1. Pendahuluan

Penelitian ini menganalisis pola tidur mahasiswa menggunakan dataset Student Sleep Patterns yang bersumber dari Kaggle (https://www.kaggle.com/datasets/arsalanjamal002/student-sleep-patterns). Dataset ini terdiri atas 500 baris (mahasiswa) dan 14 kolom. Setiap baris mewakili satu mahasiswa unik, dengan kolom-kolom yang menggambarkan atribut serta informasi terkait pola tidur mereka. Analisis dilakukan menggunakan enam metode statistika multivariat yaitu One-Way ANOVA, Two-Way ANOVA, One-Way MANOVA, Two-Way MANOVA, One-Way MANCOVA, dan Two-Way MANCOVA.

Variabel dependen: Sleep_Duration (Y1) dan Sleep_Quality (Y2)
Faktor: Gender (Male/Female/Other) dan University_Year (1st–4th Year)
Kovariat: Screen_Time, Age, Study_Hours, Caffeine_Intake, Physical_Activity, Weekday_Sleep_Start, Weekend_Sleep_Start, Weekday_Sleep_End, Weekend_Sleep_End.

2. Persiapan Data

# Library
library(tidyverse)
library(car)
library(MVN)
library(heplots)
library(rstatix)
library(corrplot)

# Import & Persiapan Data
data <- read.csv("student_sleep_patterns.csv")

# Mengurutan level faktor
data$Gender <- factor(data$Gender,
                      levels = c("Male", "Female", "Other"))
data$University_Year <- factor(data$University_Year,
                               levels = c("1st Year", "2nd Year",
                                          "3rd Year", "4th Year"))

# Cek distribusi faktor
table(data$Gender)
## 
##   Male Female  Other 
##    186    166    148
table(data$University_Year)
## 
## 1st Year 2nd Year 3rd Year 4th Year 
##      125      131      132      112

3. Statistika Deskriptif

3.1 Deskriptif seluruh variabel numerik

data %>%
  summarise(across(
    c(Sleep_Duration, Sleep_Quality, Study_Hours, Screen_Time,
      Caffeine_Intake, Physical_Activity, Age,
      Weekday_Sleep_Start, Weekend_Sleep_Start,
      Weekday_Sleep_End, Weekend_Sleep_End),
    list(Min    = ~min(.),
         Q1     = ~quantile(., 0.25),
         Median = ~median(.),
         Mean   = ~round(mean(.), 2),
         Q3     = ~quantile(., 0.75),
         Max    = ~max(.))
  ))
##   Sleep_Duration_Min Sleep_Duration_Q1 Sleep_Duration_Median
## 1                  4               5.1                   6.5
##   Sleep_Duration_Mean Sleep_Duration_Q3 Sleep_Duration_Max Sleep_Quality_Min
## 1                6.47               7.8                  9                 1
##   Sleep_Quality_Q1 Sleep_Quality_Median Sleep_Quality_Mean Sleep_Quality_Q3
## 1                3                    5               5.36                8
##   Sleep_Quality_Max Study_Hours_Min Study_Hours_Q1 Study_Hours_Median
## 1                10             0.1            2.9               6.05
##   Study_Hours_Mean Study_Hours_Q3 Study_Hours_Max Screen_Time_Min
## 1             5.98            8.8              12               1
##   Screen_Time_Q1 Screen_Time_Median Screen_Time_Mean Screen_Time_Q3
## 1            1.8                2.6             2.52            3.3
##   Screen_Time_Max Caffeine_Intake_Min Caffeine_Intake_Q1 Caffeine_Intake_Median
## 1               4                   0                  1                      2
##   Caffeine_Intake_Mean Caffeine_Intake_Q3 Caffeine_Intake_Max
## 1                 2.46                  4                   5
##   Physical_Activity_Min Physical_Activity_Q1 Physical_Activity_Median
## 1                     0                32.75                     62.5
##   Physical_Activity_Mean Physical_Activity_Q3 Physical_Activity_Max Age_Min
## 1                  62.34                93.25                   120      18
##   Age_Q1 Age_Median Age_Mean Age_Q3 Age_Max Weekday_Sleep_Start_Min
## 1     20         21    21.54     24      25                    1.08
##   Weekday_Sleep_Start_Q1 Weekday_Sleep_Start_Median Weekday_Sleep_Start_Mean
## 1                 6.0875                     10.635                    11.17
##   Weekday_Sleep_Start_Q3 Weekday_Sleep_Start_Max Weekend_Sleep_Start_Min
## 1                16.1525                   21.93                    2.05
##   Weekend_Sleep_Start_Q1 Weekend_Sleep_Start_Median Weekend_Sleep_Start_Mean
## 1                 7.2975                      12.69                    12.38
##   Weekend_Sleep_Start_Q3 Weekend_Sleep_Start_Max Weekday_Sleep_End_Min
## 1                17.3275                      22                     5
##   Weekday_Sleep_End_Q1 Weekday_Sleep_End_Median Weekday_Sleep_End_Mean
## 1                  5.9                    6.885                   6.93
##   Weekday_Sleep_End_Q3 Weekday_Sleep_End_Max Weekend_Sleep_End_Min
## 1               7.9725                  8.98                  7.02
##   Weekend_Sleep_End_Q1 Weekend_Sleep_End_Median Weekend_Sleep_End_Mean
## 1               8.0475                    9.005                   8.99
##   Weekend_Sleep_End_Q3 Weekend_Sleep_End_Max
## 1                9.925                 10.99

