Implementasi Multivariate Analysis of Variance (MANOVA) dan Multivariate Analysis of Covariance (MANCOVA) pada Student Performance Dataset
Kelas 2024B
Maris Al Sabina A. (24031554188)
Dewanggi Erchinta Dwi Putri (24031554034)
Naila Alya Furqon (24031554069)
Nuri Maulidyatul Haliza (24031554160)
Dosen Pengampu: Dinda Galuh Guminta, M.Stat.
2026-04-07
1 Library
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## biotools version 4.3library(MVN) ## Warning: package 'MVN' was built under R version 4.5.3## Registered S3 method overwritten by 'lme4':
## method from
## na.action.merMod carlibrary(corrplot)## corrplot 0.95 loadeddata <- read.csv("student_data.csv")
head(data)## school sex age address famsize Pstatus Medu Fedu Mjob Fjob reason
## 1 GP F 18 U GT3 A 4 4 at_home teacher course
## 2 GP F 17 U GT3 T 1 1 at_home other course
## 3 GP F 15 U LE3 T 1 1 at_home other other
## 4 GP F 15 U GT3 T 4 2 health services home
## 5 GP F 16 U GT3 T 3 3 other other home
## 6 GP M 16 U LE3 T 4 3 services other reputation
## guardian traveltime studytime failures schoolsup famsup paid activities
## 1 mother 2 2 0 yes no no no
## 2 father 1 2 0 no yes no no
## 3 mother 1 2 3 yes no yes no
## 4 mother 1 3 0 no yes yes yes
## 5 father 1 2 0 no yes yes no
## 6 mother 1 2 0 no yes yes yes
## nursery higher internet romantic famrel freetime goout Dalc Walc health
## 1 yes yes no no 4 3 4 1 1 3
## 2 no yes yes no 5 3 3 1 1 3
## 3 yes yes yes no 4 3 2 2 3 3
## 4 yes yes yes yes 3 2 2 1 1 5
## 5 yes yes no no 4 3 2 1 2 5
## 6 yes yes yes no 5 4 2 1 2 5
## absences G1 G2 G3
## 1 6 5 6 6
## 2 4 5 5 6
## 3 10 7 8 10
## 4 2 15 14 15
## 5 4 6 10 10
## 6 10 15 15 15str(data)## 'data.frame': 395 obs. of 33 variables:
## $ school : chr "GP" "GP" "GP" "GP" ...
## $ sex : chr "F" "F" "F" "F" ...
## $ age : int 18 17 15 15 16 16 16 17 15 15 ...
## $ address : chr "U" "U" "U" "U" ...
## $ famsize : chr "GT3" "GT3" "LE3" "GT3" ...
## $ Pstatus : chr "A" "T" "T" "T" ...
## $ Medu : int 4 1 1 4 3 4 2 4 3 3 ...
## $ Fedu : int 4 1 1 2 3 3 2 4 2 4 ...
## $ Mjob : chr "at_home" "at_home" "at_home" "health" ...
## $ Fjob : chr "teacher" "other" "other" "services" ...
## $ reason : chr "course" "course" "other" "home" ...
## $ guardian : chr "mother" "father" "mother" "mother" ...
## $ traveltime: int 2 1 1 1 1 1 1 2 1 1 ...
## $ studytime : int 2 2 2 3 2 2 2 2 2 2 ...
## $ failures : int 0 0 3 0 0 0 0 0 0 0 ...
## $ schoolsup : chr "yes" "no" "yes" "no" ...
## $ famsup : chr "no" "yes" "no" "yes" ...
## $ paid : chr "no" "no" "yes" "yes" ...
## $ activities: chr "no" "no" "no" "yes" ...
## $ nursery : chr "yes" "no" "yes" "yes" ...
## $ higher : chr "yes" "yes" "yes" "yes" ...
## $ internet : chr "no" "yes" "yes" "yes" ...
## $ romantic : chr "no" "no" "no" "yes" ...
## $ famrel : int 4 5 4 3 4 5 4 4 4 5 ...
## $ freetime : int 3 3 3 2 3 4 4 1 2 5 ...
## $ goout : int 4 3 2 2 2 2 4 4 2 1 ...
## $ Dalc : int 1 1 2 1 1 1 1 1 1 1 ...
## $ Walc : int 1 1 3 1 2 2 1 1 1 1 ...
## $ health : int 3 3 3 5 5 5 3 1 1 5 ...
## $ absences : int 6 4 10 2 4 10 0 6 0 0 ...
## $ G1 : int 5 5 7 15 6 15 12 6 16 14 ...
## $ G2 : int 6 5 8 14 10 15 12 5 18 15 ...
## $ G3 : int 6 6 10 15 10 15 11 6 19 15 ...2 Ubah Nama Kolom
colnames(data) <- c(
