Praktikum 9 soal Pak Budi
M. Ainur Rohim [A2503241023]
2024-10-26
#Rancangan Acak Kelompok Faktorial RAKL#
df <- read.csv("C:/Users/ma.rohim.EWSI/Downloads/Prak9.csv", sep = ";")
str(df)## 'data.frame': 48 obs. of 4 variables:
## $ Pupuk : chr "a0" "a0" "a0" "a0" ...
## $ Kapur : chr "b0" "b0" "b0" "b1" ...
## $ Kelompok: int 1 2 3 1 2 3 1 2 3 1 ...
## $ Yield : num 2.1 3.1 3.3 2.3 2.9 3.7 2.5 3 3.8 2 ...df## Pupuk Kapur Kelompok Yield
## 1 a0 b0 1 2.1
## 2 a0 b0 2 3.1
## 3 a0 b0 3 3.3
## 4 a0 b1 1 2.3
## 5 a0 b1 2 2.9
## 6 a0 b1 3 3.7
## 7 a0 b2 1 2.5
## 8 a0 b2 2 3.0
## 9 a0 b2 3 3.8
## 10 a0 b3 1 2.0
## 11 a0 b3 2 1.5
## 12 a0 b3 3 1.7
## 13 a1 b0 1 3.1
## 14 a1 b0 2 3.2
## 15 a1 b0 3 3.4
## 16 a1 b1 1 3.3
## 17 a1 b1 2 3.9
## 18 a1 b1 3 3.8
## 19 a1 b2 1 3.7
## 20 a1 b2 2 3.8
## 21 a1 b2 3 3.6
## 22 a1 b3 1 3.5
## 23 a1 b3 2 3.2
## 24 a1 b3 3 3.3
## 25 a2 b0 1 4.0
## 26 a2 b0 2 4.5
## 27 a2 b0 3 4.1
## 28 a2 b1 1 4.7
## 29 a2 b1 2 5.1
## 30 a2 b1 3 5.2
## 31 a2 b2 1 7.5
## 32 a2 b2 2 8.1
## 33 a2 b2 3 7.6
## 34 a2 b3 1 7.6
## 35 a2 b3 2 7.9
## 36 a2 b3 3 7.9
## 37 a3 b0 1 4.2
## 38 a3 b0 2 4.1
## 39 a3 b0 3 4.2
## 40 a3 b1 1 4.5
## 41 a3 b1 2 4.7
## 42 a3 b1 3 4.5
## 43 a3 b2 1 6.2
## 44 a3 b2 2 6.3
## 45 a3 b2 3 6.0
## 46 a3 b3 1 6.0
## 47 a3 b3 2 6.0
## 48 a3 b3 3 6.1# Mengubah variabel menjadi faktor
df$Pupuk <- as.factor(df$Pupuk)
df$Kapur <- as.factor(df$Kapur)
df$Kelompok <- as.factor(df$Kelompok)#plot interaksi
interaction.plot(df$Pupuk,df$Kapur, df$Yield,
type="l", main="Plot interaksi Pupuk dan Kapur",xlab="Pupuk",
ylab="Yield", trace.label="Kapur", col=1:3)
# Menggunakan fungsi aggregate untuk menghitung rata-rata Berat berdasarkan interaksi SM dan SS
interaction_table <- aggregate(Yield ~ Pupuk + Kapur, data = df, FUN = mean)
# Menampilkan tabel interaksi
interaction_table## Pupuk Kapur Yield
## 1 a0 b0 2.833333
## 2 a1 b0 3.233333
## 3 a2 b0 4.200000
## 4 a3 b0 4.166667
## 5 a0 b1 2.966667
## 6 a1 b1 3.666667
## 7 a2 b1 5.000000
## 8 a3 b1 4.566667
## 9 a0 b2 3.100000
## 10 a1 b2 3.700000
## 11 a2 b2 7.733333
## 12 a3 b2 6.166667
## 13 a0 b3 1.733333
## 14 a1 b3 3.333333
## 15 a2 b3 7.800000
## 16 a3 b3 6.033333#---Analisis ragam---#
model_FRAK<-aov(Yield ~ Pupuk * Kapur + Kelompok, data = df)
summary(model_FRAK)## Df Sum Sq Mean Sq F value Pr(>F)
## Pupuk 3 92.98 30.992 324.475 < 2e-16 ***
## Kapur 3 17.46 5.820 60.936 7.20e-13 ***
## Kelompok 2 0.89 0.444 4.648 0.0174 *
## Pupuk:Kapur 9 26.90 2.988 31.287 7.42e-13 ***
## Residuals 30 2.87 0.096
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(DescTools)## Warning: package 'DescTools' was built under R version 4.3.3PostHocTest(model_FRAK, method = 'hsd')##