Interpretasi: Rata-rata durasi tidur mahasiswa adalah 6,47 jam, sedikit di bawah rekomendasi 7–9 jam untuk dewasa muda. Kualitas tidur memiliki rata-rata 5,36 dari skala 1–10 dengan sebaran yang cukup lebar (SD ≈ 3), mengindikasikan variasi kualitas tidur yang tinggi antar mahasiswa. Jam belajar rata-rata 5,98 jam/hari dengan rentang yang sangat lebar (0,1–12 jam), mencerminkan perbedaan beban studi yang signifikan. Waktu mulai tidur pada hari kerja (Weekday_Sleep_Start) sangat bervariasi (1,08–21,93), menunjukkan pola tidur mahasiswa yang tidak teratur.

3.2 Deskriptif per Gender

data %>%
  group_by(Gender) %>%
  summarise(
    n                  = n(),
    Mean_Sleep_Dur     = round(mean(Sleep_Duration), 3),
    SD_Sleep_Dur       = round(sd(Sleep_Duration), 3),
    Mean_Sleep_Qual    = round(mean(Sleep_Quality), 3),
    SD_Sleep_Qual      = round(sd(Sleep_Quality), 3)
  )
## # A tibble: 3 × 6
##   Gender     n Mean_Sleep_Dur SD_Sleep_Dur Mean_Sleep_Qual SD_Sleep_Qual
##   <fct>  <int>          <dbl>        <dbl>           <dbl>         <dbl>
## 1 Male     186           6.36         1.49            5.10          3.02
## 2 Female   166           6.53         1.50            5.55          2.84
## 3 Other    148           6.55         1.47            5.47          3.03

Interpretasi: Mahasiswa laki-laki (Male, n=186) memiliki rata-rata durasi tidur paling rendah (6,358 jam) dan kualitas tidur paling rendah (5,102) dibandingkan perempuan dan kelompok Other. Mahasiswa perempuan (Female, n=166) memiliki rata-rata kualitas tidur tertinggi (5,554) dengan SD terkecil (2,842), menunjukkan pola yang lebih konsisten. Perbedaan antar kelompok gender secara deskriptif tampak kecil, selisih durasi tidur antara laki-laki dan perempuan hanya 0,17 jam sehingga perlu diuji secara inferensial apakah perbedaan tersebut signifikan.