"sekolah", "jenis_kelamin", "umur", "alamat", "jumlah_keluarga",
"status_orang_tua", "pendidikan_ibu", "pendidikan_ayah", "pekerjaan_ibu", "pekerjaan_ayah",
"alasan_sekolah", "wali", "waktu_tempuh", "waktu_belajar", "jumlah_gagal",
"dukungan_sekolah", "dukungan_keluarga", "les", "aktivitas", "tk",
"ingin_kuliah", "internet", "pacaran", "hubungan_keluarga", "waktu_luang",
"keluar", "alkohol_harian", "alkohol_akhir_pekan", "kesehatan", "absensi",
"nilai_G1", "nilai_G2", "nilai_G3"
)3 Data Preprocessing
data$jenis_kelamin <- as.factor(data$jenis_kelamin)
data$sekolah <- as.factor(data$sekolah)
data$alamat <- as.factor(data$alamat)
data$internet <- as.factor(data$internet)
data <- na.omit(data)
summary(data)## sekolah jenis_kelamin umur alamat jumlah_keluarga
## GP:349 F:208 Min. :15.0 R: 88 Length:395
## MS: 46 M:187 1st Qu.:16.0 U:307 Class :character
## Median :17.0 Mode :character
## Mean :16.7
## 3rd Qu.:18.0
## Max. :22.0
## status_orang_tua pendidikan_ibu pendidikan_ayah pekerjaan_ibu
## Length:395 Min. :0.000 Min. :0.000 Length:395
## Class :character 1st Qu.:2.000 1st Qu.:2.000 Class :character
## Mode :character Median :3.000 Median :2.000 Mode :character
## Mean :2.749 Mean :2.522
## 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000
## pekerjaan_ayah alasan_sekolah wali waktu_tempuh
## Length:395 Length:395 Length:395 Min. :1.000
## Class :character Class :character Class :character 1st Qu.:1.000
## Mode :character Mode :character Mode :character Median :1.000
## Mean :1.448
## 3rd Qu.:2.000
## Max. :4.000
## waktu_belajar jumlah_gagal dukungan_sekolah dukungan_keluarga
## Min. :1.000 Min. :0.0000 Length:395 Length:395
## 1st Qu.:1.000 1st Qu.:0.0000 Class :character Class :character
## Median :2.000 Median :0.0000 Mode :character Mode :character
## Mean :2.035 Mean :0.3342
## 3rd Qu.:2.000 3rd Qu.:0.0000
## Max. :4.000 Max. :3.0000
## les aktivitas tk ingin_kuliah
## Length:395 Length:395 Length:395 Length:395
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## internet pacaran hubungan_keluarga waktu_luang keluar
## no : 66 Length:395 Min. :1.000 Min. :1.000 Min. :1.000
## yes:329 Class :character 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:2.000
## Mode :character Median :4.000 Median :3.000 Median :3.000
## Mean :3.944 Mean :3.235 Mean :3.109
## 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000
## alkohol_harian alkohol_akhir_pekan kesehatan absensi
## Min. :1.000 Min. :1.000 Min. :1.000 Min. : 0.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:3.000 1st Qu.: 0.000
## Median :1.000 Median :2.000 Median :4.000 Median : 4.000
## Mean :1.481 Mean :2.291 Mean :3.554 Mean : 5.709
## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:5.000 3rd Qu.: 8.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :75.000
