#0 Membuat Data Frame
data_pakan_ikan <- data.frame(
Jenis_Ikan = as.factor(rep(c("Lele", "Nila", "Karper", "Bawal", "Gurami"), each = 4)),
Pakan = as.factor(rep(c("0.25 kg", "0.5 kg", "0.75 kg", "1 kg"), times = 5)),
Pertumbuhan = c(19.6, 28.2, 26.6, 24.8,
13.6, 16.0, 17.6, 19.8,
13.2, 15.0, 16.8, 18.6,
11.8, 15.4, 18.4, 21.2,
12.6, 14.8, 14.2, 13.6)
)
#0 ANOVA
anova_pakan_ikan <- aov(Pertumbuhan ~ Pakan + Jenis_Ikan, data = data_pakan_ikan)
summary(anova_pakan_ikan)
## Df Sum Sq Mean Sq F value Pr(>F)
## Pakan 3 85.83 28.61 7.767 0.00381 **
## Jenis_Ikan 4 282.81 70.70 19.195 3.77e-05 ***
## Residuals 12 44.20 3.68
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Ftabel
F_tabel_perlakuan <- qf(0.05, df1 = 3, df2 = 12, lower.tail = FALSE)
F_tabel_perlakuan
## [1] 3.490295
F_tabel_kelompok <- qf(0.05, df1 = 4, df2 = 12, lower.tail = FALSE)
F_tabel_kelompok
## [1] 3.259167
#1 Uji Asumsi Kenormalan
#1.1 Eksploratif
plot(anova_pakan_ikan, which = 2)
# Q-Q Plot untuk memeriksa normalitas residual
qqnorm(anova_pakan_ikan$residuals)
qqline(anova_pakan_ikan$residuals, col = 'red')
#Histogram
hist(anova_pakan_ikan$residuals, breaks = 4, main = "Histogram Residual ANOVA",
xlab = "Residuals", col = "brown", border = "black")
#1.2 Uji Formal Normalitas Hipotesis
#Shapiro-Wilk
shapiro.test(x = anova_pakan_ikan$residuals)
##
## Shapiro-Wilk normality test
##
## data: anova_pakan_ikan$residuals
## W = 0.94999, p-value = 0.367
#2 Uji Asumsi Nilai Harapan Sisaan = 0
t.test(anova_pakan_ikan$residuals,
mu = 0,
conf.level = 0.95)
##
## One Sample t-test
##
## data: anova_pakan_ikan$residuals
## t = -1.9532e-16, df = 19, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.713828 0.713828
## sample estimates:
## mean of x
## -6.661338e-17
#3 Asumsi Kehomogenan Ragam
#3.1 Eksploratif
plot(anova_pakan_ikan,which=1)
#3.2 Uji Formal
#Bartlett’s Test
bartlett.test(Pertumbuhan ~ Pakan, data = data_pakan_ikan)
##
## Bartlett test of homogeneity of variances
##
## data: Pertumbuhan by Pakan
## Bartlett's K-squared = 1.399, df = 3, p-value = 0.7058
bartlett.test(Pertumbuhan ~ Jenis_Ikan, data = data_pakan_ikan)
##
## Bartlett test of homogeneity of variances
##
## data: Pertumbuhan by Jenis_Ikan
## Bartlett's K-squared = 5.0096, df = 4, p-value = 0.2863
library(car)
## Loading required package: carData
leveneTest(Pertumbuhan ~ Pakan, data = data_pakan_ikan)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 0.0954 0.9614
## 16
leveneTest(Pertumbuhan ~ Jenis_Ikan, data = data_pakan_ikan)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 4 1.3063 0.3122
## 15
#4 Asumsi Saling Bebas
#4.1 Eksploratif
#Plot Sisaan vs Order
plot(anova_pakan_ikan$residuals, type = 'o', main = "Plot Residuals",
xlab = "Index", ylab = "Residuals", col = "blue", pch = 16)
#Plot ACF
acf(anova_pakan_ikan$residuals, main = "ACF Residuals", col = "grey", lwd = 2)
#Plot PACF
pacf(anova_pakan_ikan$residuals, main = "PACF Residuals", col = "pink", lwd = 2)