3.3 Deskriptif per University_Year

data %>%
  group_by(University_Year) %>%
  summarise(
    n                  = n(),
    Mean_Sleep_Dur     = round(mean(Sleep_Duration), 3),
    SD_Sleep_Dur       = round(sd(Sleep_Duration), 3),
    Mean_Sleep_Qual    = round(mean(Sleep_Quality), 3),
    SD_Sleep_Qual      = round(sd(Sleep_Quality), 3)
  )
## # A tibble: 4 × 6
##   University_Year     n Mean_Sleep_Dur SD_Sleep_Dur Mean_Sleep_Qual
##   <fct>           <int>          <dbl>        <dbl>           <dbl>
## 1 1st Year          125           6.49         1.47            5.24
## 2 2nd Year          131           6.56         1.45            5.32
## 3 3rd Year          132           6.49         1.60            5.54
## 4 4th Year          112           6.32         1.42            5.33
## # ℹ 1 more variable: SD_Sleep_Qual <dbl>

Interpretasi: Mahasiswa tahun ke-2 (2nd Year, n=131) memiliki rata-rata durasi tidur tertinggi (6,562 jam), sedangkan mahasiswa tahun ke-4 (4th Year, n=112) justru memiliki durasi tidur paling rendah (6,324 jam). Kualitas tidur cenderung meningkat dari tahun ke-1 hingga ke-3 (5,240 → 5,545), lalu sedikit menurun di tahun ke-4 (5,330). Pola ini mengindikasikan kemungkinan tekanan akademik yang meningkat di tahun akhir berdampak pada penurunan durasi dan kualitas tidur, meskipun perbedaan antar angkatan secara deskriptif masih sangat kecil.

4. Visualisasi

4.1 Histogram semua variabel numerik

data_numeric <- data %>%
  select(Sleep_Duration, Sleep_Quality, Study_Hours, Screen_Time,
         Caffeine_Intake, Physical_Activity, Age,
         Weekday_Sleep_Start, Weekend_Sleep_Start,
         Weekday_Sleep_End, Weekend_Sleep_End)

data_long <- data_numeric %>%
  pivot_longer(everything(), names_to = "Variable", values_to = "Value")

ggplot(data_long, aes(x = Value)) +
  geom_histogram(bins = 30, fill = "steelblue", color = "black", alpha = 0.7) +
  facet_wrap(~ Variable, scales = "free", ncol = 4) +
  labs(title = "Histogram Distribusi Seluruh Variabel Numerik",
       subtitle = "Setiap variabel memiliki skala sendiri (free scales)") +
  theme_minimal() +
  theme(strip.text = element_text(face = "bold", size = 10),
        axis.text.x = element_text(angle = 45, hjust = 1))

Interpretasi: Berdasarkan histogram, Sleep_Duration mendekati distribusi normal dengan puncak di sekitar 6–7 jam. Sleep_Quality tampak mendekati distribusi seragam (uniform) yang mencakup seluruh rentang 1–10, menandakan tidak ada dominasi pola kualitas tidur tertentu. Physical_Activity terdistribusi cukup merata, sementara Screen_Time dan Caffeine_Intake memiliki distribusi yang relatif simetris. Weekday_Sleep_Start dan Weekend_Sleep_Start menunjukkan distribusi bimodal atau sangat lebar, mencerminkan heterogenitas kebiasaan tidur mahasiswa. Weekday_Sleep_End dan Weekend_Sleep_End memiliki distribusi yang lebih sempit dan terpusat, menunjukkan mahasiswa cenderung bangun pada jam yang lebih konsisten.

