothesis: true location shift is not equal to 01 e 2, 1 e 3, 2 e 3, diferem significativamente
Teste de comparação multipla, Dunn
require(rcompanion)
require(dunn.test)## Loading required package: dunn.test#scheirerRayHare(GSM ~ MÉDICO + imagem_A + MÉDICO:imagem_A,
# data = dados)
dunn.test(GSM, medico:imagem, method="bh", list=TRUE)## Kruskal-Wallis rank sum test
##
## data: GSM and group
## Kruskal-Wallis chi-squared = 589.423, df = 19, p-value = 0
##
##
## Comparison of GSM by group
## (Benjamini-Hochberg)
## Col Mean-|
## Row Mean | 1:A 1:M 1:N 1:P 2:A 2:M
## ---------+------------------------------------------------------------------
## 1:M | -1.874880
## | 0.0393
## |
## 1:N | 2.290190 4.175574
## | 0.0152* 0.0000*
## |
## 1:P | -5.975277 -4.100397 -8.298943
## | 0.0000* 0.0000* 0.0000*
## |
## 2:A | 1.602905 3.508440 -0.715881 7.675878
## | 0.0677 0.0004* 0.2634 0.0000*
## |
## 2:M | -2.251329 -0.345794 -4.592427 3.821643 -3.919381
## | 0.0165* 0.3893 0.0000* 0.0001* 0.0001*
## |
## 2:N | 2.930134 4.835668 0.619029 9.003106 1.349661 5.269043
## | 0.0026* 0.0000* 0.2909 0.0000* 0.1065 0.0000*
## |
## 2:P | -6.144162 -4.238627 -8.507794 -0.071189 -7.878013 -3.958631
## | 0.0000* 0.0000* 0.0000* 0.4844 0.0000* 0.0001*
## |
## 3:A | 1.985444 3.890978 -0.331128 8.058416 0.389004 4.308385
## | 0.0309 0.0001* 0.3930 0.0000* 0.3742 0.0000*
## |
## 3:M | -2.206999 -0.301464 -4.547840 3.865973 -3.874302 0.045079
## | 0.0184* 0.4027 0.0000* 0.0001* 0.0001* 0.4898
## |
## 3:N | 3.025099 4.930634 0.714544 9.098072 1.446232 5.365614
## | 0.0019* 0.0000* 0.2623 0.0000* 0.0896 0.0000*
## |
## 3:P | -6.172250 -4.266716 -8.536045 -0.099278 -7.906577 -3.987195
## | 0.0000* 0.0000* 0.0000* 0.4781 0.0000* 0.0001*
## |
## 4:A | -1.453058 0.432325 -3.764457 4.555694 -3.089274 0.787271
## | 0.0890 0.3592 0.0001* 0.0000* 0.0015* 0.2423
## |
## 4:M | -4.969356 -3.094476 -7.287387 1.005920 -6.653511 -2.799275
## | 0.0000* 0.0015* 0.0000* 0.1800 0.0000* 0.0038*
## |
## 4:N | 1.312763 3.198147 -0.982964 7.321516 -0.277710 3.598835
## | 0.1131 0.0011* 0.1852 0.0000* 0.4100 0.0003*
## |
## 4:P | -8.429933 -6.555052 -10.76735 -2.454655 -10.17066 -6.316432
## | 0.0000* 0.0000* 0.0000* 0.0102* 0.0000* 0.0000*
## |
## 5:A | -3.804029 -1.898494 -6.154115 2.268943 -5.498326 -1.578944
## | 0.0001* 0.0375 0.0000* 0.0159* 0.0000* 