## nilai_G1 nilai_G2 nilai_G3
## Min. : 3.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 8.00 1st Qu.: 9.00 1st Qu.: 8.00
## Median :11.00 Median :11.00 Median :11.00
## Mean :10.91 Mean :10.71 Mean :10.42
## 3rd Qu.:13.00 3rd Qu.:13.00 3rd Qu.:14.00
## Max. :19.00 Max. :19.00 Max. :20.004 Statistik Deskriptif
summary(data[, c("nilai_G1","nilai_G2","nilai_G3","waktu_belajar","absensi")])## nilai_G1 nilai_G2 nilai_G3 waktu_belajar
## Min. : 3.00 Min. : 0.00 Min. : 0.00 Min. :1.000
## 1st Qu.: 8.00 1st Qu.: 9.00 1st Qu.: 8.00 1st Qu.:1.000
## Median :11.00 Median :11.00 Median :11.00 Median :2.000
## Mean :10.91 Mean :10.71 Mean :10.42 Mean :2.035
## 3rd Qu.:13.00 3rd Qu.:13.00 3rd Qu.:14.00 3rd Qu.:2.000
## Max. :19.00 Max. :19.00 Max. :20.00 Max. :4.000
## absensi
## Min. : 0.000
## 1st Qu.: 0.000
## Median : 4.000
## Mean : 5.709
## 3rd Qu.: 8.000
## Max. :75.0005 Uji Asumsi
# 1. Normalitas Univariat
cat("Uji Normalitas Univariat\n")## Uji Normalitas Univariatshapiro.test(data$nilai_G1)##
## Shapiro-Wilk normality test
##
## data: data$nilai_G1
## W = 0.97491, p-value = 2.454e-06shapiro.test(data$nilai_G2)##
## Shapiro-Wilk normality test
##
## data: data$nilai_G2
## W = 0.96914, p-value = 2.084e-07# 2. Homogenitas Kovarians
cat("\nUji Homogenitas Kovarians (Box's M)\n")##
## Uji Homogenitas Kovarians (Box's M)boxM(data[, c("nilai_G1","nilai_G2")], data$jenis_kelamin)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data[, c("nilai_G1", "nilai_G2")]
## Chi-Sq (approx.) = 0.85882, df = 3, p-value = 0.8354boxM(data[, c("nilai_G1","nilai_G2")], data$sekolah)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data[, c("nilai_G1", "nilai_G2")]
## Chi-Sq (approx.) = 24.717, df = 3, p-value = 1.769e-05# 3. Homogenitas Varians
cat("\nUji Homogenitas Varians (Levene Test)\n")##
## Uji Homogenitas Varians (Levene Test)leveneTest(nilai_G1 ~ jenis_kelamin * sekolah, data = data)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 1.2594 0.288
## 391leveneTest(nilai_G2 ~ jenis_kelamin * sekolah, data = data)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 0.6057 0.6117
## 391# 4. Dependensi
cat("\nUji Dependensi (Korelasi)\n")##
## Uji Dependensi (Korelasi)cor.test(data$nilai_G1, data$nilai_G2)##
## Pearson's product-moment correlation
##
## data: data$nilai_G1 and data$nilai_G2
## t = 32.278, df = 393, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8226117 0.8770475
## sample estimates:
## cor
## 0.8521181# 5. Multikolinearitas
cat("\nUji Multikolinearitas (VIF)\n")##
## Uji Multikolinearitas (VIF)model_lm <- lm(nilai_G1 ~ waktu_belajar + absensi, data = data)
vif(model_lm)## waktu_belajar absensi
## 1.003947 1.003947# Analisis MANOVAmodel_manova <- manova(
cbind(nilai_G1, nilai_G2) ~ jenis_kelamin + sekolah,
data = data
)
summary(model_manova, test = "Wilks")## Df Wilks approx F num Df den Df Pr(>F)
