getwd()
## [1] "C:/Users/aluno/Documents"
setwd("C:/Users/aluno/Documents")
library(boot)
library(agricolae)
## Warning: package 'agricolae' was built under R version 3.1.3
dic=read.table("dic.txt", h=TRUE)
str(dic)
## 'data.frame':    20 obs. of  2 variables:
##  $ niveis: Factor w/ 5 levels "T1","T2","T3",..: 1 1 1 1 2 2 2 2 3 3 ...
##  $ y     : num  4.6 5.1 5.8 5.5 6 7.1 7.2 6.8 5.8 7.2 ...
summary(dic)
##  niveis       y        
##  T1:4   Min.   :4.600  
##  T2:4   1st Qu.:5.675  
##  T3:4   Median :5.950  
##  T4:4   Mean   :6.120  
##  T5:4   3rd Qu.:6.800  
##         Max.   :7.200
dic
##    niveis   y
## 1      T1 4.6
## 2      T1 5.1
## 3      T1 5.8
## 4      T1 5.5
## 5      T2 6.0
## 6      T2 7.1
## 7      T2 7.2
## 8      T2 6.8
## 9      T3 5.8
## 10     T3 7.2
## 11     T3 6.9
## 12     T3 6.7
## 13     T4 5.6
## 14     T4 4.9
## 15     T4 5.9
## 16     T4 5.7
## 17     T5 5.8
## 18     T5 6.4
## 19     T5 6.6
## 20     T5 6.8
boxplot(y ~ niveis, data=dic, col="red")

Analisando o bloxplot observa se que o tratamento T5 e T4 são estatisticamente p

mod1<-aov(y~niveis,data=dic)
summary(mod1)
##             Df Sum Sq Mean Sq F value  Pr(>F)   
## niveis       4  7.597   1.899   7.277 0.00183 **
## Residuals   15  3.915   0.261                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
library(agricolae)
library(boot)
library(doBy)
## Warning: package 'doBy' was built under R version 3.1.3
## Loading required package: survival
## Loading required package: splines
## 
## Attaching package: 'survival'
## 
## The following object is masked from 'package:boot':
## 
##     aml
summaryBy(y ~ niveis, data=dic, FUN = c(length, sd))
##   niveis y.length      y.sd
## 1     T1        4 0.5196152
## 2     T2        4 0.5439056
## 3     T3        4 0.6027714
## 4     T4        4 0.4349329
## 5     T5        4 0.4320494
names(mod1)
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "contrasts"     "xlevels"       "call"          "terms"        
## [13] "model"
dic$y
##  [1] 4.6 5.1 5.8 5.5 6.0 7.1 7.2 6.8 5.8 7.2 6.9 6.7 5.6 4.9 5.9 5.7 5.8
## [18] 6.4 6.6 6.8
cv.model(mod1)
## [1] 8.347738
par(mfrow = c(2,2))
plot(mod1)

shapiro.test(mod1$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  mod1$residuals
## W = 0.8784, p-value = 0.01654
bartlett.test(y ~niveis, data = dic)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  y by niveis
## Bartlett's K-squared = 0.4424, df = 4, p-value = 0.9789
LSD.test(mod1, "niveis", p.adj="bon", console=TRUE)
## 
## Study: mod1 ~ "niveis"
## 
## LSD t Test for y 
## P value adjustment method: bonferroni 
## 
## Mean Square Error:  0.261 
## 
## niveis,  means and individual ( 95 %) CI
## 
##        y       std r      LCL      UCL Min Max
## T1 5.250 0.5196152 4 4.705541 5.794459 4.6 5.8
## T2 6.775 0.5439056 4 6.230541 7.319459 6.0 7.2
## T3 6.650 0.6027714 4 6.105541 7.194459 5.8 7.2
## T4 5.525 0.4349329 4 4.980541 6.069459 4.9 5.9
## T5 6.400 0.4320494 4 5.855541 6.944459 5.8 6.8
## 
## alpha: 0.05 ; Df Error: 15
## Critical Value of t: 3.286039 
## 
## Least Significant Difference 1.187074
## Means with the same letter are not significantly different.
## 
## Groups, Treatments and means
## a     T2      6.775 
## ab    T3      6.65 
## abc   T5      6.4 
## bc    T4      5.525 
## c     T1      5.25
test1 = LSD.test(mod1, "niveis", p.adj="bon", console=TRUE)
## 
## Study: mod1 ~ "niveis"
## 
## LSD t Test for y 
## P value adjustment method: bonferroni 
## 
## Mean Square Error:  0.261 
## 
## niveis,  means and individual ( 95 %) CI
## 
##        y       std r      LCL      UCL Min Max
## T1 5.250 0.5196152 4 4.705541 5.794459 4.6 5.8
## T2 6.775 0.5439056 4 6.230541 7.319459 6.0 7.2
## T3 6.650 0.6027714 4 6.105541 7.194459 5.8 7.2
## T4 5.525 0.4349329 4 4.980541 6.069459 4.9 5.9
## T5 6.400 0.4320494 4 5.855541 6.944459 5.8 6.8
## 
## alpha: 0.05 ; Df Error: 15
## Critical Value of t: 3.286039 
## 
## Least Significant Difference 1.187074
## Means with the same letter are not significantly different.
## 
## Groups, Treatments and means
## a     T2      6.775 
## ab    T3      6.65 
## abc   T5      6.4 
## bc    T4      5.525 
## c     T1      5.25
bar.group(test1$group, ylim=c(0,30))

test2 = TukeyHSD(mod1)
test2
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = y ~ niveis, data = dic)
## 
## $niveis
##         diff         lwr          upr     p adj
## T2-T1  1.525  0.40949396  2.640506042 0.0056636
## T3-T1  1.400  0.28449396  2.515506042 0.0110848
## T4-T1  0.275 -0.84050604  1.390506042 0.9378222
## T5-T1  1.150  0.03449396  2.265506042 0.0418184
## T3-T2 -0.125 -1.24050604  0.990506042 0.9965682
## T4-T2 -1.250 -2.36550604 -0.134493958 0.0247157
## T5-T2 -0.375 -1.49050604  0.740506042 0.8339632
## T4-T3 -1.125 -2.24050604 -0.009493958 0.0476084
## T5-T3 -0.250 -1.36550604  0.865506042 0.9551477
## T5-T4  0.875 -0.24050604  1.990506042 0.1626657
plot(test2)

teste3=HSD.test(mod1, "niveis", console=TRUE)
## 
## Study: mod1 ~ "niveis"
## 
## HSD Test for y 
## 
## Mean Square Error:  0.261 
## 
## niveis,  means
## 
##        y       std r Min Max
## T1 5.250 0.5196152 4 4.6 5.8
## T2 6.775 0.5439056 4 6.0 7.2
## T3 6.650 0.6027714 4 5.8 7.2
## T4 5.525 0.4349329 4 4.9 5.9
## T5 6.400 0.4320494 4 5.8 6.8
## 
## alpha: 0.05 ; Df Error: 15 
## Critical Value of Studentized Range: 4.366985 
## 
## Honestly Significant Difference: 1.115506 
## 
## Means with the same letter are not significantly different.
## 
## Groups, Treatments and means
## a     T2      6.775 
## a     T3      6.65 
## ab    T5      6.4 
## bc    T4      5.525 
## c     T1      5.25
bar.group(test1$group, ylim=c(0,30))