## Posthoc multiple comparisons of means : Tukey HSD
## 95% family-wise confidence level
##
## $Pupuk
## diff lwr.ci upr.ci pval
## a1-a0 0.825 0.4819288 1.1680712 1.8e-06 ***
## a2-a0 3.525 3.1819288 3.8680712 4.6e-14 ***
## a3-a0 2.575 2.2319288 2.9180712 4.6e-14 ***
## a2-a1 2.700 2.3569288 3.0430712 4.6e-14 ***
## a3-a1 1.750 1.4069288 2.0930712 1.3e-13 ***
## a3-a2 -0.950 -1.2930712 -0.6069288 1.3e-07 ***
##
## $Kapur
## diff lwr.ci upr.ci pval
## b1-b0 0.4416667 0.09859542 0.7847379 0.0076 **
## b2-b0 1.5666667 1.22359542 1.9097379 1.5e-12 ***
## b3-b0 1.1166667 0.77359542 1.4597379 4.3e-09 ***
## b2-b1 1.1250000 0.78192876 1.4680712 3.6e-09 ***
## b3-b1 0.6750000 0.33192876 1.0180712 4.9e-05 ***
## b3-b2 -0.4500000 -0.79307124 -0.1069288 0.0064 **
##
## $Kelompok
## diff lwr.ci upr.ci pval
## 2-1 0.25625 -0.01312233 0.5256223 0.0647 .
## 3-1 0.31250 0.04312767 0.5818723 0.0203 *
## 3-2 0.05625 -0.21312233 0.3256223 0.8647
##
## $`Pupuk:Kapur`
## diff lwr.ci upr.ci pval
## a1:b0-a0:b0 0.40000000 -0.54056014 1.34056014 0.95913
## a2:b0-a0:b0 1.36666667 0.42610652 2.30722681 0.00065 ***
## a3:b0-a0:b0 1.33333333 0.39277319 2.27389348 0.00093 ***
## a0:b1-a0:b0 0.13333333 -0.80722681 1.07389348 1.00000
## a1:b1-a0:b0 0.83333333 -0.10722681 1.77389348 0.12670
## a2:b1-a0:b0 2.16666667 1.22610652 3.10722681 1.5e-07 ***
## a3:b1-a0:b0 1.73333333 0.79277319 2.67389348 1.3e-05 ***
## a0:b2-a0:b0 0.26666667 -0.67389348 1.20722681 0.99916
## a1:b2-a0:b0 0.86666667 -0.07389348 1.80722681 0.09603 .
## a2:b2-a0:b0 4.90000000 3.95943986 5.84056014 4.6e-14 ***
## a3:b2-a0:b0 3.33333333 2.39277319 4.27389348 5.6e-12 ***
## a0:b3-a0:b0 -1.10000000 -2.04056014 -0.15943986 0.01070 *
## a1:b3-a0:b0 0.50000000 -0.44056014 1.44056014 0.81689
## a2:b3-a0:b0 4.96666667 4.02610652 5.90722681 4.6e-14 ***
## a3:b3-a0:b0 3.20000000 2.25943986 4.14056014 1.6e-11 ***
## a2:b0-a1:b0 0.96666667 0.02610652 1.90722681 0.03927 *
## a3:b0-a1:b0 0.93333333 -0.00722681 1.87389348 0.05341 .
## a0:b1-a1:b0 -0.26666667 -1.20722681 0.67389348 0.99916
## a1:b1-a1:b0 0.43333333 -0.50722681 1.37389348 0.92581
## a2:b1-a1:b0 1.76666667 0.82610652 2.70722681 9.0e-06 ***
## a3:b1-a1:b0 1.33333333 0.39277319 2.27389348 0.00093 ***
## a0:b2-a1:b0 -0.13333333 -1.07389348 0.80722681 1.00000
## a1:b2-a1:b0 0.46666667 -0.47389348 1.40722681 0.87836
## a2:b2-a1:b0 4.50000000 3.55943986 5.44056014 4.8e-14 ***
## a3:b2-a1:b0 