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 130
attach(dados)

Em seguida, será carregado os pacotes utilizados para esta análise:

if(!require(psych)){install.packages("psych")}
## Loading required package: psych
## Warning: package 'psych' was built under R version 3.5.3
if(!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':
## 
##     headtail
if(!require(lattice)){install.packages("lattice")}
## Loading required package: lattice
if(!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':
## 
##     Orange
if(!require(multcompView)){install.packages("multcompView")}
## Loading required package: multcompView
## Warning: package 'multcompView' was built under R version 3.5.3
if(!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## PMCMR is superseded by PMCMRplus and will be no longer maintained.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 3.5.3
require(stats)
require(reshape2)
## Loading required package: reshape2
## Warning: package 'reshape2' was built under R version 3.5.3
require(fBasics)
## Loading required package: fBasics
## Warning: package 'fBasics' was built under R version 3.5.3
## 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':
## 
##     tr
require(ExpDes)
## Loading required package: ExpDes
## 
## Attaching package: 'ExpDes'
## The following object is masked from 'package:stats':
## 
##     ccf
require(nortest)
## Loading required package: nortest
require(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':
## 
##     kurtosis, skewness
## The following object is masked from 'package:PMCMR':
## 
##     durbin.test
lado.rim<-as.factor(dados$RIM)
medico<-as.factor(dados$MÉDICO)
imagem<-as.factor(dados$IMAGEM)
summary(factor(lado.rim))
##   D   E 
## 471 448
summary(factor(medico))
##   1   2   3   4   5 
## 177 188 188 178 188
summary(factor(imagem))
##   A   M   N   P 
## 230 229 231 229

Para 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           0.191

Agora, 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-16

De 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 
## 0.2022142

Portanto, 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 47

Somatório

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 6193

Médias

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 131.76596

O 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 74.40909

Aplicando 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 = 0.008687

Como 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      b

pode-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      d

Todas as imagens diferem significativamente entre si.

imagem_A=dados[dados$IMAGEM=="A",c(1,4)]

dim(imagem_A)
## [1] 230   2
headtail(imagem_A)
##     MÉDICO GSM
## 1        1  85
## 5        1  59
## 9        2 106
## 905      4  70
## 912      5  70
## 913      5  68
imagem_P=dados[dados$IMAGEM=="P",c(1,4)]

dim(imagem_P)
## [1] 229   2
headtail(imagem_P)
##     MÉDICO GSM
## 2        1 124
## 6        1 130
## 11       2 113
## 907      4 117
## 914      5 123
## 915      5 127
imagem_M=dados[dados$IMAGEM=="M",c(1,4)]

dim(imagem_M)
## [1] 229   2
headtail(imagem_M)
##     MÉDICO GSM
## 4        1  92
## 8        1  98
## 15       2 111
## 911      4  87
## 918      5  92
## 919      5  94
imagem_N=dados[dados$IMAGEM=="N",c(1,4)]

dim(imagem_N)
## [1] 231   2
headtail(imagem_N)
##     MÉDICO GSM
## 3        1  63
## 7        1  51
## 13       2 104
## 909      4  53
## 916      5  52
## 917      5  51

Teste 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-14

Teste 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-13

Teste 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-09

Teste 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-12

Como 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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0

MEDICO 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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0

Medicos 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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0

1 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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0
wilcox.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 0

1 e 2, 1 e 3, 2 e 3, diferem significativamente