0.0705
## |
## 5:M | -6.103844 -4.198310 -8.467243 -0.030872 -7.837014 -3.917633
## | 0.0000* 0.0000* 0.0000* 0.4903 0.0000* 0.0001*
## |
## 5:N | -0.176221 1.729312 -2.505307 5.896750 -1.809199 2.110182
## | 0.4490 0.0534 0.0090* 0.0000* 0.0452 0.0231*
## |
## 5:P | -9.281090 -7.375555 -11.66288 -3.208117 -11.06796 -7.148582
## | 0.0000* 0.0000* 0.0000* 0.0011* 0.0000* 0.0000*
## Col Mean-|
## Row Mean | 2:N 2:P 3:A 3:M 3:N 3:P
## ---------+------------------------------------------------------------------
## 2:P | -9.227675
## | 0.0000*
## |
## 3:A | -0.960657 8.267017
## | 0.1904 0.0000*
## |
## 3:M | -5.223964 4.003711 -4.263306
## | 0.0000* 0.0001* 0.0000*
## |
## 3:N | 0.096570 9.324246 1.057228 5.320535
## | 0.4766 0.0000* 0.1682 0.0000*
## |
## 3:P | -9.256238 -0.028563 -8.295581 -4.032274 -9.352809
## | 0.0000* 0.4886 0.0000* 0.0001* 0.0000*
## |
## 4:A | -4.424185 4.702638 -3.474026 0.742684 -4.519700 4.730889
## | 0.0000* 0.0000* 0.0004* 0.2558 0.0000* 0.0000*
## |
## 4:M | -7.980739 1.093557 -7.036049 -2.843606 -8.075705 1.121645
## | 0.0000* 0.1598 0.0000* 0.0034* 0.0000* 0.1536
## |
## 4:N | -1.612621 7.514202 -0.662462 3.554248 -1.708136 7.542453
## | 0.0668 0.0000* 0.2772 0.0003* 0.0555 0.0000*
## |
## 4:P | -11.49789 -2.423599 -10.55320 -6.360762 -11.59286 -2.395510
## | 0.0000* 0.0111* 0.0000* 0.0000* 0.0000* 0.0118*
## |
## 5:A | -6.847988 2.379687 -5.887330 -1.624024 -6.944559 2.408250
## | 0.0000* 0.0122* 0.0000* 0.0657 0.0000* 0.0114*
## |
## 5:M | -9.186676 0.040998 -8.226018 -3.962712 -9.283247 0.069562
## | 0.0000* 0.4888 0.0000* 0.0001* 0.0000* 0.4824
## |
## 5:N | -3.158861 6.068814 -2.198203 2.065102 -3.255432 6.097377
## | 0.0012* 0.0000* 0.0187* 0.0257 0.0009* 0.0000*
## |
## 5:P | -12.41762 -3.189950 -11.45696 -7.193661 -12.51419 -3.161387
## | 0.0000* 0.0011* 0.0000* 0.0000* 0.0000* 0.0012*
## Col Mean-|
## Row Mean | 4:A 4:M 4:N 4:P 5:A 5:M
## ---------+------------------------------------------------------------------
## 4:M | -3.544137
## | 0.0003*
## |
## 4:N | 2.781492 6.309960
## | 0.0040* 0.0000*
## |
## 4:P | -7.024101 -3.460576 -9.789923
## | 0.0000* 0.0004* 0.0000*
## |
## 5:A | -2.348959 1.246575 -5.160523 4.763731
## | 0.0132* 0.1254 0.0000* 0.0000*
## |
## 5:M | -4.662087 -1.053239 -7.473651 2.463916 -2.338688
## | 0.0000* 0.1683 0.0000* 0.0100* 0.0134*
## |
