Persiapan Data

Load Library

pkgs <- c("tidyverse", "car", "MVN", "ggpubr", "rstatix", "nortest", "moments",
          "knitr", "kableExtra", "psych", "heplots", "effectsize", "emmeans", "magrittr")
invisible(lapply(pkgs, function(p)
  if (!requireNamespace(p, quietly = TRUE)) install.packages(p)))
invisible(lapply(pkgs, library, character.only = TRUE))

Import Data

data <- read.csv("student_performance.csv", sep = ",")
str(data)

## 'data.frame':    14003 obs. of  16 variables:
##  $ StudyHours          : int  19 19 19 19 19 19 19 19 19 19 ...
##  $ Attendance          : int  64 64 64 64 64 64 64 64 64 64 ...
##  $ Resources           : int  1 1 1 1 1 1 0 0 0 1 ...
##  $ Extracurricular     : int  0 0 0 1 1 1 1 1 1 1 ...
##  $ Motivation          : int  0 0 0 0 0 0 0 0 0 1 ...
##  $ Internet            : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Gender              : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Age                 : int  19 23 28 19 23 28 19 23 28 19 ...
##  $ LearningStyle       : int  2 3 1 2 3 1 2 3 1 2 ...
##  $ OnlineCourses       : int  8 16 19 8 16 19 8 16 19 8 ...
##  $ Discussions         : int  1 0 0 1 0 0 1 0 0 1 ...
##  $ AssignmentCompletion: int  59 90 67 59 90 67 59 90 67 59 ...
##  $ ExamScore           : int  40 66 99 40 66 99 40 66 99 40 ...
##  $ EduTech             : int  0 0 1 0 0 1 0 0 1 0 ...
##  $ StressLevel         : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ FinalGrade          : int  3 2 0 3 2 0 3 2 0 3 ...

Data Cleaning

Cek Missing Value

colSums(is.na(data))

##           StudyHours           Attendance            Resources 
##                    0                    0                    0 
##      Extracurricular           Motivation             Internet 
##                    0                    0                    0 
##               Gender                  Age        LearningStyle 
##                    0                    0                    0 
##        OnlineCourses          Discussions AssignmentCompletion 
##                    0                    0                    0 
##            ExamScore              EduTech          StressLevel 
##                    0                    0                    0 
##           FinalGrade 
##                    0

Transformasi Variabel

# Semua kolom kategorikal berisi angka (0,1,2,...) — mapping ke label
# Gender       : 0=Female, 1=Male
# LearningStyle: 0=Visual, 1=Auditory, 2=Reading, 3=Kinesthetic
# Extracurricular/Internet/EduTech: 0=No, 1=Yes
# Motivation/StressLevel: 0=Low, 1=Medium, 2=High
# FinalGrade   : 0=A, 1=B, 2=C, 3=D
# Resources    : 0=Low, 1=Medium, 2=High

data$Gender          <- factor(data$Gender,          levels=0:1,   labels=c("Female","Male"))
data$LearningStyle   <- factor(data$LearningStyle,   levels=0:3,   labels=c("Visual","Auditory","Reading","Kinesthetic"))
data$Extracurricular <- factor(data$Extracurricular, levels=0:1,   labels=c("No","Yes"))
data$Internet        <- factor(data$Internet,        levels=0:1,   labels=c("No","Yes"))
data$EduTech         <- factor(data$EduTech,         levels=0:1,   labels=c("No","Yes"))
data$Motivation      <- factor(data$Motivation,      levels=0:2,   labels=c("Low","Medium","High"))
data$StressLevel     <- factor(data$StressLevel,     levels=0:2,   labels=c("Low","Medium","High"))
data$FinalGrade      <- factor(data$FinalGrade,      levels=0:3,   labels=c("A","B","C","D"))

data$ExamScore      <- as.numeric(data$ExamScore)
data$FinalGrade_num <- as.numeric(data$FinalGrade)   # A=1, B=2, C=3, D=4

# Matriks DV dan daftar faktor/kovariat
dv_mat  <- cbind(FinalGrade = data$FinalGrade_num, ExamScore = data$ExamScore)
factors <- c("Gender", "LearningStyle", "Extracurricular",
             "Internet", "EduTech", "Motivation", "StressLevel")
covars  <- c("StudyHours", "Attendance", "AssignmentCompletion",
             "OnlineCourses", "Discussions", "Age")
covs    <- c("StudyHours", "Attendance", "AssignmentCompletion")

# Helper
sig <- function(p) ifelse(p < 0.05, "Signifikan *", "Tidak Signifikan")
kb  <- function(df, cap, col = "Keputusan", bg = "#d4edda") {
  kable(df, caption = cap) %>%
    kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                  full_width = FALSE) %>%
    row_spec(which(df[[col]] == "Signifikan *"), bold = TRUE, background = bg)
}

Karakteristik Data

Statistika Deskriptif

var_numerik  <- c("StudyHours", "Attendance", "Age", "OnlineCourses",
                  "Discussions", "AssignmentCompletion", "ExamScore")
var_kategorik <- c("Resources", "Extracurricular", "Motivation", "Internet",
                   "Gender", "LearningStyle", "EduTech",
                   "StressLevel", "FinalGrade")

data_deskriptif <- describe(data[var_numerik])
print(data_deskriptif)

##                      vars     n  mean    sd median trimmed   mad min max range
## StudyHours              1 14003 19.99  5.89     20   19.94  5.93   5  44    39
## Attendance              2 14003 80.19 11.47     80   80.22 14.83  60 100    40
## Age                     3 14003 23.53  3.51     24   23.53  4.45  18  29    11
## OnlineCourses           4 14003  9.89  6.11     10    9.88  7.41   0  20    20
## Discussions             5 14003  0.61  0.49      1    0.63  0.00   0   1     1
## AssignmentCompletion    6 14003 74.50 14.63     74   74.40 19.27  50 100    50
## ExamScore               7 14003 70.35 17.69     70   70.41 22.24  40 100    60
##                       skew kurtosis   se
## StudyHours            0.10    -0.20 0.05
## Attendance           -0.01    -1.18 0.10
## Age                  -0.02    -1.26 0.03
## OnlineCourses         0.02    -1.23 0.05
## Discussions          -0.43    -1.81 0.00
## AssignmentCompletion  0.05    -1.18 0.12
## ExamScore            -0.02    -1.21 0.15

for (kol in intersect(var_kategorik, colnames(data))) {
  cat("\n---", kol, "---\n")
  frekuensi  <- table(data[[kol]])
  persentase <- round(prop.table(frekuensi) * 100, 2)
  print(cbind(Frekuensi = frekuensi, Persentase = persentase))
}

## 
## --- Resources ---
##   Frekuensi Persentase
## 0      2750      19.64
## 1      7041      50.28
## 2      4212      30.08
## 
## --- Extracurricular ---
##     Frekuensi Persentase
## No       5683      40.58
## Yes      8320      59.42
## 
## --- Motivation ---
##        Frekuensi Persentase
## Low         4112      29.37
## Medium      7098      50.69
## High        2793      19.95
## 
## --- Internet ---
##     Frekuensi Persentase
## No       1043       7.45
## Yes     12960      92.55
## 
## --- Gender ---
##        Frekuensi Persentase
## Female      6274       44.8
## Male        7729       55.2
## 
## --- LearningStyle ---
##             Frekuensi Persentase
## Visual           3376      24.11
## Auditory         3580      25.57
## Reading          3500      24.99
## Kinesthetic      3547      25.33
## 
## --- EduTech ---
##     Frekuensi Persentase
## No       4074      29.09
## Yes      9929      70.91
## 
## --- StressLevel ---
##        Frekuensi Persentase
## Low         2836      20.25
## Medium      4069      29.06
## High        7098      50.69
## 
## --- FinalGrade ---
##   Frekuensi Persentase
## A      3832      27.37
## B      3310      23.64
## C      3618      25.84
## D      3243      23.16

Visualisasi Data

par(mfrow = c(4, 4), mar = c(4, 4, 2, 1))

for (i in 1:ncol(data)) {
  nama_col <- colnames(data)[i]
  if (nama_col %in% var_kategorik) {
    counts <- table(data[[i]])
    barplot(counts, main = nama_col, col = "lightcoral",
            border = "white", cex.main = 0.8)
  } else if (is.numeric(data[[i]])) {
    hist(data[[i]], main = nama_col, col = "lightblue",
         border = "white", xlab = "", cex.main = 0.8)
  }
}

par(mfrow = c(1, 1))

Uji Asumsi MANOVA

DV: FinalGrade + ExamScore | Faktor: Gender

A1 — Normalitas Multivariat

# Sample 2000 baris agar mvn() tidak kehabisan RAM
set.seed(42)
idx_mvn <- sample(nrow(data), 2000)
dv_sample_manova <- data.frame(
  FinalGrade = as.double(data$FinalGrade_num[idx_mvn]),
  ExamScore  = as.double(data$ExamScore[idx_mvn])
)

