library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
data <- data.frame(
Treatment = rep(c("A", "B", "C", "D"), each = 3)[1:12],
Block = c(1,2,4, 2,3,4, 1,2,3, 1,3,4),
Value = c(79,83,86, 75,78,84, 86,88,90, 92,94,80)
)
model <- aov(Value ~ Treatment + Block, data = data)
summary(model)
## Df Sum Sq Mean Sq F value Pr(>F)
## Treatment 3 189.6 63.19 2.397 0.154
## Block 1 4.8 4.80 0.182 0.682
## Residuals 7 184.5 26.36
treatment_means <- data %>%
group_by(Treatment) %>%
summarise(Mean = mean(Value))
block_means <- data %>%
group_by(Block) %>%
summarise(Mean = mean(Value))
print("Treatment Means:")
## [1] "Treatment Means:"
print(treatment_means)
## # A tibble: 4 × 2
## Treatment Mean
## <chr> <dbl>
## 1 A 82.7
## 2 B 79
## 3 C 88
## 4 D 88.7
print("\nBlock Means:")
## [1] "\nBlock Means:"
print(block_means)
## # A tibble: 4 × 2
## Block Mean
## <dbl> <dbl>
## 1 1 85.7
## 2 2 82
## 3 3 87.3
## 4 4 83.3
# Input data
data <- data.frame(
Tekanan = c(1, 2, 3, 4),
A = c(79, 83, NA, 86),
B = c(NA, 75, 78, 84),
C = c(86, 88, 90, NA),
D = c(92, NA, 94, 80)
)
# Ubah data ke long format
library(tidyr)
data_long <- data %>%
pivot_longer(cols = A:D, names_to = "Logam", values_to = "Nilai") %>%
na.omit()
# Analisis varians
model <- aov(Nilai ~ Logam + Tekanan, data = data_long)
summary(model)
## Df Sum Sq Mean Sq F value Pr(>F)
## Logam 3 189.6 63.19 2.397 0.154
## Tekanan 1 4.8 4.80 0.182 0.682
## Residuals 7 184.5 26.36
# Uji Tukey HSD
tukey <- TukeyHSD(model, "Logam")
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## Tekanan
print(tukey)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Nilai ~ Logam + Tekanan, data = data_long)
##
## $Logam
## diff lwr upr p adj
## B-A -3.6666667 -17.543551 10.21022 0.8178877
## C-A 5.3333333 -8.543551 19.21022 0.6060830
## D-A 6.0000000 -7.876884 19.87688 0.5206258
## C-B 9.0000000 -4.876884 22.87688 0.2274683
## D-B 9.6666667 -4.210218 23.54355 0.1856738
## D-C 0.6666667 -13.210218 14.54355 0.9984283
# Visualisasi
plot(tukey, las = 1, col = "blue")
# Input data
data_aircrew <- data.frame(
Bahan_Mentah = rep(1:5, each = 5),
Operator = rep(1:5, times = 5),
Uji_Perakitan = c(
"α", "γ", "ε", "β", "δ",
"β", "δ", "α", "γ", "ε",
"γ", "ε", "β", "δ", "α",
"δ", "α", "γ", "ε", "β",
"ε", "β", "δ", "α", "γ"
),
Nilai = c(
21, 22, 17, 23, 29,
27, 24, 32, 27, 33,
28, 38, 26, 29, 21,
26, 31, 26, 23, 22,
29, 32, 27, 28, 32
)
)
# Analisis varians (ANOVA)
model_aircrew <- aov(Nilai ~ as.factor(Bahan_Mentah) + as.factor(Operator) + as.factor(Uji_Perakitan), data = data_aircrew)
summary(model_aircrew)
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(Bahan_Mentah) 4 171.84 42.96 1.730 0.208