2.93333333 1.99277319 3.87389348 1.4e-10 ***
## a0:b3-a1:b0 -1.50000000 -2.44056014 -0.55943986 0.00016 ***
## a1:b3-a1:b0 0.10000000 -0.84056014 1.04056014 1.00000
## a2:b3-a1:b0 4.56666667 3.62610652 5.50722681 4.7e-14 ***
## a3:b3-a1:b0 2.80000000 1.85943986 3.74056014 4.3e-10 ***
## a3:b0-a2:b0 -0.03333333 -0.97389348 0.90722681 1.00000
## a0:b1-a2:b0 -1.23333333 -2.17389348 -0.29277319 0.00270 **
## a1:b1-a2:b0 -0.53333333 -1.47389348 0.40722681 0.74344
## a2:b1-a2:b0 0.80000000 -0.14056014 1.74056014 0.16509
## a3:b1-a2:b0 0.36666667 -0.57389348 1.30722681 0.98007
## a0:b2-a2:b0 -1.10000000 -2.04056014 -0.15943986 0.01070 *
## a1:b2-a2:b0 -0.50000000 -1.44056014 0.44056014 0.81689
## a2:b2-a2:b0 3.53333333 2.59277319 4.47389348 1.3e-12 ***
## a3:b2-a2:b0 1.96666667 1.02610652 2.90722681 1.1e-06 ***
## a0:b3-a2:b0 -2.46666667 -3.40722681 -1.52610652 8.5e-09 ***
## a1:b3-a2:b0 -0.86666667 -1.80722681 0.07389348 0.09603 .
## a2:b3-a2:b0 3.60000000 2.65943986 4.54056014 8.1e-13 ***
## a3:b3-a2:b0 1.83333333 0.89277319 2.77389348 4.5e-06 ***
## a0:b1-a3:b0 -1.20000000 -2.14056014 -0.25943986 0.00383 **
## a1:b1-a3:b0 -0.50000000 -1.44056014 0.44056014 0.81689
## a2:b1-a3:b0 0.83333333 -0.10722681 1.77389348 0.12670
## a3:b1-a3:b0 0.40000000 -0.54056014 1.34056014 0.95913
## a0:b2-a3:b0 -1.06666667 -2.00722681 -0.12610652 0.01494 *
## a1:b2-a3:b0 -0.46666667 -1.40722681 0.47389348 0.87836
## a2:b2-a3:b0 3.56666667 2.62610652 4.50722681 1.0e-12 ***
## a3:b2-a3:b0 2.00000000 1.05943986 2.94056014 8.0e-07 ***
## a0:b3-a3:b0 -2.43333333 -3.37389348 -1.49277319 1.2e-08 ***
## a1:b3-a3:b0 -0.83333333 -1.77389348 0.10722681 0.12670
## a2:b3-a3:b0 3.63333333 2.69277319 4.57389348 6.4e-13 ***
## a3:b3-a3:b0 1.86666667 0.92610652 2.80722681 3.2e-06 ***
## a1:b1-a0:b1 0.70000000 -0.24056014 1.64056014 0.33437
## a2:b1-a0:b1 2.03333333 1.09277319 2.97389348 5.7e-07 ***
## a3:b1-a0:b1 1.60000000 0.65943986 2.54056014 5.3e-05 ***
## a0:b2-a0:b1 0.13333333 -0.80722681 1.07389348 1.00000
## a1:b2-a0:b1 0.73333333 -0.20722681 1.67389348 0.26858
## a2:b2-a0:b1 4.76666667 3.82610652 5.70722681 4.7e-14 ***
## a3:b2-a0:b1 3.20000000 2.25943986 4.14056014 1.6e-11 ***
## a0:b3-a0:b1 -1.23333333 -2.17389348 -0.29277319 0.00270 **
## a1:b3-a0:b1 0.36666667 -0.57389348 1.30722681 0.98007
## a2:b3-a0:b1 4.83333333 3.89277319 5.77389348 4.6e-14 ***
## a3:b3-a0:b1 3.06666667 2.12610652 4.00722681 4.6e-11 ***
## a2:b1-a1:b1 1.33333333 0.39277319 2.27389348 0.00093 ***
## a3:b1-a1:b1 0.90000000 -0.04056014 1.84056014 0.07197 .