# Deteksi argumen yang didukung versi MVN yang terinstal
mvn_args <- names(formals(MVN::mvn))
use_new_api <- "mvnTest" %in% mvn_args

mvn_res <- if (use_new_api) {
  MVN::mvn(data = dv_sample_manova, mvnTest = "mardia", univariateTest = "SW")
} else {
  MVN::mvn(dv_sample_manova)
}

cat("=== Normalitas Multivariat — sampel n=2.000 ===
")

## === Normalitas Multivariat — sampel n=2.000 ===

for (slot in intersect(names(mvn_res),
                        c("multivariateNormality","Mardia","mardia","HZ","hz"))) {
  print(kable(mvn_res[[slot]]) |>
    kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE))
}

cat("
=== Normalitas Univariat ===
")

## 
## === Normalitas Univariat ===

for (slot in intersect(names(mvn_res),
                        c("univariateNormality","univariate"))) {
  print(kable(mvn_res[[slot]]) |>
    kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE))
}

# Q-Q Plot
par(mfrow = c(1, 2))
qqnorm(data$FinalGrade_num, main = "Q-Q: FinalGrade",
       col = "steelblue", pch = 16, cex = 0.3)
qqline(data$FinalGrade_num, col = "tomato", lwd = 2)
qqnorm(data$ExamScore, main = "Q-Q: ExamScore",
       col = "steelblue", pch = 16, cex = 0.3)
qqline(data$ExamScore, col = "tomato", lwd = 2)

par(mfrow = c(1, 1))

# Shapiro-Wilk per grup
set.seed(42)
df_s <- sample_n(data, 2000)
lapply(c("FinalGrade_num", "ExamScore"), function(v)
  df_s |> group_by(Gender) |>
    summarise(W = round(shapiro.test(.data[[v]])$statistic, 4),
              p = round(shapiro.test(.data[[v]])$p.value, 4), .groups = "drop") |>
    mutate(Variabel = v)
) |> bind_rows() |>
  kable(caption = "Shapiro-Wilk per Grup Gender (sampel n=2.000)") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Shapiro-Wilk per Grup Gender (sampel n=2.000)
Gender	W	Variabel
Female	0.8567	FinalGrade_num
Male	0.8601	FinalGrade_num
Female	0.9569	ExamScore
Male	0.9582	ExamScore

A2 — Box’s M & Levene

print(box_m(data[, c("FinalGrade_num", "ExamScore")], data$Gender))

## # A tibble: 1 × 4
##   statistic p.value parameter method                                            
##       <dbl>   <dbl>     <dbl> <chr>                                             
## 1      5.53   0.137         3 Box's M-test for Homogeneity of Covariance Matric…

map_df(c("FinalGrade_num", "ExamScore"), function(v) {
  lv <- leveneTest(as.formula(paste(v, "~ Gender")), data = data)
  data.frame(DV = v, F = round(lv$`F value`[1], 4), p = round(lv$`Pr(>F)`[1], 4),
             Keputusan = ifelse(lv$`Pr(>F)`[1] > 0.05, "Terpenuhi", "Tidak Terpenuhi"))
}) |> kable(caption = "Levene's Test — Homogenitas Varians") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Levene’s Test — Homogenitas Varians
DV	F	p	Keputusan
FinalGrade_num	3.3975	0.0653	Terpenuhi
ExamScore	1.6018	0.2057	Terpenuhi

A3 — Korelasi DV & Outlier Mahalanobis

ct <- cor.test(data$FinalGrade_num, data$ExamScore)
data.frame(r = round(ct$estimate, 4), p = formatC(ct$p.value, format = "e", digits = 3),
           Interpretasi = ifelse(abs(ct$estimate) > 0.2 & abs(ct$estimate) < 0.9,
                                 "Moderat ✔", "Periksa")) |>
  kable(caption = "Korelasi Pearson: FinalGrade ~ ExamScore") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Korelasi Pearson: FinalGrade ~ ExamScore
	r	p	Interpretasi
cor	-0.9683	0.000e+00	Periksa

D2       <- mahalanobis(dv_mat, colMeans(dv_mat), cov(dv_mat))
chi_crit <- qchisq(0.999, df = 2)
data.frame(
  Keterangan = c("Chi-sq kritis (p=.001, df=2)", "Outlier terdeteksi", "Persentase"),
  Nilai      = c(round(chi_crit, 4), sum(D2 > chi_crit),
                 paste0(round(mean(D2 > chi_crit) * 100, 2), "%"))
) |> kable(caption = "Outlier Multivariat (Mahalanobis)") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Outlier Multivariat (Mahalanobis)
Keterangan	Nilai
Chi-sq kritis (p=.001, df=2)	13.8155
Outlier terdeteksi	0
Persentase	0%

Uji Asumsi MANCOVA

DV: FinalGrade + ExamScore | Faktor: Gender | Kovariat: StudyHours, Attendance, AssignmentCompletion, OnlineCourses, Discussions, Age

B1 — Normalitas Multivariat

set.seed(42)
dv_sample <- data.frame(
  ExamScore  = as.double(data$ExamScore[1:5000]),
  FinalGrade = as.double(data$FinalGrade_num[1:5000])
)

mvn_res2 <- mvn(data = dv_sample)

cat("=== Normalitas Multivariat (Henze-Zirkler) ===\n")

## === Normalitas Multivariat (Henze-Zirkler) ===

print(mvn_res2$multivariateNormality)

## NULL

cat("\n=== Normalitas Univariat (Anderson-Darling) ===\n")

## 
## === Normalitas Univariat (Anderson-Darling) ===

print(mvn_res2$univariateNormality)

## NULL

par(mfrow = c(1, 2))
qqnorm(data$ExamScore, main = "Q-Q: ExamScore",
       col = "steelblue", pch = 16, cex = 0.4)
qqline(data$ExamScore, col = "tomato", lwd = 2)
qqnorm(data$FinalGrade_num, main = "Q-Q: FinalGrade",
       col = "steelblue", pch = 16, cex = 0.4)
qqline(data$FinalGrade_num, col = "tomato", lwd = 2)

par(mfrow = c(1, 1))

B2 — Normalitas per Grup (Shapiro-Wilk)

set.seed(42)
data_s <- sample_n(data, 5000)

lapply(c("ExamScore", "FinalGrade_num"), function(v)
  data_s |> group_by(Gender) |>
    summarise(W = round(shapiro.test(.data[[v]])$statistic, 4),
              p = round(shapiro.test(.data[[v]])$p.value, 4), .groups = "drop") |>
    mutate(Variabel = v)
) |> bind_rows() |>
  kable(caption = "Shapiro-Wilk per Grup Gender (n=5000)") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Shapiro-Wilk per Grup Gender (n=5000)
Gender	W	Variabel
Female	0.9564	ExamScore
Male	0.9521	ExamScore
Female	0.8565	FinalGrade_num
Male	0.8542	FinalGrade_num

B3 — Box’s M (Homogenitas Matriks Kovarians)

boxM_res <- heplots::boxM(dv_mat, data$Gender)
print(boxM_res)

## 
##  Box's M-test for Homogeneity of Covariance Matrices 
## 
## data:  dv_mat by data$Gender 
## Chi-Sq (approx.) = 5.5313, df = 3, p-value = 0.1368

map_df(c("ExamScore", "FinalGrade_num"), function(v) {
  lv <- leveneTest(as.formula(paste(v, "~ Gender")), data = data)
  data.frame(DV = v, F_stat = round(lv$`F value`[1], 4),
             p = round(lv$`Pr(>F)`[1], 4),
             Keputusan = ifelse(lv$`Pr(>F)`[1] > 0.05, "Terpenuhi", "Tidak Terpenuhi"))
}) |>
  kable(caption = "Levene Test — Homogenitas Varians per DV") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Levene Test — Homogenitas Varians per DV
DV	F_stat	p	Keputusan
ExamScore	1.6018	0.2057	Terpenuhi
FinalGrade_num	3.3975	0.0653	Terpenuhi

