# DCA con diferente numero de repeticiones
# Ejemplo:5) Los datos corresponden al tiempo de coagulaci昼㸳n (en segundos) de sangre extra攼㹤da a 24 animales,
#asignados aleatoriamente a cuatro dietas diferentes.
#Dieta
#A B C D
#62 63 68 56
#60 67 66 62
#63 71 71 60
#59 64 67 61
# 65 68 63
# 66 68 64
# 63
# 59
#concen = tiempo
tiempo<-c(62,60,63,59,63,67,71,64,65,66,68,66,71,67
,68,68,56,62,60,61,63,64,63,59)
trat<-c(rep(1,4),rep(2,6),rep(3,6),rep(4,8))
trat
## [1] 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4
# creando un data.frame
datos<-data.frame(trat=factor(trat,labels = c("DIETA A","DIETA B","DIETA C","DIETA D")),tiempo)
datos
## trat tiempo
## 1 DIETA A 62
## 2 DIETA A 60
## 3 DIETA A 63
## 4 DIETA A 59
## 5 DIETA B 63
## 6 DIETA B 67
## 7 DIETA B 71
## 8 DIETA B 64
## 9 DIETA B 65
## 10 DIETA B 66
## 11 DIETA C 68
## 12 DIETA C 66
## 13 DIETA C 71
## 14 DIETA C 67
## 15 DIETA C 68
## 16 DIETA C 68
## 17 DIETA D 56
## 18 DIETA D 62
## 19 DIETA D 60
## 20 DIETA D 61
## 21 DIETA D 63
## 22 DIETA D 64
## 23 DIETA D 63
## 24 DIETA D 59
# Diagrama de cajas
plot(datos,col=terrain.colors(4))
# cuadro ANVA
resp<-aov(tiempo~trat,data=datos)
anova(resp)
## Analysis of Variance Table
##
## Response: tiempo
## Df Sum Sq Mean Sq F value Pr(>F)
## trat 3 228 76.0 13.571 4.658e-05 ***
## Residuals 20 112 5.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# residuales e IC
resp<-lm(tiempo~trat-1,data=datos)
summary(resp)
##
## Call:
## lm(formula = tiempo ~ trat - 1, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.00 -1.25 0.00 1.25 5.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## tratDIETA A 61.0000 1.1832 51.55 <2e-16 ***
## tratDIETA B 66.0000 0.9661 68.32 <2e-16 ***
## tratDIETA C 68.0000 0.9661 70.39 <2e-16 ***
## tratDIETA D 61.0000 0.8367 72.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.366 on 20 degrees of freedom
## Multiple R-squared: 0.9989, Adjusted R-squared: 0.9986
## F-statistic: 4399 on 4 and 20 DF, p-value: < 2.2e-16
# intervalos de confianza
confint(resp,level=0.99)
## 0.5 % 99.5 %
## tratDIETA A 57.63335 64.36665
## tratDIETA B 63.25114 68.74886
## tratDIETA C 65.25114 70.74886
## tratDIETA D 58.61942 63.38058
# histograma de frecuencias
h<-hist(resp$residuals, col=terrain.colors(10))
xfit <- seq(min(resp$residuals), max(resp$residuals),length = 20)
yfit <- dnorm(xfit,mean=mean(resp$residuals),sd=sd(resp$residuals))
yfit <- yfit*diff(h$mids[1:2])*length(resp$residuals)
lines(xfit, yfit, col = "blue", lwd = 2)
# graficos de probabilidad normal
qqnorm(resp$residuals)
qqline(resp$residuals,col="blue", lwd=2)
# test de normalidad
shapiro.test(resp$residuals)
##
## Shapiro-Wilk normality test
##
## data: resp$residuals
## W = 0.97831, p-value = 0.8629
# grafico de residuales
plot(resp$fitted.values,resp$residuals,main="Estimado vs
Residual")
abline(h=0,lty=2)
#
plot(resp$residuals~trat,main="Tratamiento vs Residual")
#test de homogeneidad de varianzas
bartlett.test(tiempo~trat)
##
## Bartlett test of homogeneity of variances
##
## data: tiempo by trat
## Bartlett's K-squared = 1.668, df = 3, p-value = 0.6441
# independencia
plot(resp$residuals,xlab="Orden de corrida")
abline(h=0,lty=2)
# test de Durwin Watson
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(lmtest)
dwtest(resp)
##
## Durbin-Watson test
##
## data: resp
## DW = 2.2054, p-value = 0.4505
## alternative hypothesis: true autocorrelation is greater than 0
# comparaciones multiples
library(agricolae)
# LSDL
LSD.test(resp,"trat",alpha=0.05,console=TRUE)
##
## Study: resp ~ "trat"
##
## LSD t Test for tiempo
##
## Mean Square Error: 5.6
##
## trat, means and individual ( 95 %) CI
##
## tiempo std r LCL UCL Min Max
## DIETA A 61 1.825742 4 58.53185 63.46815 59 63
## DIETA B 66 2.828427 6 63.98477 68.01523 63 71
## DIETA C 68 1.673320 6 65.98477 70.01523 66 71
## DIETA D 61 2.618615 8 59.25476 62.74524 56 64
##
## Alpha: 0.05 ; DF Error: 20
## Critical Value of t: 2.085963
##
## Groups according to probability of means differences and alpha level( 0.05 )
##
## Treatments with the same letter are not significantly different.
##
## tiempo groups
## DIETA C 68 a
## DIETA B 66 a
## DIETA A 61 b
## DIETA D 61 b
# duncan test
duncan.test(resp,"trat",alpha=0.05,console=TRUE)
##
## Study: resp ~ "trat"
##
## Duncan's new multiple range test
## for tiempo
##
## Mean Square Error: 5.6
##
## trat, means
##
## tiempo std r Min Max
## DIETA A 61 1.825742 4 59 63
## DIETA B 66 2.828427 6 63 71
## DIETA C 68 1.673320 6 66 71
## DIETA D 61 2.618615 8 56 64
##
## Groups according to probability of means differences and alpha level( 0.05 )
##
## Means with the same letter are not significantly different.
##
## tiempo groups
## DIETA C 68 a
## DIETA B 66 a
## DIETA A 61 b
## DIETA D 61 b
# tukey test
cmT <- HSD.test(resp, "trat", console=TRUE)
##
## Study: resp ~ "trat"
##
## HSD Test for tiempo
##
## Mean Square Error: 5.6
##
## trat, means
##
## tiempo std r Min Max
## DIETA A 61 1.825742 4 59 63
## DIETA B 66 2.828427 6 63 71
## DIETA C 68 1.673320 6 66 71
## DIETA D 61 2.618615 8 56 64
##
## Alpha: 0.05 ; DF Error: 20
## Critical Value of Studentized Range: 3.958293
##
## Groups according to probability of means differences and alpha level( 0.05 )
##
## Treatments with the same letter are not significantly different.
##
## tiempo groups
## DIETA C 68 a
## DIETA B 66 a
## DIETA A 61 b
## DIETA D 61 b