4.2 Heatmap korelasi semua variabel numerik

cor_matrix <- cor(data_numeric, use = "complete.obs")

corrplot(cor_matrix,
         method = "color",
         type = "upper",
         order = "hclust",
         tl.col = "black",
         tl.srt = 45,
         diag = FALSE,
         title = "Matriks Korelasi Antar Seluruh Variabel Numerik",
         mar = c(0, 0, 2, 0),
         addCoef.col = "black",
         number.cex = 0.7,
         tl.cex = 0.8)

Interpretasi: Heatmap korelasi menunjukkan bahwa hampir tidak ada korelasi kuat antar variabel numerik dalam dataset ini, seluruh koefisien korelasi berada jauh di bawah 0,3 (baik positif maupun negatif). Korelasi antara Sleep_Duration dan Sleep_Quality sangat lemah (r ≈ -0,016), mengindikasikan bahwa durasi tidur yang lebih lama tidak serta merta berarti kualitas tidur yang lebih baik pada mahasiswa. Tidak adanya multikolinearitas antar kovariat merupakan hal yang baik untuk analisis MANCOVA, karena kovariat dapat dimasukkan ke model tanpa masalah kolinearitas.

5. Uji Asumsi ANOVA (Univariat)

5.1 Normalitas Shapiro-Wilk per kelompok

# Per Gender
data %>% group_by(Gender) %>%
  summarise(
    W_Dur  = shapiro.test(Sleep_Duration)$statistic,
    p_Dur  = shapiro.test(Sleep_Duration)$p.value,
    W_Qual = shapiro.test(Sleep_Quality)$statistic,
    p_Qual = shapiro.test(Sleep_Quality)$p.value
  )
## # A tibble: 3 × 5
##   Gender W_Dur       p_Dur W_Qual        p_Qual
##   <fct>  <dbl>       <dbl>  <dbl>         <dbl>
## 1 Male   0.944 0.00000113   0.917 0.00000000883
## 2 Female 0.936 0.000000831  0.939 0.00000154   
## 3 Other  0.948 0.0000243    0.918 0.000000185
# Per University_Year
data %>% group_by(University_Year) %>%
  summarise(
    W_Dur  = shapiro.test(Sleep_Duration)$statistic,
    p_Dur  = shapiro.test(Sleep_Duration)$p.value,
    W_Qual = shapiro.test(Sleep_Quality)$statistic,
    p_Qual = shapiro.test(Sleep_Quality)$p.value
  )
## # A tibble: 4 × 5
##   University_Year W_Dur      p_Dur W_Qual      p_Qual
##   <fct>           <dbl>      <dbl>  <dbl>       <dbl>
## 1 1st Year        0.949 0.000135    0.937 0.0000185  
## 2 2nd Year        0.944 0.0000352   0.922 0.00000121 
## 3 3rd Year        0.922 0.00000119  0.906 0.000000130
## 4 4th Year        0.951 0.000438    0.930 0.0000182

Interpretasi: Uji Shapiro-Wilk menguji normalitas data pada setiap kelompok. Untuk Sleep_Duration, nilai W mendekati 1 pada semua kelompok gender maupun angkatan, mengindikasikan distribusi yang mendekati normal. Untuk Sleep_Quality, nilai W cenderung lebih kecil karena distribusinya yang mendekati seragam (uniform) sehingga kemungkinan besar melanggar asumsi normalitas (p < 0,05). Namun, karena ukuran sampel setiap kelompok ≥ 100, asumsi normalitas tidak kritis karena berdasarkan Central Limit Theorem distribusi rata-rata sampel mendekati normal sehingga ANOVA tetap valid dan robust.

5.2 Homogenitas Varians (Levene’s Test)

leveneTest(Sleep_Duration ~ Gender,          data = data)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   2  0.1558 0.8558
##       497
leveneTest(Sleep_Quality  ~ University_Year, data = data)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   3  1.5431 0.2025
##       496
leveneTest(Sleep_Duration ~ University_Year, data = data)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   3  1.6705 0.1724
##       496
leveneTest(Sleep_Quality  ~ Gender,          data = data)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   2  1.7286 0.1786
##       497

Interpretasi: Levene’s Test menguji kesamaan varians antar kelompok. Nilai p-value yang diperoleh untuk seluruh kombinasi faktor-variabel dependen menunjukkan bahwa tidak ada bukti yang cukup untuk menolak H₀ (p > 0,05), artinya varians Sleep_Duration maupun Sleep_Quality homogen di seluruh kelompok gender dan angkatan. Terpenuhinya asumsi homogenitas varians memperkuat validitas penggunaan ANOVA standar beserta uji post-hoc Tukey HSD.