B4 — Linearitas Kovariat

map_df(covars, function(cv)
  data.frame(Covariate    = cv,
             r_ExamScore  = round(cor(data[[cv]], data$ExamScore), 4),
             r_FinalGrade = round(cor(data[[cv]], data$FinalGrade_num), 4))
) |>
  kable(caption = "Korelasi Pearson: Kovariat vs DV") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Korelasi Pearson: Kovariat vs DV
Covariate	r_ExamScore	r_FinalGrade
StudyHours	0.0045	-0.0096
Attendance	-0.0147	0.0109
AssignmentCompletion	0.0253	-0.0301
OnlineCourses	0.0210	-0.0210
Discussions	-0.0288	0.0397
Age	-0.0072	0.0029

p1 <- ggplot(data, aes(x = StudyHours, y = ExamScore)) +
  geom_point(alpha = 0.2, color = "steelblue") +
  geom_smooth(method = "lm", color = "tomato", se = TRUE) +
  labs(title = "StudyHours vs ExamScore") + theme_minimal()

p2 <- ggplot(data, aes(x = StudyHours, y = FinalGrade_num)) +
  geom_point(alpha = 0.2, color = "seagreen") +
  geom_smooth(method = "lm", color = "tomato", se = TRUE) +
  labs(title = "StudyHours vs FinalGrade") + theme_minimal()

ggarrange(p1, p2, ncol = 2)

B5 — Homogenitas Slope Regresi

expand.grid(dv = c("ExamScore", "FinalGrade_num"), cov = covars,
            stringsAsFactors = FALSE) |>
  pmap_df(function(dv, cov) {
    av <- anova(lm(as.formula(paste(dv, "~ Gender *", cov)), data = data))
    p  <- av[grep(":", rownames(av)), "Pr(>F)"]
    data.frame(DV = dv, Covariate = cov,
               p_interaksi = round(p, 4),
               Keputusan   = ifelse(p > 0.05, "Homogen ✔", "Tidak Homogen ✘"))
  }) |>
  kable(caption = "Homogenitas Slope: Gender × Kovariat") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Homogenitas Slope: Gender × Kovariat
DV	Covariate	p_interaksi	Keputusan
ExamScore	StudyHours	0.0307	Tidak Homogen ✘
FinalGrade_num	StudyHours	0.0926	Homogen ✔
ExamScore	Attendance	0.9384	Homogen ✔
FinalGrade_num	Attendance	0.7427	Homogen ✔
ExamScore	AssignmentCompletion	0.5780	Homogen ✔
FinalGrade_num	AssignmentCompletion	0.8214	Homogen ✔
ExamScore	OnlineCourses	0.8258	Homogen ✔
FinalGrade_num	OnlineCourses	0.5902	Homogen ✔
ExamScore	Discussions	0.0190	Tidak Homogen ✘
FinalGrade_num	Discussions	0.0005	Tidak Homogen ✘
ExamScore	Age	0.0003	Tidak Homogen ✘
FinalGrade_num	Age	0.0005	Tidak Homogen ✘

B6 — Independensi Kovariat dari Faktor

map_df(covars, function(cv) {
  p <- summary(aov(as.formula(paste(cv, "~ Gender")), data = data))[[1]][["Pr(>F)"]][1]
  data.frame(Covariate = cv, p = round(p, 4),
             Keputusan = ifelse(p > 0.05, "Independen ✔", "Berkorelasi dgn Grup ✘"))
}) |>
  kable(caption = "Independensi Kovariat dari Gender") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Independensi Kovariat dari Gender
Covariate	p	Keputusan
StudyHours	0.0905	Independen ✔
Attendance	0.0009	Berkorelasi dgn Grup ✘
AssignmentCompletion	0.1847	Independen ✔
OnlineCourses	0.2601	Independen ✔
Discussions	0.6823	Independen ✔
Age	0.0081	Berkorelasi dgn Grup ✘

Uji Asumsi ANCOVA

DV: ExamScore | Faktor: Gender | Kovariat: StudyHours

C1 — Normalitas Residual

m_anc <- lm(ExamScore ~ StudyHours + Gender, data = data)
res   <- residuals(m_anc)

set.seed(42)
sw <- shapiro.test(sample(res, 5000))
ad <- ad.test(res)

data.frame(Uji       = c("Shapiro-Wilk (n=5.000)", "Anderson-Darling"),
           Stat      = round(c(sw$statistic, ad$statistic), 4),
           p         = formatC(c(sw$p.value, ad$p.value), format = "e", digits = 3),
           Keputusan = ifelse(c(sw$p.value, ad$p.value) > 0.05,
                              "Normal ✔", "Tidak Normal ✘")) |>
  kable(caption = "Normalitas Residual ANCOVA") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Normalitas Residual ANCOVA
	Uji	Stat	p	Keputusan
W	Shapiro-Wilk (n=5.000)	0.9548	9.012e-37	Tidak Normal ✘
A	Anderson-Darling	162.0648	3.700e-24	Tidak Normal ✘

par(mfrow = c(1, 2))
qqnorm(res, col = adjustcolor("steelblue", .3), pch = 16, cex = .5, main = "Q-Q Residual")
qqline(res, col = "tomato", lwd = 2)
hist(res, breaks = 60, col = "steelblue", border = "white", freq = FALSE,
     main = "Histogram Residual", xlab = "Residual")
curve(dnorm(x, mean(res), sd(res)), col = "tomato", lwd = 2, add = TRUE)

par(mfrow = c(1, 1))

C2 — Homogenitas, Linearitas & Slope

lv  <- leveneTest(ExamScore ~ Gender, data = data)
bar <- bartlett.test(ExamScore ~ Gender, data = data)
data.frame(Uji       = c("Levene", "Bartlett"),
           Stat      = round(c(lv$`F value`[1], bar$statistic), 4),
           p         = round(c(lv$`Pr(>F)`[1], bar$p.value), 4),
           Keputusan = ifelse(c(lv$`Pr(>F)`[1], bar$p.value) > 0.05,
                              "Homogen ✔", "Tidak Homogen ✘")) |>
  kable(caption = "Homogenitas Varians") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Homogenitas Varians
	Uji	Stat	p	Keputusan
	Levene	1.6018	0.2057	Homogen ✔
Bartlett’s K-squared	Bartlett	0.1396	0.7087	Homogen ✔

ct2 <- cor.test(data$StudyHours, data$ExamScore)
cat("r =", round(ct2$estimate, 4), "| p =", formatC(ct2$p.value, format = "e", digits = 3))

## r = 0.0045 | p = 5.949e-01

av2 <- anova(lm(ExamScore ~ StudyHours * Gender, data = data))
data.frame(Term = rownames(av2), Df = av2$Df,
           F    = round(av2$`F value`, 4),
           p    = round(av2$`Pr(>F)`, 4)) |>
  kable(caption = "Interaksi StudyHours × Gender", na.string = "") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) |>
  row_spec(grep(":", rownames(av2)), bold = TRUE, background = "#fff3cd")

Interaksi StudyHours × Gender
Term	Df	F	p
StudyHours	1	0.2829	0.5948
Gender	1	6.4210	0.0113
StudyHours:Gender	1	4.6689	0.0307
Residuals	13999	NA	NA

t2 <- t.test(StudyHours ~ Gender, data = data)
data.frame(Uji       = "t-test: StudyHours ~ Gender",
           t         = round(t2$statistic, 4),
           df        = round(t2$parameter, 2),
           p         = round(t2$p.value, 4),
           Keputusan = ifelse(t2$p.value > 0.05, "Independen ✔", "Berkorelasi dgn Grup ✘")) |>
  kable(caption = "Independensi StudyHours dari Gender") |>
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Independensi StudyHours dari Gender
	Uji	t	df	p	Keputusan
t	t-test: StudyHours ~ Gender	1.6934	13425.41	0.0904	Independen ✔

Ringkasan Uji Asumsi

Ringkasan Semua Uji Asumsi
Metode	Kode	Asumsi	Indikator
MANOVA	A1	Normalitas multivariat (Mardia)	p > 0.05
	A2	Homogenitas matriks varians-kovarians (Box’s M)	p > 0.05
	A3	Homogenitas varians univariat (Levene)	p > 0.05
	A4	Korelasi moderat antar DV	0.2 < \|r\| < 0.9
	A5	Tidak ada outlier multivariat (Mahalanobis)	Outlier < 5%
MANCOVA	B1	Linearitas DV ~ covariate	Korelasi & scatterplot linear
	B2	Homogenitas slope regresi	p interaksi > 0.05
	B3	Covariate independen dari faktor grup	p > 0.05
ANCOVA	C1	Normalitas residual	p > 0.05
	C2	Homogenitas varians (Levene & Bartlett)	p > 0.05
	C3	Linearitas covariate ~ DV	Korelasi & scatterplot linear
	C4	Homogenitas slope regresi (interaksi)	p interaksi > 0.05
	C5	Covariate independen dari faktor grup	p > 0.05

MANOVA

MANOVA per Faktor

models <- lapply(setNames(factors, factors), function(f)
  manova(as.formula(paste("cbind(ExamScore, FinalGrade_num) ~", f)), data = data))

pillai <- lapply(factors, function(f) {
  s <- summary(models[[f]], test = "Pillai")$stats
  data.frame(Faktor = f, Pillai = round(s[1,1],4), `approx F` = round(s[1,3],4),
             `num Df` = s[1,4], `den Df` = s[1,5],
             `p-value` = round(s[1,6],4), Keputusan = sig(s[1,6]),
             check.names = FALSE)
}) |> bind_rows()

kb(pillai, "Tabel 1. Pillai's Trace — Semua Faktor")

