karakteristik <- c(14,12,13,11,17,14,11,12,14,13,11,10,13,13,12,12,12,10,9,8)
aditif <- factor(c(2,3,4,5,1,2,4,5,1,3,4,5,1,2,3,4,1,2,3,5))
mobil <- factor(c(rep(1,4),rep(2,4),rep(3,4),rep(4,4), rep(5,4)))
dat <- data.frame(karakteristik,aditif,mobil)
dat
## karakteristik aditif mobil
## 1 14 2 1
## 2 12 3 1
## 3 13 4 1
## 4 11 5 1
## 5 17 1 2
## 6 14 2 2
## 7 11 4 2
## 8 12 5 2
## 9 14 1 3
## 10 13 3 3
## 11 11 4 3
## 12 10 5 3
## 13 13 1 4
## 14 13 2 4
## 15 12 3 4
## 16 12 4 4
## 17 12 1 5
## 18 10 2 5
## 19 9 3 5
## 20 8 5 5
#correct model
mod<-lm(karakteristik~mobil+aditif, data=dat)
anova(mod)
## Analysis of Variance Table
##
## Response: karakteristik
## Df Sum Sq Mean Sq F value Pr(>F)
## mobil 4 31.200 7.8000 8.5657 0.002158 **
## aditif 4 35.733 8.9333 9.8103 0.001247 **
## Residuals 11 10.017 0.9106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qf(0.95, df1=4, df2=7)
## [1] 4.120312
#p-value
1-pf(9.81, df1=4, df2=7)
## [1] 0.005359056
#Alternatif fungsi lm di R, dapat digunakan fungsi aov untuk memperoleh hasil analisis variansi dari BIBD
options(digits = 10)
mod2 <- aov(karakteristik~mobil+aditif)
summary(mod2)
## Df Sum Sq Mean Sq F value Pr(>F)
## mobil 4 31.20000 7.800000 8.56572 0.0021578 **
## aditif 4 35.73333 8.933333 9.81032 0.0012467 **
## Residuals 11 10.01667 0.910606
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Interval kepercayaan 95% bagi Tau i - Tau j dengan prosedur tukey
qtukey(0.95,nmeans = 5, df = 11)
## [1] 4.573596254
library(multcomp)
## Warning: package 'multcomp' was built under R version 4.4.1
## Loading required package: mvtnorm
## Warning: package 'mvtnorm' was built under R version 4.4.1
## Loading required package: survival
## Loading required package: TH.data
## Warning: package 'TH.data' was built under R version 4.4.1
## Loading required package: MASS
##
## Attaching package: 'TH.data'
## The following object is masked from 'package:MASS':
##
## geyser
contr <- glht(mod2, linfct = mcp(aditif = "Tukey"))
summary(contr)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: aov(formula = karakteristik ~ mobil + aditif)
##
## Linear Hypotheses:
## Estimate Std. Error t value Pr(>|t|)
## 2 - 1 == 0 -1.4666667 0.6968906 -2.10459 0.2837969
## 3 - 1 == 0 -2.4000000 0.6968906 -3.44387 0.0355415 *
## 4 - 1 == 0 -3.1333333 0.6968906 -4.49616 0.0065177 **
## 5 - 1 == 0 -4.0000000 0.6968906 -5.73978 < 0.001 ***
## 3 - 2 == 0 -0.9333333 0.6968906 -1.33928 0.6745762
## 4 - 2 == 0 -1.6666667 0.6968906 -2.39158 0.1883599
## 5 - 2 == 0 -2.5333333 0.6968906 -3.63519 0.0258461 *
## 4 - 3 == 0 -0.7333333 0.6968906 -1.05229 0.8262270
## 5 - 3 == 0 -1.6000000 0.6968906 -2.29591 0.2167189
## 5 - 4 == 0 -0.8666667 0.6968906 -1.24362 0.7279676
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
confint(contr)
##
## Simultaneous Confidence Intervals
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: aov(formula = karakteristik ~ mobil + aditif)
##
## Quantile = 3.2353434
## 95% family-wise confidence level
##
##
## Linear Hypotheses:
## Estimate lwr upr
## 2 - 1 == 0 -1.4666667 -3.7213472 0.7880139
## 3 - 1 == 0 -2.4000000 -4.6546805 -0.1453195
## 4 - 1 == 0 -3.1333333 -5.3880139 -0.8786528
## 5 - 1 == 0 -4.0000000 -6.2546805 -1.7453195
## 3 - 2 == 0 -0.9333333 -3.1880139 1.3213472
## 4 - 2 == 0 -1.6666667 -3.9213472 0.5880139
## 5 - 2 == 0 -2.5333333 -4.7880139 -0.2786528
## 4 - 3 == 0 -0.7333333 -2.9880139 1.5213472
## 5 - 3 == 0 -1.6000000 -3.8546805 0.6546805
## 5 - 4 == 0 -0.8666667 -3.1213472 1.3880139
library(ggplot2)
library(ggpubr)
## Warning: package 'ggpubr' was built under R version 4.4.1
ggplot(data=dat,aes(x=aditif,y=karakteristik))+
geom_boxplot()+
labs(x = "Aditif", y="karakteristik")
library(ggplot2)
library(ggpubr)
ggplot(data=dat,aes(x=mobil,y=karakteristik))+
geom_boxplot()+
labs(x = "mobil", y="karakteristik")
#p-value
1-pf(9.81, df1=4, df2=7)
## [1] 0.00535905595
#Pengecekan asumsi-asumsi dalam BIBD
shapiro.test(residuals(mod))
##
## Shapiro-Wilk normality test
##
## data: residuals(mod)
## W = 0.9649207, p-value = 0.6460521
plot(mod,2)
#homogenitas
plot(fitted.values(mod),residuals(mod),xlab="Nilai
dugaan",ylab="Residual")
abline(h=0,lty="dashed")
#Cek ada pengaruh interaksi antara Aditif dan mobil
with(dat,interaction.plot(aditif,mobil,karakteristik))
