Tugas Praktikum Uji Asumsi – Metode Perancangan Percobaan
Shafi Faris Arif Rabbani
2025-02-25
Sumber : Journal of Technology and Food Processing (JTFP) “Rancangan Acak Lengkap Dan Rancangan Acak Kelompok Pada pH Gelatin Kulit Domba Dengan Pretreatment Larutan NaOH” Klik di sini
IMPORT DATA
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdata_ph <- read_xlsx("D:/M S I/Documents/Data pH Gelatin pada Domba dengan Pretreatment Larutan NaOH.xlsx")
data_ph## # A tibble: 16 × 3
## NaOH Kelompok `Hasil Pengukuran`
## <dbl> <dbl> <dbl>
## 1 0.5 1 5.37
## 2 0.5 2 5.39
## 3 0.5 3 5.36
## 4 0.5 4 5.38
## 5 1 1 5.29
## 6 1 2 5.33
## 7 1 3 5.31
## 8 1 4 5.28
## 9 1.5 1 5.16
## 10 1.5 2 5.21
## 11 1.5 3 5.19
## 12 1.5 4 5.23
## 13 2 1 5.02
## 14 2 2 5.14
## 15 2 3 5.09
## 16 2 4 5.13data_ph$NaOH <- as.numeric(data_ph$NaOH)
data_ph$Kelompok <- as.numeric(data_ph$Kelompok)
data_ph$`Hasil Pengukuran` <- as.numeric(data_ph$`Hasil Pengukuran`)ANOVA
data_ph$NaOH <- as.factor(data_ph$NaOH)
data_ph$Kelompok <- as.factor(data_ph$Kelompok)anova_pH <- aov(`Hasil Pengukuran` ~ Kelompok + NaOH, data = data_ph)
summary(anova_pH)## Df Sum Sq Mean Sq F value Pr(>F)
## Kelompok 3 0.00745 0.00248 3.664 0.0566 .
## NaOH 3 0.17975 0.05992 88.402 5.37e-07 ***
## Residuals 9 0.00610 0.00068
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1F_tabelkelompok <- qf(0.05,3,9,lower.tail = FALSE)
F_tabelkelompok## [1] 3.862548F_tabelNaOH <- qf(0.05,3,9,lower.tail = FALSE)
F_tabelNaOH## [1] 3.862548F-hit NaOH>F-tabel 5%, sehingga terdapat cukup bukti untuk perlakuan NaOH sangat mempengaruhi kualitas pH gelatin kulit domba, dan berarti ada pula salah satu perlakuan larutan NaOH yang pengaruhnya sangat menonjol jika dibandingkan dengan perlakuan larutan NaOH yang lain.
F-hit kelompok<F-tabel 5%, sehingga terdapat cukup bukti untuk menyatakan bahwa proses pengelompokan data tidak memberikan pengaruh terhadap kualitas pH gelatin kulit domba.
ASUMSI KENORMALAN
Eksploratif
Normal Probability (Q-Q) Plot
plot(anova_pH, which = 2)
qqnorm(anova_pH$residuals); qqline(anova_pH$residuals, col = 'green')
### HISTOGRAM
hist(anova_pH$residuals,breaks = 6)
## Uji Formal dengan Uji Shapiro-Wilk Hipotesis : H0 : Sisaan menyebar
normal H1 : Sisaan tidak menyebar normal
shapiro.test(x = anova_pH$residuals)##
## Shapiro-Wilk normality test
##
## data: anova_pH$residuals
## W = 0.92647, p-value = 0.2143Berdasarkan uji Shapiro-Wilk, didapatkan p-value = 0.2143 > α = 0.05, maka tidak tolak H0, sehingga dapat disimpulkan bahwa sisaan berdistribusi normal pada taraf nyata 5%.
Nilai Harapan Sisan = 0
t.test(anova_pH$residuals, mu = 0, conf.level = 0.95) ##
## One Sample t-test
##
## data: anova_pH$residuals
## t = 2.0968e-16, df = 15, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.01074569 0.01074569
## sample estimates:
## mean of x
## 1.057097e-18Berdasarkan uji t, didapatkan p−value = 1 > α = 0.05 yang artinya tidak tolak H0, sehingga dapat disimpulkan bahwa pada taraf nyata 5%, belum cukup bukti untuk menyatakan bahwa nilai harapan sisaan tidak sama dengan 0.
Asumsi Kehomegenan Ragam
Eksploratif
Plot Residual vs Fitted Value
plot(anova_pH,which=1)
## Uji Formal dengan Bartlett-test## Hipotesis: H0 : Ragam sisaan
homogen. H1 : Ragam sisaan tidak homogen.
bartlett.test(`Hasil Pengukuran` ~ NaOH, data = data_ph)##
## Bartlett test of homogeneity of variances
##
## data: Hasil Pengukuran by NaOH
## Bartlett's K-squared = 5.3074, df = 3, p-value = 0.1506bartlett.test(`Hasil Pengukuran` ~ Kelompok, data = data_ph)##
## Bartlett test of homogeneity of variances
##
## data: Hasil Pengukuran by Kelompok
## Bartlett's K-squared = 0.4633, df = 3, p-value = 0.9269Berdasarkan uji Bartlett-test, didapatkan p−value = 0.1506 dan 0.9269 > α=0.05, maka tidak tolak H0, sehingga dapat disimpulkan bahwa ragam sisaan perlakuan dan kelompok homogen pada taraf nyata 5%.