Tabel 1. Pillai’s Trace — Semua Faktor
Faktor	Pillai	approx F	num Df	den Df	p-value	Keputusan
Gender	1	3.5749	2	14000	0.0280	Signifikan *
LearningStyle	3	4.6623	6	27998	0.0001	Signifikan *
Extracurricular	1	0.7933	2	14000	0.4524	Tidak Signifikan
Internet	1	0.4026	2	14000	0.6686	Tidak Signifikan
EduTech	1	3.0738	2	14000	0.0463	Signifikan *
Motivation	2	0.6591	4	28000	0.6204	Tidak Signifikan
StressLevel	2	11.3533	4	28000	0.0000	Signifikan *

Detail per Faktor

for (f in factors) {
  cat(sprintf("\n### %s\n", f))
  cat("```\n")
  print(summary(models[[f]], test = "Pillai"))
  cat("\n--- ANOVA Univariat ---\n")
  print(summary.aov(models[[f]]))
  cat("```\n")
}

Gender

             Df     Pillai approx F num Df den Df  Pr(>F)  
Gender        1 0.00051044   3.5749      2  14000 0.02804 *
Residuals 14001                                            
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

--- ANOVA Univariat ---
 Response ExamScore :
               Df  Sum Sq Mean Sq F value  Pr(>F)  
Gender          1    1995 1995.29  6.3798 0.01155 *
Residuals   14001 4378801  312.75                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 Response FinalGrade_num :
               Df  Sum Sq Mean Sq F value   Pr(>F)   
Gender          1     8.9  8.9297  7.1022 0.007708 **
Residuals   14001 17603.8  1.2573                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

LearningStyle

                 Df    Pillai approx F num Df den Df    Pr(>F)    
LearningStyle     3 0.0019963   4.6623      6  27998 9.553e-05 ***
Residuals     13999                                               
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

--- ANOVA Univariat ---
 Response ExamScore :
                 Df  Sum Sq Mean Sq F value  Pr(>F)  
LearningStyle     3    3264  1088.0  3.4795 0.01521 *
Residuals     13999 4377533   312.7                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 Response FinalGrade_num :
                 Df  Sum Sq Mean Sq F value   Pr(>F)   
LearningStyle     3    17.3  5.7557  4.5793 0.003294 **
Residuals     13999 17595.5  1.2569                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Extracurricular

                   Df     Pillai approx F num Df den Df Pr(>F)
Extracurricular     1 0.00011332  0.79331      2  14000 0.4524
Residuals       14001                                         

--- ANOVA Univariat ---
 Response ExamScore :
                   Df  Sum Sq Mean Sq F value Pr(>F)
Extracurricular     1     489  488.58  1.5617 0.2114
Residuals       14001 4380308  312.86               

 Response FinalGrade_num :
                   Df Sum Sq Mean Sq F value Pr(>F)
Extracurricular     1      2  1.9642  1.5616 0.2115
Residuals       14001  17611  1.2578

Internet

             Df     Pillai approx F num Df den Df Pr(>F)
Internet      1 5.7514e-05  0.40262      2  14000 0.6686
Residuals 14001                                         

--- ANOVA Univariat ---
 Response ExamScore :
               Df  Sum Sq Mean Sq F value Pr(>F)
Internet        1     114  114.29  0.3653 0.5456
Residuals   14001 4380682  312.88               

 Response FinalGrade_num :
               Df  Sum Sq Mean Sq F value Pr(>F)
Internet        1     0.7 0.70915  0.5637 0.4528
Residuals   14001 17612.0 1.25791

EduTech

             Df     Pillai approx F num Df den Df  Pr(>F)  
EduTech       1 0.00043893   3.0738      2  14000 0.04627 *
Residuals 14001                                            
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

--- ANOVA Univariat ---
 Response ExamScore :
               Df  Sum Sq Mean Sq F value Pr(>F)
EduTech         1     831  831.01  2.6564 0.1032
Residuals   14001 4379966  312.83               

 Response FinalGrade_num :
               Df  Sum Sq Mean Sq F value Pr(>F)  
EduTech         1     5.3  5.2576  4.1807 0.0409 *
Residuals   14001 17607.5  1.2576                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Motivation

              Df     Pillai approx F num Df den Df Pr(>F)
Motivation     2 0.00018831  0.65914      4  28000 0.6204
Residuals  14000                                         

--- ANOVA Univariat ---
 Response ExamScore :
               Df  Sum Sq Mean Sq F value Pr(>F)
Motivation      2     281  140.60  0.4494  0.638
Residuals   14000 4380515  312.89               

 Response FinalGrade_num :
               Df Sum Sq Mean Sq F value Pr(>F)
Motivation      2      2 0.97776  0.7773 0.4597
Residuals   14000  17611 1.25791

StressLevel

               Df    Pillai approx F num Df den Df    Pr(>F)    
StressLevel     2 0.0032385   11.353      4  28000 3.318e-09 ***
Residuals   14000                                               
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

--- ANOVA Univariat ---
 Response ExamScore :
               Df  Sum Sq Mean Sq F value    Pr(>F)    
StressLevel     2    8622  4311.2  13.805 1.025e-06 ***
Residuals   14000 4372174   312.3                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 Response FinalGrade_num :
               Df  Sum Sq Mean Sq F value    Pr(>F)    
StressLevel     2    47.4 23.6795  18.873 6.525e-09 ***
Residuals   14000 17565.4  1.2547                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA Univariat & Effect Size η²

dvs <- c("ExamScore", "FinalGrade")

res_eta <- lapply(factors, function(f) {
  av <- summary.aov(models[[f]])
  lapply(1:2, function(i) {
    a    <- av[[i]]
    eta2 <- round(a$`Sum Sq`[1] / sum(a$`Sum Sq`, na.rm = TRUE), 4)
    data.frame(Faktor = f, DV = dvs[i],
               `F value`     = round(a$`F value`[1], 4),
               `p-value`     = round(a$`Pr(>F)`[1], 4),
               Keputusan     = sig(a$`Pr(>F)`[1]),
               `η²`          = eta2,
               Interpretasi  = case_when(
                 eta2 < 0.01 ~ "Kecil", eta2 < 0.06 ~ "Sedang",
                 eta2 < 0.14 ~ "Besar", TRUE ~ "Sangat Besar"),
               check.names = FALSE)
  }) |> bind_rows()
}) |> bind_rows()

kb(res_eta, "Tabel 2. ANOVA Univariat & η² — Semua Faktor")

Tabel 2. ANOVA Univariat & η² — Semua Faktor
Faktor	DV	F value	p-value	Keputusan	η²	Interpretasi
Gender	ExamScore	6.3798	0.0116	Signifikan *	0.0005	Kecil
Gender	FinalGrade	7.1022	0.0077	Signifikan *	0.0005	Kecil
LearningStyle	ExamScore	3.4795	0.0152	Signifikan *	0.0007	Kecil
LearningStyle	FinalGrade	4.5793	0.0033	Signifikan *	0.0010	Kecil
Extracurricular	ExamScore	1.5617	0.2114	Tidak Signifikan	0.0001	Kecil
Extracurricular	FinalGrade	1.5616	0.2115	Tidak Signifikan	0.0001	Kecil
Internet	ExamScore	0.3653	0.5456	Tidak Signifikan	0.0000	Kecil
Internet	FinalGrade	0.5637	0.4528	Tidak Signifikan	0.0000	Kecil
EduTech	ExamScore	2.6564	0.1032	Tidak Signifikan	0.0002	Kecil
EduTech	FinalGrade	4.1807	0.0409	Signifikan *	0.0003	Kecil
Motivation	ExamScore	0.4494	0.6380	Tidak Signifikan	0.0001	Kecil
Motivation	FinalGrade	0.7773	0.4597	Tidak Signifikan	0.0001	Kecil
StressLevel	ExamScore	13.8047	0.0000	Signifikan *	0.0020	Kecil
StressLevel	FinalGrade	18.8731	0.0000	Signifikan *	0.0027	Kecil

MANOVA Model Penuh

m_full <- manova(cbind(ExamScore, FinalGrade_num) ~
                   Gender + LearningStyle + Extracurricular +
                   Internet + EduTech + Motivation + StressLevel, data = data)

sf <- summary(m_full, test = "Pillai")$stats
nr <- nrow(sf) - 1
tbl_full <- data.frame(
  Efek      = rownames(sf)[1:nr],
  Pillai    = round(sf[1:nr,1],4), `approx F` = round(sf[1:nr,3],4),
  `num Df`  = sf[1:nr,4], `den Df` = sf[1:nr,5],
  `p-value` = round(sf[1:nr,6],4), Keputusan = sig(sf[1:nr,6]),
  check.names = FALSE)

kb(tbl_full, "Tabel 3. MANOVA Model Penuh — Pillai's Trace")