## as.factor(Operator) 4 47.44 11.86 0.478 0.752
## as.factor(Uji_Perakitan) 4 10.64 2.66 0.107 0.978
## Residuals 12 297.92 24.83
# Uji Tukey HSD
tukey_bahan <- TukeyHSD(model_aircrew, "as.factor(Bahan_Mentah)")
print(tukey_bahan)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Nilai ~ as.factor(Bahan_Mentah) + as.factor(Operator) + as.factor(Uji_Perakitan), data = data_aircrew)
##
## $`as.factor(Bahan_Mentah)`
## diff lwr upr p adj
## 2-1 6.2 -3.844543 16.244543 0.3364788
## 3-1 6.0 -4.044543 16.044543 0.3656022
## 4-1 3.2 -6.844543 13.244543 0.8435507
## 5-1 7.2 -2.844543 17.244543 0.2150673
## 3-2 -0.2 -10.244543 9.844543 0.9999957
## 4-2 -3.0 -13.044543 7.044543 0.8709633
## 5-2 1.0 -9.044543 11.044543 0.9974811
## 4-3 -2.8 -12.844543 7.244543 0.8957632
## 5-3 1.2 -8.844543 11.244543 0.9949156
## 5-4 4.0 -6.044543 14.044543 0.7135068
tukey_operator <- TukeyHSD(model_aircrew, "as.factor(Operator)")
print(tukey_operator)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Nilai ~ as.factor(Bahan_Mentah) + as.factor(Operator) + as.factor(Uji_Perakitan), data = data_aircrew)
##
## $`as.factor(Operator)`
## diff lwr upr p adj
## 2-1 3.2 -6.844543 13.244543 0.8435507
## 3-1 -0.6 -10.644543 9.444543 0.9996604
## 4-1 -0.2 -10.244543 9.844543 0.9999957
## 5-1 1.2 -8.844543 11.244543 0.9949156
## 3-2 -3.8 -13.844543 6.244543 0.7484002
## 4-2 -3.4 -13.444543 6.644543 0.8137769
## 5-2 -2.0 -12.044543 8.044543 0.9663186
## 4-3 0.4 -9.644543 10.444543 0.9999321
## 5-3 1.8 -8.244543 11.844543 0.9768950
## 5-4 1.4 -8.644543 11.444543 0.9908732
tukey_uji <- TukeyHSD(model_aircrew, "as.factor(Uji_Perakitan)")
print(tukey_uji)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Nilai ~ as.factor(Bahan_Mentah) + as.factor(Operator) + as.factor(Uji_Perakitan), data = data_aircrew)
##
## $`as.factor(Uji_Perakitan)`
## diff lwr upr p adj
## β-α -6.000000e-01 -10.644543 9.444543 0.9996604
## γ-α 4.000000e-01 -9.644543 10.444543 0.9999321
## δ-α 4.000000e-01 -9.644543 10.444543 0.9999321
## ε-α 1.400000e+00 -8.644543 11.444543 0.9908732
## γ-β 1.000000e+00 -9.044543 11.044543 0.9974811
## δ-β 1.000000e+00 -9.044543 11.044543 0.9974811
## ε-β 2.000000e+00 -8.044543 12.044543 0.9663186
## δ-γ 3.552714e-15 -10.044543 10.044543 1.0000000
## ε-γ 1.000000e+00 -9.044543 11.044543 0.9974811
## ε-δ 1.000000e+00 -9.044543 11.044543 0.9974811
# Visualisasi
plot(tukey_bahan, las = 1, col = "blue")
plot(tukey_operator, las = 1, col = "green")
plot(tukey_uji, las = 1, col = "purple")
library(dplyr)
# Membuat data dalam bentuk data frame
latin_square_data <- data.frame(
Kapal = rep(1:4, each = 4),
Operator = rep(1:4, times = 4),
Nilai = c(20, 24, 15, 5, 25, 15, 8, 37, 34, 9, 56, 35, 7, 52, 40, 25)
)
# Tambahkan faktor untuk Kapal dan Operator
latin_square_data$Kapal <- factor(latin_square_data$Kapal)