6. Model 1 — One-Way ANOVA

6.1 Model A (Y = Sleep_Duration; Faktor = Gender)

anova1A <- aov(Sleep_Duration ~ Gender, data = data)
summary(anova1A)
##              Df Sum Sq Mean Sq F value Pr(>F)
## Gender        2    3.9   1.948   0.882  0.415
## Residuals   497 1097.6   2.208
TukeyHSD(anova1A)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Duration ~ Gender, data = data)
## 
## $Gender
##                    diff        lwr       upr     p adj
## Female-Male  0.17386319 -0.1991469 0.5468733 0.5171725
## Other-Male   0.19125981 -0.1935496 0.5760692 0.4726677
## Other-Female 0.01739661 -0.3775512 0.4123444 0.9941064

Interpretasi: Hasil One-Way ANOVA menunjukkan F(2, 497) = 0,882 dengan p-value > 0,05, sehingga H₀ gagal ditolak. Tidak terdapat perbedaan yang signifikan rata-rata durasi tidur antar kelompok gender. Meskipun secara deskriptif laki-laki tidur rata-rata 6,358 jam, perempuan 6,532 jam, dan kelompok Other 6,549 jam, perbedaan selisih ±0,19 jam tersebut tidak cukup besar untuk dinyatakan signifikan secara statistik. Hasil post-hoc Tukey HSD mengkonfirmasi tidak ada satu pun pasangan gender yang berbeda secara signifikan (seluruh p adj > 0,05). Dapat disimpulkan bahwa gender tidak memengaruhi durasi tidur mahasiswa dalam dataset ini.

6.2 Model B (Y = Sleep_Quality; Faktor = University_Year)

anova1B <- aov(Sleep_Quality ~ University_Year, data = data)
summary(anova1B)
##                  Df Sum Sq Mean Sq F value Pr(>F)
## University_Year   3      7   2.213    0.25  0.861
## Residuals       496   4387   8.844
TukeyHSD(anova1B)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Quality ~ University_Year, data = data)
## 
## $University_Year
##                           diff        lwr       upr     p adj
## 2nd Year-1st Year  0.080610687 -0.8779222 1.0391436 0.9963995
## 3rd Year-1st Year  0.305454545 -0.6513038 1.2622129 0.8435917
## 4th Year-1st Year  0.090357143 -0.9070853 1.0877996 0.9955126
## 3rd Year-2nd Year  0.224843858 -0.7205939 1.1702816 0.9279200
## 4th Year-2nd Year  0.009746456 -0.9768423 0.9963352 0.9999941
## 4th Year-3rd Year -0.215097403 -1.1999622 0.7697674 0.9429555

Interpretasi: Hasil One-Way ANOVA menunjukkan F(3, 496) = 0,250 dengan p-value > 0,05, sehingga H₀ gagal ditolak. Tidak terdapat perbedaan signifikan rata-rata kualitas tidur antar tahun angkatan. Rata-rata kualitas tidur antara 5,240 (1st Year) hingga 5,545 (3rd Year), ini menunjukkan perbedaan yang sangat kecil. Post-hoc Tukey HSD mengkonfirmasi tidak ada pasangan angkatan yang berbeda secara signifikan. Dapat disimpulkan bahwa tahun angkatan tidak memengaruhi kualitas tidur mahasiswa secara signifikan.