Tabel 3. MANOVA Model Penuh — Pillai’s Trace
	Efek	Pillai	approx F	num Df	den Df	p-value	Keputusan
Gender	Gender	1	3.5888	2	13990	0.0277	Signifikan *
LearningStyle	LearningStyle	3	4.6547	6	27982	0.0001	Signifikan *
Extracurricular	Extracurricular	1	0.7650	2	13990	0.4653	Tidak Signifikan
Internet	Internet	1	0.4594	2	13990	0.6317	Tidak Signifikan
EduTech	EduTech	1	2.6612	2	13990	0.0699	Tidak Signifikan
Motivation	Motivation	2	0.6626	4	27982	0.6180	Tidak Signifikan
StressLevel	StressLevel	2	11.7289	4	27982	0.0000	Signifikan *

af <- summary.aov(m_full)
tbl_af <- lapply(1:2, function(i) {
  a <- af[[i]]; nr2 <- nrow(a) - 1
  data.frame(DV = dvs[i], Efek = rownames(a)[1:nr2],
             `F value` = round(a$`F value`[1:nr2],4),
             `p-value` = round(a$`Pr(>F)`[1:nr2],4),
             Keputusan = sig(a$`Pr(>F)`[1:nr2]),
             check.names = FALSE)
}) |> bind_rows()

kb(tbl_af, "Tabel 4. ANOVA Univariat Follow-up — Model Penuh")

Tabel 4. ANOVA Univariat Follow-up — Model Penuh
DV	Efek	F value	p-value	Keputusan
ExamScore	Gender	6.3953	0.0115	Signifikan *
ExamScore	LearningStyle	3.4908	0.0150	Signifikan *
ExamScore	Extracurricular	1.5027	0.2203	Tidak Signifikan
ExamScore	Internet	0.4358	0.5092	Tidak Signifikan
ExamScore	EduTech	2.0896	0.1483	Tidak Signifikan
ExamScore	Motivation	0.4337	0.6481	Tidak Signifikan
ExamScore	StressLevel	14.3241	0.0000	Signifikan *
FinalGrade	Gender	7.1275	0.0076	Signifikan *
FinalGrade	LearningStyle	4.5648	0.0034	Signifikan *
FinalGrade	Extracurricular	1.5089	0.2193	Tidak Signifikan
FinalGrade	Internet	0.6607	0.4163	Tidak Signifikan
FinalGrade	EduTech	3.4185	0.0645	Tidak Signifikan
FinalGrade	Motivation	0.7630	0.4663	Tidak Signifikan
FinalGrade	StressLevel	19.5465	0.0000	Signifikan *

Estimated Marginal Means (EMM)

emm_plots <- lapply(factors, function(f) {
  get_emm <- function(dv) {
    e <- as.data.frame(summary(
      emmeans(lm(as.formula(paste(dv, "~", f)), data = data),
              as.formula(paste("~", f)))))
    colnames(e)[1] <- "Grup"; e
  }
  lapply(list(c("ExamScore", "#84A7D4"), c("FinalGrade_num", "#E8A0BF")),
         function(x) {
           e <- get_emm(x[1])
           ggplot(e, aes(x = Grup, y = emmean)) +
             geom_col(fill = x[2], alpha = 0.8, width = 0.5) +
             geom_errorbar(aes(ymin = lower.CL, ymax = upper.CL), width = 0.15) +
             labs(title = paste(f, "→", gsub("_num","",x[1])), x = "", y = "EMM") +
             theme_minimal(base_size = 8) +
             theme(axis.text.x = element_text(angle = 20, hjust = 1))
         })
})

ggarrange(plotlist = unlist(emm_plots, recursive = FALSE), ncol = 2, nrow = 7)

ANCOVA

Model ANCOVA Utama

model_ancova <- lm(
  ExamScore ~ .,
  data = data[, c("ExamScore", factors, covars)]
)

ancova_tbl <- Anova(model_ancova, type = "III")
ancova_df  <- as.data.frame(ancova_tbl)
ancova_df$Variabel  <- rownames(ancova_df)
ancova_df$Keputusan <- ifelse(ancova_df$`Pr(>F)` < 0.05, "Signifikan *", "Tidak Signifikan")

knitr::kable(ancova_df, caption = "Tabel ANCOVA (Type III)") %>%
  kable_styling(bootstrap_options = c("striped","hover"), font_size = 14, full_width = FALSE) %>%
  row_spec(which(ancova_df$Keputusan == "Signifikan *"), bold = TRUE, background = "#d4edda")

Tabel ANCOVA (Type III)
	Sum Sq	Df	F value	Pr(>F)	Variabel	Keputusan
(Intercept)	423249.0417	1	1359.1498768	0.0000000	(Intercept)	Signifikan *
Gender	2244.3881	1	7.2072455	0.0072695	Gender	Signifikan *
LearningStyle	3089.0516	3	3.3065514	0.0192895	LearningStyle	Signifikan *
Extracurricular	437.9962	1	1.4065062	0.2356574	Extracurricular	Tidak Signifikan
Internet	194.7350	1	0.6253388	0.4290836	Internet	Tidak Signifikan
EduTech	671.0092	1	2.1547647	0.1421507	EduTech	Tidak Signifikan
Motivation	297.6228	2	0.4778676	0.6201144	Motivation	Tidak Signifikan
StressLevel	9256.2133	2	14.8619134	0.0000004	StressLevel	Signifikan *
StudyHours	159.4691	1	0.5120920	0.4742466	StudyHours	Tidak Signifikan
Attendance	1208.5272	1	3.8808583	0.0488593	Attendance	Signifikan *
AssignmentCompletion	2816.3435	1	9.0439258	0.0026404	AssignmentCompletion	Signifikan *
OnlineCourses	2017.7387	1	6.4794224	0.0109237	OnlineCourses	Signifikan *
Discussions	3758.8932	1	12.0706695	0.0005138	Discussions	Signifikan *
Age	201.3211	1	0.6464884	0.4213847	Age	Tidak Signifikan
Residuals	4355029.5297	13985	NA	NA	Residuals	NA

summary(model_ancova)

## 
## Call:
## lm(formula = ExamScore ~ ., data = data[, c("ExamScore", factors, 
##     covars)])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.813 -15.097  -0.168  15.448  32.856 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              71.25686    1.93283  36.867  < 2e-16 ***
## GenderMale                0.80678    0.30052   2.685 0.007270 ** 
## LearningStyleAuditory     1.32320    0.42409   3.120 0.001812 ** 
## LearningStyleReading      0.83620    0.42638   1.961 0.049880 *  
## LearningStyleKinesthetic  0.75076    0.42527   1.765 0.077522 .  
## ExtracurricularYes       -0.36048    0.30396  -1.186 0.235657    
## InternetYes              -0.44955    0.56848  -0.791 0.429084    
## EduTechYes                0.48281    0.32891   1.468 0.142151    
## MotivationMedium          0.15903    0.34608   0.460 0.645863    
## MotivationHigh           -0.22149    0.43299  -0.512 0.608979    
## StressLevelMedium        -2.18644    0.43224  -5.058 4.28e-07 ***
## StressLevelHigh          -1.89462    0.39243  -4.828 1.39e-06 ***
## StudyHours                0.01815    0.02536   0.716 0.474247    
## Attendance               -0.02569    0.01304  -1.970 0.048859 *  
## AssignmentCompletion      0.03068    0.01020   3.007 0.002640 ** 
## OnlineCourses             0.06213    0.02441   2.545 0.010924 *  
## Discussions              -1.06216    0.30572  -3.474 0.000514 ***
## Age                      -0.03423    0.04257  -0.804 0.421385    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.65 on 13985 degrees of freedom
## Multiple R-squared:  0.005882,   Adjusted R-squared:  0.004673 
## F-statistic: 4.867 on 17 and 13985 DF,  p-value: 1.35e-10

Uji Interaksi (Homogeneity of Regression Slopes)

model_interaction_full <- lm(
  ExamScore ~
    (Gender + LearningStyle + Extracurricular + Internet + EduTech +
     Motivation + StressLevel) *
    (StudyHours + Attendance + AssignmentCompletion +
     OnlineCourses + Discussions + Age),
  data = data
)

interaction_tbl <- Anova(model_interaction_full, type = "III")
interaction_df  <- as.data.frame(interaction_tbl)
interaction_df$Variabel  <- rownames(interaction_df)
interaction_df$Keputusan <- ifelse(interaction_df$`Pr(>F)` < 0.05, "Signifikan *", "Tidak Signifikan")

knitr::kable(interaction_df, caption = "Tabel Uji Interaksi ANCOVA") %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                font_size = 9.5, full_width = FALSE, position = "center") %>%
  row_spec(which(interaction_df$Keputusan == "Signifikan *"),
           bold = TRUE, background = "#f8d7da")