## a0:b2-a1:b1 -0.56666667 -1.50722681 0.37389348 0.66160
## a1:b2-a1:b1 0.03333333 -0.90722681 0.97389348 1.00000
## a2:b2-a1:b1 4.06666667 3.12610652 5.00722681 7.5e-14 ***
## a3:b2-a1:b1 2.50000000 1.55943986 3.44056014 6.2e-09 ***
## a0:b3-a1:b1 -1.93333333 -2.87389348 -0.99277319 1.6e-06 ***
## a1:b3-a1:b1 -0.33333333 -1.27389348 0.60722681 0.99161
## a2:b3-a1:b1 4.13333333 3.19277319 5.07389348 6.5e-14 ***
## a3:b3-a1:b1 2.36666667 1.42610652 3.30722681 2.2e-08 ***
## a3:b1-a2:b1 -0.43333333 -1.37389348 0.50722681 0.92581
## a0:b2-a2:b1 -1.90000000 -2.84056014 -0.95943986 2.2e-06 ***
## a1:b2-a2:b1 -1.30000000 -2.24056014 -0.35943986 0.00133 **
## a2:b2-a2:b1 2.73333333 1.79277319 3.67389348 7.6e-10 ***
## a3:b2-a2:b1 1.16666667 0.22610652 2.10722681 0.00541 **
## a0:b3-a2:b1 -3.26666667 -4.20722681 -2.32610652 9.3e-12 ***
## a1:b3-a2:b1 -1.66666667 -2.60722681 -0.72610652 2.6e-05 ***
## a2:b3-a2:b1 2.80000000 1.85943986 3.74056014 4.3e-10 ***
## a3:b3-a2:b1 1.03333333 0.09277319 1.97389348 0.02076 *
## a0:b2-a3:b1 -1.46666667 -2.40722681 -0.52610652 0.00022 ***
## a1:b2-a3:b1 -0.86666667 -1.80722681 0.07389348 0.09603 .
## a2:b2-a3:b1 3.16666667 2.22610652 4.10722681 2.0e-11 ***
## a3:b2-a3:b1 1.60000000 0.65943986 2.54056014 5.3e-05 ***
## a0:b3-a3:b1 -2.83333333 -3.77389348 -1.89277319 3.2e-10 ***
## a1:b3-a3:b1 -1.23333333 -2.17389348 -0.29277319 0.00270 **
## a2:b3-a3:b1 3.23333333 2.29277319 4.17389348 1.2e-11 ***
## a3:b3-a3:b1 1.46666667 0.52610652 2.40722681 0.00022 ***
## a1:b2-a0:b2 0.60000000 -0.34056014 1.54056014 0.57573
## a2:b2-a0:b2 4.63333333 3.69277319 5.57389348 4.7e-14 ***
## a3:b2-a0:b2 3.06666667 2.12610652 4.00722681 4.6e-11 ***
## a0:b3-a0:b2 -1.36666667 -2.30722681 -0.42610652 0.00065 ***
## a1:b3-a0:b2 0.23333333 -0.70722681 1.17389348 0.99982
## a2:b3-a0:b2 4.70000000 3.75943986 5.64056014 4.7e-14 ***
## a3:b3-a0:b2 2.93333333 1.99277319 3.87389348 1.4e-10 ***
## a2:b2-a1:b2 4.03333333 3.09277319 4.97389348 8.2e-14 ***
## a3:b2-a1:b2 2.46666667 1.52610652 3.40722681 8.5e-09 ***
## a0:b3-a1:b2 -1.96666667 -2.90722681 -1.02610652 1.1e-06 ***
## a1:b3-a1:b2 -0.36666667 -1.30722681 0.57389348 0.98007
## a2:b3-a1:b2 4.10000000 3.15943986 5.04056014 7.0e-14 ***
## a3:b3-a1:b2 2.33333333 1.39277319 3.27389348 3.0e-08 ***
## a3:b2-a2:b2 -1.56666667 -2.50722681 -0.62610652 7.6e-05 ***
## a0:b3-a2:b2 -6.00000000 -6.94056014 -5.05943986 4.6e-14 ***
## a1:b3-a2:b2 -4.40000000 -5.34056014 -3.45943986 5.0e-14 ***
## a2:b3-a2:b2 0.06666667 -0.87389348 1.00722681 1.00000
## a3:b3-a2:b2 -1.70000000 -2.64056014 -0.75943986 1.8e-05 ***
## a0:b3-a3:b2 -4.43333333 -5.37389348 -3.49277319 4.9e-14 ***
## a1:b3-a3:b2 -2.83333333 -3.77389348 -1.89277319 3.2e-10 ***
## a2:b3-a3:b2 1.63333333 0.69277319 2.57389348 3.7e-05 ***
## a3:b3-a3:b2 -0.13333333 -1.07389348 0.80722681 1.00000
## a1:b3-a0:b3 1.60000000 0.65943986 2.54056014 5.3e-05 ***
## a2:b3-a0:b3 6.06666667 5.12610652 7.00722681 4.6e-14 ***
## a3:b3-a0:b3 4.30000000 3.35943986 5.24056014 5.2e-14 ***
## a2:b3-a1:b3 4.46666667 3.52610652 5.40722681 4.9e-14 ***
## a3:b3-a1:b3 2.70000000 1.75943986 3.64056014 1.0e-09 ***
## a3:b3-a2:b3 -1.76666667 -2.70722681 -0.82610652 9.0e-06 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#plot interval kepercayaan
plot(TukeyHSD(model_FRAK, conf.level= .95 ), las = 2 ) # las 2 artinya harus tegak lurus thd sumbu
library(sjPlot)## Warning: package 'sjPlot' was built under R version 4.3.3## Learn more about sjPlot with 'browseVignettes("sjPlot")'.library(fBasics)## Warning: package 'fBasics' was built under R version 4.3.3library(lmtest)## Warning: package 'lmtest' was built under R version 4.3.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.3.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(car)## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:fBasics':
##
## densityPlot## The following object is masked from 'package:DescTools':
##
## Recodeplot_model(model_FRAK,type = "diag")## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif## [[1]]
##
## [[2]]## `geom_smooth()` using formula = 'y ~ x'
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula = 'y ~ x'
vif(model_FRAK)## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif## GVIF Df GVIF^(1/(2*Df))
## Pupuk 64 3 2.000000
## Kapur 64 3 2.000000
## Kelompok 1 2 1.000000
## Pupuk:Kapur 1792 9 1.516146res <- residuals(model_FRAK)
shapiroTest(res)##