latin_square_data$Operator <- factor(latin_square_data$Operator)
# Model ANOVA untuk desain bujur sangkar latin
anova_model <- aov(Nilai ~ Kapal + Operator + as.factor((1:4)[latin_square_data$Kapal]), data = latin_square_data)
# Output hasil ANOVA
summary(anova_model)
## Df Sum Sq Mean Sq F value Pr(>F)
## Kapal 3 810.2 270.06 0.873 0.490
## Operator 3 137.2 45.73 0.148 0.929
## Residuals 9 2784.6 309.40
# Visualisasi data (opsional)
library(ggplot2)
ggplot(latin_square_data, aes(x = Operator, y = Nilai, color = Kapal)) +
geom_point(size = 3) +
geom_line(aes(group = Kapal)) +
theme_minimal() +
labs(title = "Tingkat Kecelakaan Berdasarkan Jenis Kapal dan Operator",
x = "Operator",
y = "Tingkat Kecelakaan")
# Library yang diperlukan
library(dplyr)
library(tidyr)
library(ggplot2)
# 1. Aplikasi RBSL (Rancangan Bujur Sangkar Latin)
# Contoh: Analisis produktivitas koperasi berdasarkan 4 jenis produk (A, B, C, D) dan 4 cabang koperasi
rbsl_data <- data.frame(
Cabang = rep(1:4, each = 4),
Produk = rep(1:4, times = 4),
Nilai = c(80, 85, 90, 88, 78, 82, 87, 84, 88, 91, 85, 86, 81, 83, 79, 87)
)
rbsl_data$Cabang <- factor(rbsl_data$Cabang)
rbsl_data$Produk <- factor(rbsl_data$Produk)
# Model ANOVA untuk RBSL
anova_rbsl <- aov(Nilai ~ Cabang + Produk, data = rbsl_data)
# Hasil ANOVA untuk RBSL
cat("Hasil ANOVA RBSL:\n")
## Hasil ANOVA RBSL:
summary(anova_rbsl)
## Df Sum Sq Mean Sq F value Pr(>F)
## Cabang 3 70.25 23.42 1.938 0.194
## Produk 3 46.75 15.58 1.290 0.336
## Residuals 9 108.75 12.08
# RSBY
rby_data <- data.frame(
Harga = factor(rep(c("H1", "H2"), each = 4)),
Kualitas = factor(rep(c("K1", "K2"), times = 4)),
Lokasi = factor(rep(c("L1", "L2"), each = 2, times = 2)),
Pendapatan = c(100, 105, 95, 98, 110, 115, 90, 92)
)
# Model ANOVA untuk RBSY
anova_rbsy <- aov(Pendapatan ~ Harga * Kualitas * Lokasi, data = rby_data)
# Hasil ANOVA untuk RBSY
cat("\nHasil ANOVA RBSY:\n")
##
## Hasil ANOVA RBSY:
summary(anova_rbsy)
## Df Sum Sq Mean Sq
## Harga 1 10.1 10.1
## Kualitas 1 28.1 28.1
## Lokasi 1 378.1 378.1
## Harga:Kualitas 1 0.1 0.1
## Harga:Lokasi 1 120.1 120.1
## Kualitas:Lokasi 1 3.1 3.1
## Harga:Kualitas:Lokasi 1 0.1 0.1
# Visualisasi opsional untuk kedua model
library(ggplot2)
# Visualisasi RBSL
ggplot(rbsl_data, aes(x = Produk, y = Nilai, color = Cabang)) +
geom_point(size = 3) +
geom_line(aes(group = Cabang)) +
theme_minimal() +
labs(title = "Produktivitas Berdasarkan Produk dan Cabang",
x = "Produk",
y = "Nilai Produktivitas")
# Visualisasi RBSY
ggplot(rby_data, aes(x = Harga, y = Pendapatan, fill = Lokasi)) +
geom_bar(stat = "identity", position = "dodge") +
facet_grid(~Kualitas) +
theme_minimal() +
labs(title = "Pendapatan Berdasarkan Harga, Kualitas, dan Lokasi",
x = "Harga",
y = "Pendapatan")