## 5:N | 1.299847 4.874383 -1.511715 8.391539 3.689127 6.027815
## | 0.1150 0.0000* 0.0800 0.0000* 0.0002* 0.0000*
## |
## 5:P | -7.857725 -4.230485 -10.66928 -0.713329 -5.569637 -3.230949
## | 0.0000* 0.0000* 0.0000* 0.2612 0.0000* 0.0010*
## Col Mean-|
## Row Mean | 5:N
## ---------+-----------
## 5:P | -9.258764
## | 0.0000*
##
##
## List of pairwise comparisons: Z statistic (adjusted p-value)
## -------------------------------
## 1:A - 1:M : -1.874880 (0.0393)
## 1:A - 1:N : 2.290190 (0.0152)*
## 1:M - 1:N : 4.175574 (0.0000)*
## 1:A - 1:P : -5.975277 (0.0000)*
## 1:M - 1:P : -4.100397 (0.0000)*
## 1:N - 1:P : -8.298943 (0.0000)*
## 1:A - 2:A : 1.602905 (0.0677)
## 1:M - 2:A : 3.508440 (0.0004)*
## 1:N - 2:A : -0.715881 (0.2634)
## 1:P - 2:A : 7.675878 (0.0000)*
## 1:A - 2:M : -2.251329 (0.0165)*
## 1:M - 2:M : -0.345794 (0.3893)
## 1:N - 2:M : -4.592427 (0.0000)*
## 1:P - 2:M : 3.821643 (0.0001)*
## 2:A - 2:M : -3.919381 (0.0001)*
## 1:A - 2:N : 2.930134 (0.0026)*
## 1:M - 2:N : 4.835668 (0.0000)*
## 1:N - 2:N : 0.619029 (0.2909)
## 1:P - 2:N : 9.003106 (0.0000)*
## 2:A - 2:N : 1.349661 (0.1065)
## 2:M - 2:N : 5.269043 (0.0000)*
## 1:A - 2:P : -6.144162 (0.0000)*
## 1:M - 2:P : -4.238627 (0.0000)*
## 1:N - 2:P : -8.507794 (0.0000)*
## 1:P - 2:P : -0.071189 (0.4844)
## 2:A - 2:P : -7.878013 (0.0000)*
## 2:M - 2:P : -3.958631 (0.0001)*
## 2:N - 2:P : -9.227675 (0.0000)*
## 1:A - 3:A : 1.985444 (0.0309)
## 1:M - 3:A : 3.890978 (0.0001)*
## 1:N - 3:A : -0.331128 (0.3930)
## 1:P - 3:A : 8.058416 (0.0000)*
## 2:A - 3:A : 0.389004 (0.3742)
## 2:M - 3:A : 4.308385 (0.0000)*
## 2:N - 3:A : -0.960657 (0.1904)
## 2:P - 3:A : 8.267017 (0.0000)*
## 1:A - 3:M : -2.206999 (0.0184)*
## 1:M - 3:M : -0.301464 (0.4027)
## 1:N - 3:M : -4.547840 (0.0000)*
## 1:P - 3:M : 3.865973 (0.0001)*
## 2:A - 3:M : -3.874302 (0.0001)*
## 2:M - 3:M : 0.045079 (0.4898)
## 2:N - 3:M : -5.223964 (0.0000)*
## 2:P - 3:M : 4.003711 (0.0001)*
## 3:A - 3:M : -4.263306 (0.0000)*
## 1:A - 3:N : 3.025099 (0.0019)*
## 1:M - 3:N : 4.930634 (0.0000)*
## 1:N - 3:N : 0.714544 (0.2623)
## 1:P - 3:N : 9.098072 (0.0000)*
## 2:A - 3:N : 1.446232 (0.0896)
## 2:M - 3:N : 5.365614 (0.0000)*
## 2:N - 3:N : 0.096570 (0.4766)
## 2:P - 3:N : 9.324246 (0.0000)*
## 3:A - 3:N : 1.057228 (0.1682)
## 3:M - 3:N : 5.320535 (0.0000)*
## 1:A - 3:P : -6.172250 (0.0000)*
## 1:M - 3:P : -4.266716 (0.0000)*
## 1:N - 3:P : -8.536045 (0.0000)*
## 1:P - 3:P : -0.099278 (0.4781)
## 2:A - 3:P : -7.906577 (0.0000)*
## 2:M - 3:P : -3.987195 (0.0001)*
## 2:N - 3:P : -9.256238 (0.0000)*
## 2:P - 3:P : -0.028563 (0.4886)
## 3:A - 3:P : -8.295581 (0.0000)*
## 3:M - 3:P : -4.032274 (0.0001)*
## 3:N - 3:P : -9.352809 (0.0000)*
## 1:A - 4:A : -1.453058 (0.0890)
## 1:M - 4:A : 0.432325 (0.3592)
## 1:N - 4:A : -3.764457 (0.0001)*
## 1:P - 4:A : 4.555694 (0.0000)*
## 2:A - 4:A : -3.089274 (0.0015)*
## 2:M - 4:A : 0.787271 (0.2423)
## 2:N - 4:A : -4.424185 (0.0000)*
## 2:P - 4:A : 4.702638 (0.0000)*
## 3:A - 4:A : -3.474026 (0.0004)*
## 3:M - 4:A : 0.742684 (0.2558)
## 3:N - 4:A : -4.519700 (0.0000)*
## 3:P - 4:A : 4.730889 (0.0000)*
## 1:A - 4:M : -4.969356 (0.0000)*
## 1:M - 4:M : -3.094476 (0.0015)*
## 1:N - 4:M : -7.287387 (0.0000)*
## 1:P - 4:M : 1.005920 (0.1800)
## 2:A - 4:M : -6.653511 (0.0000)*
## 2:M - 4:M : -2.799275 (0.0038)*
## 2:N - 4:M : -7.980739 (0.0000)*
## 2:P - 4:M : 1.093557 (0.1598)
## 3:A - 4:M : -7.036049 (0.0000)*
## 3:M - 4:M : -2.843606 (0.0034)*
## 3:N - 4:M : -8.075705 (0.0000)*
## 3:P - 4:M : 1.121645 (0.1536)
## 4:A - 4:M : -3.544137 (0.0003)*
## 1:A - 4:N : 1.312763 (0.1131)
## 1:M - 4:N : 3.198147 (0.0011)*
## 1:N - 4:N : -0.982964 (0.1852)
## 1:P - 4:N : 7.321516 (0.0000)*
## 2:A - 4:N : -0.277710 (0.4100)
## 2:M - 4:N : 3.598835 (0.0003)*
## 2:N - 4:N : -1.612621 (0.0668)
## 2:P - 4:N : 7.514202 (0.0000)*
## 3:A - 4:N : -0.662462 (0.2772)
## 3:M - 4:N : 3.554248 (0.0003)*
## 3:N - 4:N : -1.708136 (0.0555)
## 3:P - 4:N : 7.542453 (0.0000)*
## 4:A - 4:N : 2.781492 (0.0040)*
## 4:M - 4:N : 6.309960 (0.0000)*
## 1:A - 4:P : -8.429933 (0.0000)*
## 1:M - 4:P : -6.555052 (0.0000)*
## 1:N - 4:P : -10.76735 (0.0000)*
## 1:P - 4:P : -2.454655 (0.0102)*
## 2:A - 4:P : -10.17066 (0.0000)*
## 2:M - 4:P : -6.316432 (0.0000)*
## 2:N - 4:P : -11.49789 (0.0000)*
## 2:P - 4:P : -2.423599 (0.0111)*
## 3:A - 4:P : -10.55320 (0.0000)*
## 3:M - 4:P : -6.360762 (0.0000)*
## 3:N - 4:P : -11.59286 (0.0000)*
## 3:P - 4:P : -2.395510 (0.0118)*
## 4:A - 4:P : -7.024101 (0.0000)*
## 4:M - 4:P : -3.460576 (0.0004)*
## 4:N - 4:P : -9.789923 (0.0000)*
## 1:A - 5:A : -3.804029 (0.0001)*
## 1:M - 5:A : -1.898494 (0.0375)
## 1:N - 5:A : -6.154115 (0.0000)*
## 1:P - 5:A : 