Asumsi Saling Bebas
Ekploratif
Plot Sisaan vs Order
plot(anova_pH$residuals, type = 'o'); abline(h = 0, col = 'red')
Berdasarkan plot Sisaan vs Order, terlihat bahwa sisaanya membentuk pola
yang stasioner (bergerak di sekitar titik 0) sehingga dapat dikatakan
sisaan saling bebas.
Plot ACF
acf(anova_pH$residuals)
Berdasarkan plot ACF, terlihat tidak ada autokorelasi karena garis
vertikal di tiap lag tidak lebih tinggi dari garis biru horizontal.
Plot PACF
pacf(anova_pH$residuals)
Berdasarkan plot PACF, terlihat tidak ada autokorelasi karena garis
vertikal di tiap lag tidak lebih tinggi dari garis biru horizontal.
Uji Formal dengan Durbin-Watson test
library(car)## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.3.3##
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## somedurbinWatsonTest(anova_pH)## lag Autocorrelation D-W Statistic p-value
## 1 -0.3422131 2.477459 0.784
## Alternative hypothesis: rho != 0Berdasarkan uji Durbin-Watson pada library car, didapatkan p−value = 0.864 > α=0.05, maka tak tolak H0, sehingga dapat disimpulkan bahwa sisaan saling bebas pada taraf nyata 5%
Asumsi Keaditifan
Eksplorasi
library(ggplot2)
ggplot(data_ph, aes(x = NaOH, y = `Hasil Pengukuran`, colour = Kelompok)) +
geom_point(data = data_ph, aes(y = `Hasil Pengukuran`)) +
geom_line(data = data_ph, aes(y = `Hasil Pengukuran`, group = Kelompok)) +
theme_bw()
Grafik menunjukkan bahwa peningkatan konsentrasi NaOH menyebabkan
penurunan hasil pengukuran di semua kelompok. Meskipun tren penurunan
serupa, terdapat variasi antar kelompok dalam tingkat penurunan. Hal ini
mengindikasikan bahwa NaOH memiliki efek negatif terhadap variabel yang
diukur.
Uji Formal dengan Uji Tukey
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## smithslibrary(additivityTests)## Warning: package 'additivityTests' was built under R version 4.3.3anova_pH_wide <- dcast(data_ph, Kelompok~NaOH,value.var="Hasil Pengukuran")
Y<-as.matrix(anova_pH_wide[-1])
tukey.test(Y,alpha=0.05)##
## Tukey test on 5% alpha-level:
##
## Test statistic: 11.29
## Critival value: 5.318
## The additivity hypothesis was rejected.Berdasarkan uji Tukey, Fhitung = 11.29 > Ftabel = 5.318 maka tolak H0, sehingga pada taraf nyata 5%, dapat disimpulkan bahwa model tidak aditif.
Uji Lanjut (Duncan-test)
library(agricolae)## Warning: package 'agricolae' was built under R version 4.3.3hasil_duncan_NaOH <- duncan.test(anova_pH, "NaOH", alpha = 0.05)
print(hasil_duncan_NaOH)## $statistics
## MSerror Df Mean CV
## 0.0006777778 9 5.2425 0.4965983
##
## $parameters
## test name.t ntr alpha
## Duncan NaOH 4 0.05
##
## $duncan
## Table CriticalRange
## 2 3.199173 0.04164390
## 3 3.339138 0.04346583
## 4 3.419765 0.04451536
##
## $means
## Hasil Pengukuran std r se Min Max Q25 Q50 Q75
## 0.5 5.3750 0.01290994 4 0.01301708 5.36 5.39 5.3675 5.375 5.3825
## 1 5.3025 0.02217356 4 0.01301708 5.28 5.33 5.2875 5.300 5.3150
## 1.5 5.1975 0.02986079 4 0.01301708 5.16 5.23 5.1825 5.200 5.2150
## 2 5.0950 0.05446712 4 0.01301708 5.02 5.14 5.0725 5.110 5.1325
##
## $comparison
## NULL
##
## $groups
## Hasil Pengukuran groups
## 0.5 5.3750 a
## 1 5.3025 b
## 1.5 5.1975 c
## 2 5.0950 d
##
## attr(,"class")
## [1] "group"Konsentrasi NaOH berpengaruh signifikan terhadap hasil pengukuran (p < 0.001), dengan tren bahwa semakin tinggi konsentrasi NaOH, semakin rendah hasil pengukuran. Model tidak aditif, menunjukkan kemungkinan adanya interaksi faktor lain. Data memenuhi asumsi normalitas dan homogenitas varians, sehingga hasil ANOVA valid. Uji Duncan menunjukkan perbedaan signifikan antar kelompok, dengan NaOH 0.5 menghasilkan nilai tertinggi dan NaOH 2.0 terendah.