7. Model 2 — Two-Way ANOVA

7.1 Model A (Y = Sleep_Duration; F1 = Gender; F2 = University_Year)

anova2A <- aov(Sleep_Duration ~ Gender + University_Year +
                 Gender:University_Year, data = data)
summary(anova2A)
##                         Df Sum Sq Mean Sq F value Pr(>F)
## Gender                   2    3.9   1.948   0.879  0.416
## University_Year          3    3.8   1.280   0.577  0.630
## Gender:University_Year   6   12.2   2.038   0.919  0.481
## Residuals              488 1081.6   2.216
TukeyHSD(anova2A)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Duration ~ Gender + University_Year + Gender:University_Year, data = data)
## 
## $Gender
##                    diff        lwr       upr     p adj
## Female-Male  0.17386319 -0.1998267 0.5475531 0.5183796
## Other-Male   0.19125981 -0.1942509 0.5767706 0.4739223
## Other-Female 0.01739661 -0.3782710 0.4130642 0.9941272
## 
## $University_Year
##                           diff        lwr       upr     p adj
## 2nd Year-1st Year  0.078810440 -0.4010505 0.5586714 0.9744717
## 3rd Year-1st Year -0.002034263 -0.4810069 0.4769383 0.9999995
## 4th Year-1st Year -0.168280594 -0.6676205 0.3310593 0.8209928
## 3rd Year-2nd Year -0.080844704 -0.5541500 0.3924606 0.9714381
## 4th Year-2nd Year -0.247091034 -0.7409973 0.2468153 0.5699476
## 4th Year-3rd Year -0.166246331 -0.6592896 0.3267969 0.8207596
## 
## $`Gender:University_Year`
##                                         diff        lwr       upr     p adj
## Female:1st Year-Male:1st Year    0.463689218 -0.5847110 1.5120894 0.9521750
## Other:1st Year-Male:1st Year     0.313995215 -0.7687264 1.3967168 0.9984976
## Male:2nd Year-Male:1st Year      0.035437710 -0.9574905 1.0283659 1.0000000
## Female:2nd Year-Male:1st Year    0.358732057 -0.7239896 1.4414537 0.9950914
## Other:2nd Year-Male:1st Year     0.687004662 -0.3882428 1.7622521 0.6243003
## Male:3rd Year-Male:1st Year      0.330113636 -0.6902970 1.3505243 0.9960088
## Female:3rd Year-Male:1st Year    0.312474747 -0.7240757 1.3490252 0.9978653
## Other:3rd Year-Male:1st Year     0.081876457 -0.9933710 1.1571239 1.0000000
## Male:4th Year-Male:1st Year      0.111363636 -0.9567349 1.1794622 1.0000000
## Female:4th Year-Male:1st Year    0.026363636 -1.0417349 1.0944622 1.0000000
## Other:4th Year-Male:1st Year     0.126988636 -1.0088941 1.2628714 0.9999999
## Other:1st Year-Female:1st Year  -0.149694002 -1.2382343 0.9388463 0.9999991
## Male:2nd Year-Female:1st Year   -0.428251507 -1.4275214 0.5710183 0.9618031
## Female:2nd Year-Female:1st Year -0.104957160 -1.1934974 0.9835831 1.0000000
## Other:2nd Year-Female:1st Year   0.223315444 -0.8577909 1.3044218 0.9999427
## Male:3rd Year-Female:1st Year   -0.133575581 -1.1601581 0.8930070 0.9999995
## Female:3rd Year-Female:1st Year -0.151214470 -1.1938412 0.8914123 0.9999985
## Other:3rd Year-Female:1st Year  -0.381812761 -1.4629191 0.6992936 0.9915677
## Male:4th Year-Female:1st Year   -0.352325581 -1.4263220 0.7216709 0.9954949
## Female:4th Year-Female:1st Year -0.437325581 -1.5113220 0.6366709 0.9738376
## Other:4th Year-Female:1st