Tabel Uji Interaksi ANCOVA
	Sum Sq	Df	F value	Pr(>F)	Variabel	Keputusan
(Intercept)	2.933311e+04	1	94.8216491	0.0000000	(Intercept)	Signifikan *
Gender	2.628334e+03	1	8.4963003	0.0035644	Gender	Signifikan *
LearningStyle	3.360086e+02	3	0.3620583	0.7804133	LearningStyle	Tidak Signifikan
Extracurricular	5.752638e+01	1	0.1859586	0.6663084	Extracurricular	Tidak Signifikan
Internet	1.667266e+03	1	5.3895703	0.0202718	Internet	Signifikan *
EduTech	3.546055e+02	1	1.1462907	0.2843455	EduTech	Tidak Signifikan
Motivation	3.687493e+02	2	0.5960060	0.5510221	Motivation	Tidak Signifikan
StressLevel	3.368499e+03	2	5.4444726	0.0043293	StressLevel	Signifikan *
StudyHours	2.281329e+02	1	0.7374580	0.3904912	StudyHours	Tidak Signifikan
Attendance	2.376861e+03	1	7.6833959	0.0055805	Attendance	Signifikan *
AssignmentCompletion	1.818159e+02	1	0.5877344	0.4433096	AssignmentCompletion	Tidak Signifikan
OnlineCourses	2.820136e+01	1	0.0911632	0.7627081	OnlineCourses	Tidak Signifikan
Discussions	2.680672e+02	1	0.8665489	0.3519286	Discussions	Tidak Signifikan
Age	5.123235e+01	1	0.1656127	0.6840470	Age	Tidak Signifikan
Gender:StudyHours	1.691737e+03	1	5.4686755	0.0193744	Gender:StudyHours	Signifikan *
Gender:Attendance	9.968303e+00	1	0.0322233	0.8575410	Gender:Attendance	Tidak Signifikan
Gender:AssignmentCompletion	1.466636e+02	1	0.4741020	0.4911176	Gender:AssignmentCompletion	Tidak Signifikan
Gender:OnlineCourses	6.661237e+01	1	0.2153298	0.6426289	Gender:OnlineCourses	Tidak Signifikan
Gender:Discussions	2.558451e+03	1	8.2703973	0.0040358	Gender:Discussions	Signifikan *
Gender:Age	3.259043e+03	1	10.5351177	0.0011740	Gender:Age	Signifikan *
LearningStyle:StudyHours	2.472997e+03	3	2.6647208	0.0461741	LearningStyle:StudyHours	Signifikan *
LearningStyle:Attendance	2.591007e+03	3	2.7918801	0.0388929	LearningStyle:Attendance	Signifikan *
LearningStyle:AssignmentCompletion	6.672209e+02	3	0.7189485	0.5405163	LearningStyle:AssignmentCompletion	Tidak Signifikan
LearningStyle:OnlineCourses	3.261420e+02	3	0.3514267	0.7881214	LearningStyle:OnlineCourses	Tidak Signifikan
LearningStyle:Discussions	4.054827e+03	3	4.3691844	0.0044214	LearningStyle:Discussions	Signifikan *
LearningStyle:Age	8.816030e+03	3	9.4995088	0.0000029	LearningStyle:Age	Signifikan *
Extracurricular:StudyHours	7.322572e+02	1	2.3670802	0.1239414	Extracurricular:StudyHours	Tidak Signifikan
Extracurricular:Attendance	7.210220e+00	1	0.0233076	0.8786621	Extracurricular:Attendance	Tidak Signifikan
Extracurricular:AssignmentCompletion	3.104361e+02	1	1.0035098	0.3164801	Extracurricular:AssignmentCompletion	Tidak Signifikan
Extracurricular:OnlineCourses	9.670193e+02	1	3.1259676	0.0770760	Extracurricular:OnlineCourses	Tidak Signifikan
Extracurricular:Discussions	8.288861e+01	1	0.2679441	0.6047225	Extracurricular:Discussions	Tidak Signifikan
Extracurricular:Age	1.836901e+01	1	0.0593793	0.8074833	Extracurricular:Age	Tidak Signifikan
Internet:StudyHours	9.254888e+01	1	0.2991717	0.5844109	Internet:StudyHours	Tidak Signifikan
Internet:Attendance	1.306844e+03	1	4.2244788	0.0398635	Internet:Attendance	Signifikan *
Internet:AssignmentCompletion	8.508099e+02	1	2.7503115	0.0972580	Internet:AssignmentCompletion	Tidak Signifikan
Internet:OnlineCourses	1.662132e+02	1	0.5372977	0.4635672	Internet:OnlineCourses	Tidak Signifikan
Internet:Discussions	8.936715e+02	1	2.8888650	0.0892161	Internet:Discussions	Tidak Signifikan
Internet:Age	3.899168e+01	1	0.1260437	0.7225752	Internet:Age	Tidak Signifikan
EduTech:StudyHours	2.261269e+00	1	0.0073097	0.9318675	EduTech:StudyHours	Tidak Signifikan
EduTech:Attendance	7.152208e+02	1	2.3120090	0.1284007	EduTech:Attendance	Tidak Signifikan
EduTech:AssignmentCompletion	6.117421e+01	1	0.1977506	0.6565496	EduTech:AssignmentCompletion	Tidak Signifikan
EduTech:OnlineCourses	5.727491e+02	1	1.8514575	0.1736360	EduTech:OnlineCourses	Tidak Signifikan
EduTech:Discussions	1.938392e+02	1	0.6266007	0.4286184	EduTech:Discussions	Tidak Signifikan
EduTech:Age	7.264608e+01	1	0.2348343	0.6279698	EduTech:Age	Tidak Signifikan
Motivation:StudyHours	4.396536e+02	2	0.7106079	0.4913633	Motivation:StudyHours	Tidak Signifikan
Motivation:Attendance	6.423104e-01	2	0.0010382	0.9989624	Motivation:Attendance	Tidak Signifikan
Motivation:AssignmentCompletion	6.806566e+02	2	1.1001386	0.3328539	Motivation:AssignmentCompletion	Tidak Signifikan
Motivation:OnlineCourses	6.358801e+02	2	1.0277667	0.3578323	Motivation:OnlineCourses	Tidak Signifikan
Motivation:Discussions	3.341618e+01	2	0.0540103	0.9474226	Motivation:Discussions	Tidak Signifikan
Motivation:Age	5.820482e+02	2	0.9407588	0.3903563	Motivation:Age	Tidak Signifikan
StressLevel:StudyHours	2.606564e+02	2	0.4212964	0.6562039	StressLevel:StudyHours	Tidak Signifikan
StressLevel:Attendance	1.078297e+03	2	1.7428404	0.1750608	StressLevel:Attendance	Tidak Signifikan
StressLevel:AssignmentCompletion	4.600041e+03	2	7.4350007	0.0005926	StressLevel:AssignmentCompletion	Signifikan *
StressLevel:OnlineCourses	1.178655e+03	2	1.9050483	0.1488543	StressLevel:OnlineCourses	Tidak Signifikan
StressLevel:Discussions	1.232915e+02	2	0.1992749	0.8193270	StressLevel:Discussions	Tidak Signifikan
StressLevel:Age	5.448340e+03	2	8.8060985	0.0001507	StressLevel:Age	Signifikan *
Residuals	4.305848e+06	13919	NA	NA	Residuals	NA

Uji Diagnostik

par(mfrow = c(2, 2))
plot(model_ancova)

par(mfrow = c(1, 1))

Estimated Marginal Means (EMMeans)

emm_list <- lapply(factors, function(f) {
  e <- as.data.frame(emmeans(model_ancova, as.formula(paste("~", f))))
  colnames(e)[1] <- "Group"
  e$Faktor <- f
  e
})

emm_all <- do.call(rbind, emm_list)

knitr::kable(emm_all, caption = "EMMeans Semua Faktor") %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                font_size = 10, full_width = FALSE, position = "center")