2.268943 (0.0159)*
## 2:A - 5:A : -5.498326 (0.0000)*
## 2:M - 5:A : -1.578944 (0.0705)
## 2:N - 5:A : -6.847988 (0.0000)*
## 2:P - 5:A : 2.379687 (0.0122)*
## 3:A - 5:A : -5.887330 (0.0000)*
## 3:M - 5:A : -1.624024 (0.0657)
## 3:N - 5:A : -6.944559 (0.0000)*
## 3:P - 5:A : 2.408250 (0.0114)*
## 4:A - 5:A : -2.348959 (0.0132)*
## 4:M - 5:A : 1.246575 (0.1254)
## 4:N - 5:A : -5.160523 (0.0000)*
## 4:P - 5:A : 4.763731 (0.0000)*
## 1:A - 5:M : -6.103844 (0.0000)*
## 1:M - 5:M : -4.198310 (0.0000)*
## 1:N - 5:M : -8.467243 (0.0000)*
## 1:P - 5:M : -0.030872 (0.4903)
## 2:A - 5:M : -7.837014 (0.0000)*
## 2:M - 5:M : -3.917633 (0.0001)*
## 2:N - 5:M : -9.186676 (0.0000)*
## 2:P - 5:M : 0.040998 (0.4888)
## 3:A - 5:M : -8.226018 (0.0000)*
## 3:M - 5:M : -3.962712 (0.0001)*
## 3:N - 5:M : -9.283247 (0.0000)*
## 3:P - 5:M : 0.069562 (0.4824)
## 4:A - 5:M : -4.662087 (0.0000)*
## 4:M - 5:M : -1.053239 (0.1683)
## 4:N - 5:M : -7.473651 (0.0000)*
## 4:P - 5:M : 2.463916 (0.0100)*
## 5:A - 5:M : -2.338688 (0.0134)*
## 1:A - 5:N : -0.176221 (0.4490)
## 1:M - 5:N : 1.729312 (0.0534)
## 1:N - 5:N : -2.505307 (0.0090)*
## 1:P - 5:N : 5.896750 (0.0000)*
## 2:A - 5:N : -1.809199 (0.0452)
## 2:M - 5:N : 2.110182 (0.0231)*
## 2:N - 5:N : -3.158861 (0.0012)*
## 2:P - 5:N : 6.068814 (0.0000)*
## 3:A - 5:N : -2.198203 (0.0187)*
## 3:M - 5:N : 2.065102 (0.0257)
## 3:N - 5:N : -3.255432 (0.0009)*
## 3:P - 5:N : 6.097377 (0.0000)*
## 4:A - 5:N : 1.299847 (0.1150)
## 4:M - 5:N : 4.874383 (0.0000)*
## 4:N - 5:N : -1.511715 (0.0800)
## 4:P - 5:N : 8.391539 (0.0000)*
## 5:A - 5:N : 3.689127 (0.0002)*
## 5:M - 5:N : 6.027815 (0.0000)*
## 1:A - 5:P : -9.281090 (0.0000)*
## 1:M - 5:P : -7.375555 (0.0000)*
## 1:N - 5:P : -11.66288 (0.0000)*
## 1:P - 5:P : -3.208117 (0.0011)*
## 2:A - 5:P : -11.06796 (0.0000)*
## 2:M - 5:P : -7.148582 (0.0000)*
## 2:N - 5:P : -12.41762 (0.0000)*
## 2:P - 5:P : -3.189950 (0.0011)*
## 3:A - 5:P : -11.45696 (0.0000)*
## 3:M - 5:P : -7.193661 (0.0000)*
## 3:N - 5:P : -12.51419 (0.0000)*
## 3:P - 5:P : -3.161387 (0.0012)*
## 4:A - 5:P : -7.857725 (0.0000)*
## 4:M - 5:P : -4.230485 (0.0000)*
## 4:N - 5:P : -10.66928 (0.0000)*
## 4:P - 5:P : -0.713329 (0.2612)
## 5:A - 5:P : -5.569637 (0.0000)*
## 5:M - 5:P : -3.230949 (0.0010)*
## 5:N - 5:P : -9.258764 (0.0000)*
##
## alpha = 0.05
## Reject Ho if p <= alpha/2