## jenis_kelamin 1 0.99095 1.78530 2 391 0.1691
## sekolah 1 0.99652 0.68302 2 391 0.5057
## Residuals 392summary.aov(model_manova)## Response nilai_G1 :
## Df Sum Sq Mean Sq F value Pr(>F)
## jenis_kelamin 1 36.6 36.611 3.3365 0.06852 .
## sekolah 1 2.6 2.628 0.2395 0.62486
## Residuals 392 4301.5 10.973
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response nilai_G2 :
## Df Sum Sq Mean Sq F value Pr(>F)
## jenis_kelamin 1 46.3 46.265 3.2884 0.07053 .
## sekolah 1 13.4 13.368 0.9502 0.33027
## Residuals 392 5515.0 14.069
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 16 Analisis MANCOVA
model_mancova <- manova(
cbind(nilai_G1, nilai_G2) ~ jenis_kelamin + sekolah + waktu_belajar + absensi,
data = data
)
summary(model_mancova, test = "Wilks")## Df Wilks approx F num Df den Df Pr(>F)
## jenis_kelamin 1 0.99061 1.8440 2 389 0.1595657
## sekolah 1 0.99649 0.6847 2 389 0.5048647
## waktu_belajar 1 0.96091 7.9116 2 389 0.0004286 ***
## absensi 1 0.99975 0.0490 2 389 0.9522323
## Residuals 390
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary.aov(model_mancova)## Response nilai_G1 :
## Df Sum Sq Mean Sq F value Pr(>F)
## jenis_kelamin 1 36.6 36.611 3.4547 0.06383 .
## sekolah 1 2.6 2.628 0.2480 0.61880
## waktu_belajar 1 168.1 168.112 15.8631 8.124e-05 ***
## absensi 1 0.3 0.285 0.0269 0.86987
## Residuals 390 4133.1 10.598
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response nilai_G2 :
## Df Sum Sq Mean Sq F value Pr(>F)
## jenis_kelamin 1 46.3 46.265 3.3684 0.0672183 .
## sekolah 1 13.4 13.368 0.9733 0.3244641
## waktu_belajar 1 157.4 157.375 11.4581 0.0007841 ***
## absensi 1 1.1 1.084 0.0790 0.7788629
## Residuals 390 5356.6 13.735
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 17 Visualisasi
7.1 Scatter Plot
ggplot(data, aes(x = waktu_belajar, y = nilai_G3)) +
geom_point() +
geom_smooth(method = "lm") +
ggtitle("Pengaruh Waktu Belajar terhadap Nilai")## `geom_smooth()` using formula = 'y ~ x'
# Korelasi
cor(data[, c("nilai_G1","nilai_G2","waktu_belajar","absensi")])## nilai_G1 nilai_G2 waktu_belajar absensi
## nilai_G1 1.0000000 0.8521181 0.16061192 -0.03100290
## nilai_G2 0.8521181 1.0000000 0.13588000 -0.03177670
## waktu_belajar 0.1606119 0.1358800 1.00000000 -0.06270018
## absensi -0.0310029 -0.0317767 -0.06270018 1.000000008 Heatmap Korelasi
cor_matrix <- cor(data[, c("nilai_G1","nilai_G2","nilai_G3","waktu_belajar","absensi")])
corrplot(cor_matrix, method = "color", type = "upper")
# Boxplot Jenis Kelamin
ggplot(data, aes(x = jenis_kelamin, y = nilai_G1)) +
geom_boxplot() +
ggtitle("Nilai G1 berdasarkan Jenis Kelamin")