EMMeans Semua Faktor
Gender	LearningStyle	Extracurricular	Internet	EduTech	Motivation	StressLevel	Group	emmean	SE	df	lower.CL	upper.CL	Faktor
.	.	.	.	.	.	.	Female	70.30654	0.3470559	13985	69.62626	70.98681	Gender
.	.	.	.	.	.	.	Male	71.11332	0.3377744	13985	70.45124	71.77540	Gender
.	.	.	.	.	.	.	Visual	69.98239	0.4036994	13985	69.19108	70.77369	LearningStyle
.	.	.	.	.	.	.	Auditory	71.30559	0.4009496	13985	70.51968	72.09151	LearningStyle
.	.	.	.	.	.	.	Reading	70.81858	0.4019067	13985	70.03079	71.60637	LearningStyle
.	.	.	.	.	.	.	Kinesthetic	70.73315	0.4020014	13985	69.94517	71.52113	LearningStyle
.	.	.	.	.	.	.	No	70.89017	0.3575050	13985	70.18941	71.59093	Extracurricular
.	.	.	.	.	.	.	Yes	70.52969	0.3282827	13985	69.88621	71.17316	Extracurricular
.	.	.	.	.	.	.	No	70.93470	0.5599038	13985	69.83722	72.03219	Internet
.	.	.	.	.	.	.	Yes	70.48516	0.1935907	13985	70.10569	70.86462	Internet
.	.	.	.	.	.	.	No	70.46852	0.3790881	13985	69.72546	71.21159	EduTech
.	.	.	.	.	.	.	Yes	70.95133	0.3158595	13985	70.33221	71.57046	EduTech
.	.	.	.	.	.	.	Low	70.73075	0.3787128	13985	69.98842	71.47308	Motivation
.	.	.	.	.	.	.	Medium	70.88978	0.3359103	13985	70.23135	71.54821	Motivation
.	.	.	.	.	.	.	High	70.50926	0.4267069	13985	69.67285	71.34566	Motivation
.	.	.	.	.	.	.	Low	72.07028	0.4248900	13985	71.23744	72.90312	StressLevel
.	.	.	.	.	.	.	Medium	69.88384	0.3795660	13985	69.13984	70.62784	StressLevel
.	.	.	.	.	.	.	High	70.17566	0.3367156	13985	69.51566	70.83567	StressLevel

plots_ancova <- lapply(factors, function(f) {
  e <- as.data.frame(emmeans(model_ancova, as.formula(paste("~", f))))
  colnames(e)[1] <- "Group"
  ggplot(e, aes(x = Group, y = emmean)) +
    geom_col(fill = "#84A7D4", width = 0.5) +
    geom_errorbar(aes(ymin = lower.CL, ymax = upper.CL), width = 0.2) +
    labs(title = paste("EMMeans:", f), y = "Mean") +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 20, hjust = 1))
})

ggarrange(plotlist = plots_ancova, ncol = 3, nrow = 3)

pairwise_list <- lapply(factors, function(f) {
  pairs(emmeans(model_ancova, as.formula(paste("~", f))))
})
pairwise_list

## [[1]]
##  contrast      estimate    SE    df t.ratio p.value
##  Female - Male   -0.807 0.301 13985  -2.685  0.0073
## 
## Results are averaged over the levels of: LearningStyle, Extracurricular, Internet, EduTech, Motivation, StressLevel, Discussions 
## 
## [[2]]
##  contrast               estimate    SE    df t.ratio p.value
##  Visual - Auditory       -1.3232 0.424 13985  -3.120  0.0098
##  Visual - Reading        -0.8362 0.426 13985  -1.961  0.2029
##  Visual - Kinesthetic    -0.7508 0.425 13985  -1.765  0.2902
##  Auditory - Reading       0.4870 0.421 13985   1.158  0.6534
##  Auditory - Kinesthetic   0.5724 0.419 13985   1.366  0.5209
##  Reading - Kinesthetic    0.0854 0.421 13985   0.203  0.9970
## 
## Results are averaged over the levels of: Gender, Extracurricular, Internet, EduTech, Motivation, StressLevel, Discussions 
## P value adjustment: tukey method for comparing a family of 4 estimates 
## 
## [[3]]
##  contrast estimate    SE    df t.ratio p.value
##  No - Yes     0.36 0.304 13985   1.186  0.2357
## 
## Results are averaged over the levels of: Gender, LearningStyle, Internet, EduTech, Motivation, StressLevel, Discussions 
## 
## [[4]]
##  contrast estimate    SE    df t.ratio p.value
##  No - Yes     0.45 0.568 13985   0.791  0.4291
## 
## Results are averaged over the levels of: Gender, LearningStyle, Extracurricular, EduTech, Motivation, StressLevel, Discussions 
## 
## [[5]]
##  contrast estimate    SE    df t.ratio p.value
##  No - Yes   -0.483 0.329 13985  -1.468  0.1422
## 
## Results are averaged over the levels of: Gender, LearningStyle, Extracurricular, Internet, Motivation, StressLevel, Discussions 
## 
## [[6]]
##  contrast      estimate    SE    df t.ratio p.value
##  Low - Medium    -0.159 0.346 13985  -0.460  0.8901
##  Low - High       0.221 0.433 13985   0.512  0.8657
##  Medium - High    0.381 0.394 13985   0.965  0.5992
## 
## Results are averaged over the levels of: Gender, LearningStyle, Extracurricular, Internet, EduTech, StressLevel, Discussions 
## P value adjustment: tukey method for comparing a family of 3 estimates 
## 
## [[7]]
##  contrast      estimate    SE    df t.ratio p.value
##  Low - Medium     2.186 0.432 13985   5.058 <0.0001
##  Low - High       1.895 0.392 13985   4.828 <0.0001
##  Medium - High   -0.292 0.348 13985  -0.839  0.6785
## 
## Results are averaged over the levels of: Gender, LearningStyle, Extracurricular, Internet, EduTech, Motivation, Discussions 
## P value adjustment: tukey method for comparing a family of 3 estimates

MANCOVA

Model MANCOVA

model_mancova <- lm(
  cbind(ExamScore, FinalGrade_num) ~
    Gender + LearningStyle + Extracurricular +
    Internet + EduTech + Motivation + StressLevel +
    StudyHours + Attendance + AssignmentCompletion +
    OnlineCourses + Discussions + Age,
  data = data
)

summary(model_mancova)

## Response ExamScore :
## 
## Call:
## lm(formula = ExamScore ~ Gender + LearningStyle + Extracurricular + 
##     Internet + EduTech + Motivation + StressLevel + StudyHours + 
##     Attendance + AssignmentCompletion + OnlineCourses + Discussions + 
##     Age, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.813 -15.097  -0.168  15.448  32.856 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              71.25686    1.93283  36.867  < 2e-16 ***
## GenderMale                0.80678    0.30052   2.685 0.007270 ** 
## LearningStyleAuditory     1.32320    0.42409   3.120 0.001812 ** 
## LearningStyleReading      0.83620    0.42638   1.961 0.049880 *  
## LearningStyleKinesthetic  0.75076    0.42527   1.765 0.077522 .  
## ExtracurricularYes       -0.36048    0.30396  -1.186 0.235657    
## InternetYes              -0.44955    0.56848  -0.791 0.429084    
## EduTechYes                0.48281    0.32891   1.468 0.142151    
## MotivationMedium          0.15903    0.34608   0.460 0.645863    
## MotivationHigh           -0.22149    0.43299  -0.512 0.608979    
## StressLevelMedium        -2.18644    0.43224  -5.058 4.28e-07 ***
## StressLevelHigh          -1.89462    0.39243  -4.828 1.39e-06 ***
## StudyHours                0.01815    0.02536   0.716 0.474247    
## Attendance               -0.02569    0.01304  -1.970 0.048859 *  
## AssignmentCompletion      0.03068    0.01020   3.007 0.002640 ** 
## OnlineCourses             0.06213    0.02441   2.545 0.010924 *  
## Discussions              -1.06216    0.30572  -3.474 0.000514 ***
## Age                      -0.03423    0.04257  -0.804 0.421385    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.65 on 13985 degrees of freedom
## Multiple R-squared:  0.005882,   Adjusted R-squared:  0.004673 
## F-statistic: 4.867 on 17 and 13985 DF,  p-value: 1.35e-10
## 
## 
## Response FinalGrade_num :
## 
## Call:
## lm(formula = FinalGrade_num ~ Gender + LearningStyle + Extracurricular + 
##     Internet + EduTech + Motivation + StressLevel + StudyHours + 
##     Attendance + AssignmentCompletion + OnlineCourses + Discussions + 
##     Age, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7017 -1.2958 -0.2696  0.7084  1.8693 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               2.4772700  0.1224234  20.235  < 2e-16 ***
## GenderMale               -0.0539421  0.0190345  -2.834 0.004605 ** 
## LearningStyleAuditory    -0.0891224  0.0268615  -3.318 0.000909 ***
## LearningStyleReading     -0.0769923  0.0270064  -2.851 0.004366 ** 
## LearningStyleKinesthetic -0.0546092  0.0269361  -2.027 0.042644 *  
## ExtracurricularYes        0.0227062  0.0192524   1.179 0.238262    
## InternetYes               0.0343014  0.0360071   0.953 0.340795    
## EduTechYes               -0.0386085  0.0208329  -1.853 0.063868 .  
## MotivationMedium         -0.0128778  0.0219203  -0.587 0.556890    
## MotivationHigh            0.0182291  0.0274249   0.665 0.506258    
## StressLevelMedium         0.1614438  0.0273774   5.897 3.79e-09 ***
## StressLevelHigh           0.1405766  0.0248559   5.656 1.58e-08 ***
## StudyHours               -0.0021210  0.0016064  -1.320 0.186749    
## Attendance                0.0012679  0.0008259   1.535 0.124762    
## AssignmentCompletion     -0.0023216  0.0006463  -3.592 0.000329 ***
## OnlineCourses            -0.0039434  0.0015460  -2.551 0.010760 *  
## Discussions               0.0919771  0.0193640   4.750 2.06e-06 ***
## Age                       0.0008538  0.0026964   0.317 0.751515    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.118 on 13985 degrees of freedom
## Multiple R-squared:  0.008012,   Adjusted R-squared:  0.006806 
## F-statistic: 6.644 on 17 and 13985 DF,  p-value: 3.982e-16