#4.2 Uji Formal
#Durbin-Watson test
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
dwtest(anova_pakan_ikan, alternative = "two.sided")
##
## Durbin-Watson test
##
## data: anova_pakan_ikan
## DW = 1.6172, p-value = 0.09591
## alternative hypothesis: true autocorrelation is not 0
#5 Asumsi Keaditifan
#5.1 Eksploratif
library(ggplot2)
ggplot(data_pakan_ikan, aes(x = Pakan, y = Pertumbuhan, colour = Jenis_Ikan)) +
geom_point(aes(y = Pertumbuhan)) +
geom_line(aes(y = Pertumbuhan, group = Jenis_Ikan)) +
theme_bw() +
labs(title = "Pengaruh Perlakuan terhadap Pertumbuhan",
x = "Perlakuan (Jenis Pakan)",
y = "Pertumbuhan (kg)",
colour = "Kelompok (Jenis Ikan)") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
#5.2 Uji Formal
#Uji Tukey
library(reshape2)
library(additivityTests)
anova_pakan_ikan_wide <- dcast(data_pakan_ikan, Jenis_Ikan ~ Pakan, value.var = "Pertumbuhan")
Y <- as.matrix(anova_pakan_ikan_wide[-1])
tukey.test(Y, alpha = 0.05)
##
## Tukey test on 5% alpha-level:
##
## Test statistic: 1.043
## Critival value: 4.844
## The additivity hypothesis cannot be rejected.
#6 Asumsi Uji Lanjut
#Uji Duncan
library(agricolae)
hasil_duncan_perlakuan <- duncan.test(anova_pakan_ikan, "Pakan", alpha = 0.05)
print(hasil_duncan_perlakuan)
## $statistics
## MSerror Df Mean CV
## 3.683333 12 17.59 10.91075
##
## $parameters
## test name.t ntr alpha
## Duncan Pakan 4 0.05
##
## $duncan
## Table CriticalRange
## 2 3.081307 2.644664
## 3 3.225244 2.768204
## 4 3.312453 2.843055
##
## $means
## Pertumbuhan std r se Min Max Q25 Q50 Q75
## 0.25 kg 14.16 3.115766 5 0.8582929 11.8 19.6 12.6 13.2 13.6
## 0.5 kg 17.88 5.787227 5 0.8582929 14.8 28.2 15.0 15.4 16.0
## 0.75 kg 18.72 4.678889 5 0.8582929 14.2 26.6 16.8 17.6 18.4
## 1 kg 19.60 4.081666 5 0.8582929 13.6 24.8 18.6 19.8 21.2
##
## $comparison
## NULL
##
## $groups
## Pertumbuhan groups
## 1 kg 19.60 a
## 0.75 kg 18.72 a
## 0.5 kg 17.88 a
## 0.25 kg 14.16 b
##
## attr(,"class")
## [1] "group"
hasil_duncan_kelompok <- duncan.test(anova_pakan_ikan, "Jenis_Ikan", alpha = 0.05)
print(hasil_duncan_kelompok)
## $statistics
## MSerror Df Mean CV
## 3.683333 12 17.59 10.91075
##
## $parameters
## test name.t ntr alpha
## Duncan Jenis_Ikan 5 0.05
##
## $duncan
## Table CriticalRange
## 2 3.081307 2.956824
## 3 3.225244 3.094946
## 4 3.312453 3.178632
## 5 3.370172 3.234019
##
## $means
## Pertumbuhan std r se Min Max Q25 Q50 Q75
## Bawal 16.70 4.0348482 4 0.9596006 11.8 21.2 14.50 16.9 19.10
## Gurami 13.80 0.9380832 4 0.9596006 12.6 14.8 13.35 13.9 14.35
## Karper 15.90 2.3237900 4 0.9596006 13.2 18.6 14.55 15.9 17.25
## Lele 24.80 3.7345236 4 0.9596006 19.6 28.2 23.50 25.7 27.00
## Nila 16.75 2.6147020 4 0.9596006 13.6 19.8 15.40 16.8 18.15
##
## $comparison
## NULL
##
## $groups
## Pertumbuhan groups
## Lele 24.80 a
## Nila 16.75 b
## Bawal 16.70 b
## Karper 15.90 b
## Gurami 13.80 b
##
## attr(,"class")
## [1] "group"