## Title:
## Shapiro - Wilk Normality Test
##
## Test Results:
## STATISTIC:
## W: 0.984
## P VALUE:
## 0.7497leveneTest(Yield~Pupuk*Kapur*Pupuk:Kapur, data=df)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 15 0.9768 0.4994
## 32library(doebioresearch)## Warning: package 'doebioresearch' was built under R version 4.3.3frbd2fact(df[4], df$Kelompok, df$Pupuk, df$Kapur, 3)## $Yield
## $Yield[[1]]
## Analysis of Variance Table
##
## Response: dependent.var
## Df Sum Sq Mean Sq F value Pr(>F)
## replicationvector 2 0.888 0.4440 4.6481 0.01744 *
## fact.A 3 92.976 30.9919 324.4751 < 2.2e-16 ***
## fact.B 3 17.461 5.8202 60.9357 7.200e-13 ***
## fact.A:fact.B 9 26.895 2.9884 31.2871 7.416e-13 ***
## Residuals 30 2.865 0.0955
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $Yield[[2]]
## [1] "R Square 0.98"
##
## $Yield[[3]]
## [1] "SEm of A: 0.089 , SEd of A: 0.126 , SEm of B: 0.089 , SEd of B 0.126 , SEm of AB: 0.178 , SEd of AB: 0.252"
##
## $Yield[[4]]
##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.984, p-value = 0.7497
##
##
## $Yield[[5]]
## [1] "Normality assumption is not violated"
##
## $Yield[[6]]
## [1] "The means of one or more levels of first factor are not same, so go for multiple comparison test"
##
## $Yield[[7]]
## $Yield[[7]][[1]]
## MSerror Df Mean CV MSD
## 0.09551389 30 4.389583 7.040605 0.3430712
##
## $Yield[[7]][[2]]
## test name.t ntr StudentizedRange alpha
## Tukey fact.A 4 3.845401 0.05
##
## $Yield[[7]][[3]]
## dependent.var groups
## a2 6.183333 a
## a3 5.233333 b
## a1 3.483333 c
## a0 2.658333 d
##
##
## $Yield[[8]]
## [1] "The means of one or more levels of second factor are not same, so go for multiple comparison test"
##
## $Yield[[9]]
## $Yield[[9]][[1]]
## MSerror Df Mean CV MSD
## 0.09551389 30 4.389583 7.040605 0.3430712
##
## $Yield[[9]][[2]]
## test name.t ntr StudentizedRange alpha
## Tukey fact.B 4 3.845401 0.05
##
## $Yield[[9]][[3]]
## dependent.var groups
## b2 5.175000 a
## b3 4.725000 b
## b1 4.050000 c
## b0 3.608333 d
##
##
## $Yield[[10]]
## [1] "The means of levels of interaction between two factors are not same, so go for multiple comparison test"
##
## $Yield[[11]]
## $Yield[[11]][[1]]
## MSerror Df Mean CV MSD
## 0.09551389 30 4.389583 7.040605 0.9405601
##
## $Yield[[11]][[2]]
## test name.t ntr StudentizedRange alpha
## Tukey fact.A:fact.B 16 5.271254 0.05
##
## $Yield[[11]][[3]]
## dependent.var groups
## a2:b3 7.800000 a
## a2:b2 7.733333 a
## a3:b2 6.166667 b
## a3:b3 6.033333 b
## a2:b1 5.000000 c
## a3:b1 4.566667 cd
## a2:b0 4.200000 cde
## a3:b0 4.166667 cdef
## a1:b2 3.700000 defg
## a1:b1 3.666667 defg
## a1:b3 3.333333 efg
## a1:b0 3.233333 fg
## a0:b2 3.100000 g
## a0:b1 2.966667 g
## a0:b0 2.833333 g
## a0:b3 1.733333 h