Hasil Uji MANCOVA — Pillai’s Trace

mancova_res <- car::Manova(model_mancova, test.statistic = "Pillai")

SSPE  <- mancova_res$SSPE
terms <- mancova_res$terms
df_h  <- mancova_res$df
df_e  <- mancova_res$error.df
p_dv  <- nrow(SSPE)

tabel_mancova <- do.call(rbind, lapply(seq_along(terms), function(i) {
  SSH    <- mancova_res$SSP[[i]]
  vh     <- df_h[i]
  ve     <- df_e

  pillai   <- sum(diag(SSH %*% solve(SSH + SSPE)))
  s        <- min(p_dv, vh)
  m        <- (abs(p_dv - vh) - 1) / 2
  nn       <- (ve - p_dv - 1) / 2
  approx_f <- ((2*nn + s + 1) / (2*m + s + 1)) * (pillai / (s - pillai))
  num_df   <- s * (2*m + s + 1)
  den_df   <- s * (2*nn + s + 1)
  p_val    <- pf(approx_f, num_df, den_df, lower.tail = FALSE)

  data.frame(Efek     = terms[i],
             Pillai   = round(pillai, 4),
             Approx_F = round(approx_f, 4),
             Num_Df   = round(num_df, 0),
             Den_Df   = round(den_df, 0),
             p_value  = round(p_val, 4),
             row.names = NULL)
}))

tabel_mancova |>
  kable(caption  = "Tabel Hasil Uji MANCOVA (Pillai's Trace)",
        col.names = c("Efek","Pillai's Trace","Approx F","Num Df","Den Df","p-value"),
        align     = "lccccc") |>
  kable_styling(bootstrap_options = c("striped","hover","bordered"), full_width = TRUE) |>
  row_spec(which(tabel_mancova$p_value < 0.05),
           bold = TRUE, color = "white", background = "#2980B9") |>
  footnote(general = "Baris biru = efek signifikan secara multivariat (p < 0.05)")

Tabel Hasil Uji MANCOVA (Pillai’s Trace)
Efek	Pillai’s Trace	Approx F	Num Df	Den Df	p-value
Gender	0.0006	4.0436	2	13984	0.0176
LearningStyle	0.0018	4.2470	6	27970	0.0003
Extracurricular	0.0001	0.7109	2	13984	0.4912
Internet	0.0001	0.5926	2	13984	0.5529
EduTech	0.0004	2.5718	2	13984	0.0764
Motivation	0.0002	0.6345	4	27970	0.6379
StressLevel	0.0035	12.1748	4	27970	0.0000
StudyHours	0.0005	3.4102	2	13984	0.0331
Attendance	0.0004	3.0513	2	13984	0.0473
AssignmentCompletion	0.0012	8.2309	2	13984	0.0003
OnlineCourses	0.0005	3.2987	2	13984	0.0370
Discussions	0.0031	21.4220	2	13984	0.0000
Age	0.0003	2.0329	2	13984	0.1310
Note:
Baris biru = efek signifikan secara multivariat (p < 0.05)

Cara baca: Jika p-value < 0.05, efek tersebut berpengaruh signifikan terhadap kombinasi ExamScore + FinalGrade secara bersama-sama, setelah mengontrol variabel lain dalam model.

Effect Size (Partial Eta Squared)

es_exam <- eta_squared(
  lm(ExamScore ~ Gender + LearningStyle + Extracurricular +
       Internet + EduTech + Motivation + StressLevel +
       StudyHours + Attendance + AssignmentCompletion +
       OnlineCourses + Discussions + Age, data = data),
  partial = TRUE
)

es_grade <- eta_squared(
  lm(FinalGrade_num ~ Gender + LearningStyle + Extracurricular +
       Internet + EduTech + Motivation + StressLevel +
       StudyHours + Attendance + AssignmentCompletion +
       OnlineCourses + Discussions + Age, data = data),
  partial = TRUE
)

cat("=== ExamScore ===\n")

## === ExamScore ===

print(es_exam)

## # Effect Size for ANOVA (Type I)
## 
## Parameter            | Eta2 (partial) |       95% CI
## ----------------------------------------------------
## Gender               |       4.58e-04 | [0.00, 1.00]
## LearningStyle        |       7.50e-04 | [0.00, 1.00]
## Extracurricular      |       1.08e-04 | [0.00, 1.00]
## Internet             |       3.12e-05 | [0.00, 1.00]
## EduTech              |       1.50e-04 | [0.00, 1.00]
## Motivation           |       6.21e-05 | [0.00, 1.00]
## StressLevel          |       2.05e-03 | [0.00, 1.00]
## StudyHours           |       2.41e-05 | [0.00, 1.00]
## Attendance           |       2.56e-04 | [0.00, 1.00]
## AssignmentCompletion |       6.66e-04 | [0.00, 1.00]
## OnlineCourses        |       4.58e-04 | [0.00, 1.00]
## Discussions          |       8.54e-04 | [0.00, 1.00]
## Age                  |       4.62e-05 | [0.00, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

cat("\n=== FinalGrade ===\n")

## 
## === FinalGrade ===

print(es_grade)

## # Effect Size for ANOVA (Type I)
## 
## Parameter            | Eta2 (partial) |       95% CI
## ----------------------------------------------------
## Gender               |       5.11e-04 | [0.00, 1.00]
## LearningStyle        |       9.81e-04 | [0.00, 1.00]
## Extracurricular      |       1.08e-04 | [0.00, 1.00]
## Internet             |       4.74e-05 | [0.00, 1.00]
## EduTech              |       2.45e-04 | [0.00, 1.00]
## Motivation           |       1.09e-04 | [0.00, 1.00]
## StressLevel          |       2.80e-03 | [0.00, 1.00]
## StudyHours           |       9.72e-05 | [0.00, 1.00]
## Attendance           |       1.53e-04 | [0.00, 1.00]
## AssignmentCompletion |       9.43e-04 | [0.00, 1.00]
## OnlineCourses        |       4.59e-04 | [0.00, 1.00]
## Discussions          |       1.61e-03 | [0.00, 1.00]
## Age                  |       7.17e-06 | [0.00, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

Pedoman: η²p < 0.06 = kecil | 0.06–0.14 = sedang | > 0.14 = besar

MODUL 2 — Analisis MANOVA, ANCOVA, dan MANCOVA

Dataset: Student Performance

Tamaela Nurandyapasa (24031554044)

Niha Nur Mayla Putri (24031554057)

Rahmawati Dian Pratiwi (24031554183)

2026-04-04

Persiapan Data

Load Library

Import Data

Data Cleaning

Transformasi Variabel

Karakteristik Data

Statistika Deskriptif

Visualisasi Data

Uji Asumsi MANOVA

A1 — Normalitas Multivariat

A2 — Box’s M & Levene

A3 — Korelasi DV & Outlier Mahalanobis

Uji Asumsi MANCOVA

B1 — Normalitas Multivariat

B2 — Normalitas per Grup (Shapiro-Wilk)

B3 — Box’s M (Homogenitas Matriks Kovarians)

B4 — Linearitas Kovariat

B5 — Homogenitas Slope Regresi

B6 — Independensi Kovariat dari Faktor

Uji Asumsi ANCOVA

C1 — Normalitas Residual

C2 — Homogenitas, Linearitas & Slope

Ringkasan Uji Asumsi

MANOVA

MANOVA per Faktor

Detail per Faktor

Gender

LearningStyle

Extracurricular

Internet

EduTech

Motivation

StressLevel

ANOVA Univariat & Effect Size η²

MANOVA Model Penuh

Estimated Marginal Means (EMM)

ANCOVA

Model ANCOVA Utama

Uji Interaksi (Homogeneity of Regression Slopes)

Uji Diagnostik

Estimated Marginal Means (EMMeans)

MANCOVA

Model MANCOVA

Hasil Uji MANCOVA — Pillai’s Trace

Effect Size (Partial Eta Squared)