Year  -0.336700581 -1.4781310 0.8047298 0.9982458
## Male:2nd Year-Other:1st Year    -0.278557505 -1.3137789 0.7566639 0.9992493
## Female:2nd Year-Other:1st Year   0.044736842 -1.0768973 1.1663710 1.0000000
## Other:2nd Year-Other:1st Year    0.373009447 -0.7414115 1.4874304 0.9946429
## Male:3rd Year-Other:1st Year     0.016118421 -1.0454912 1.0777280 1.0000000
## Female:3rd Year-Other:1st Year  -0.001520468 -1.0786527 1.0756117 1.0000000
## Other:3rd Year-Other:1st Year   -0.232118758 -1.3465397 0.8823022 0.9999377
## Male:4th Year-Other:1st Year    -0.202631579 -1.3101566 0.9048934 0.9999832
## Female:4th Year-Other:1st Year  -0.287631579 -1.3951566 0.8198934 0.9994628
## Other:4th Year-Other:1st Year   -0.187006579 -1.3600396 0.9860265 0.9999960
## Female:2nd Year-Male:2nd Year    0.323294347 -0.7119271 1.3585158 0.9970734
## Other:2nd Year-Male:2nd Year     0.651566952 -0.3758348 1.6789687 0.6354477
## Male:3rd Year-Male:2nd Year      0.294675926 -0.6751876 1.2645394 0.9977093
## Female:3rd Year-Male:2nd Year    0.277037037 -0.7097933 1.2638674 0.9988856
## Other:3rd Year-Male:2nd Year     0.046438746 -0.9809630 1.0738405 1.0000000
## Male:4th Year-Male:2nd Year      0.075925926 -0.9439916 1.0958435 1.0000000
## Female:4th Year-Male:2nd Year   -0.009074074 -1.0289916 1.0108435 1.0000000
## Other:4th Year-Male:2nd Year     0.091550926 -0.9991492 1.1822511 1.0000000
## Other:2nd Year-Female:2nd Year   0.328272605 -0.7861484 1.4426936 0.9982680
## Male:3rd Year-Female:2nd Year   -0.028618421 -1.0902280 1.0329912 1.0000000
## Female:3rd Year-Female:2nd Year -0.046257310 -1.1233895 1.0308749 1.0000000
## Other:3rd Year-Female:2nd Year  -0.276855601 -1.3912766 0.8375654 0.9996484
## Male:4th Year-Female:2nd Year   -0.247368421 -1.3548934 0.8601566 0.9998753
## Female:4th Year-Female:2nd Year -0.332368421 -1.4398934 0.7751566 0.9979503
## Other:4th Year-Female:2nd Year  -0.231743421 -1.4047765 0.9412896 0.9999634
## Male:3rd Year-Other:2nd Year    -0.356891026 -1.4108767 0.6970947 0.9940853
## Female:3rd Year-Other:2nd Year  -0.374529915 -1.4441489 0.6950891 0.9921502
## Other:3rd Year-Other:2nd Year   -0.605128205 -1.7122890 0.5020326 0.8203011
## Male:4th Year-Other:2nd Year    -0.575641026 -1.6758604 0.5245783 0.8592592
## Female:4th Year-Other:2nd Year  -0.660641026 -1.7608604 0.4395783 0.7123176
## Other:4th Year-Other:2nd Year   -0.560016026 -1.7261539 0.6061219 0.9166827
## Female:3rd Year-Male:3rd Year   -0.017638889 -1.0321169 0.9968391 1.0000000
## Other:3rd Year-Male:3rd Year    -0.248237179 -1.3022229 0.8057485 0.9997902
## Male:4th Year-Male:3rd Year     -0.218750000 -1.2654416 0.8279416 0.9999356
## Female:4th Year-Male:3rd Year   -0.303750000 -1.3504416 0.7429416 0.9984884
## Other:4th Year-Male:3rd Year    -0.203125000 -1.3189020 0.9126520 0.9999841
## Other:3rd Year-Female:3rd Year  -0.230598291 -1.3002173 0.8390207 0.9999122
## Male:4th Year-Female:3rd Year   -0.201111111 -1.2635433 0.8613211 0.9999763
## Female:4th Year-Female:3rd Year -0.286111111 -1.3485433 0.7763211 0.9992436
## Other:4th Year-Female:3rd Year  -0.185486111 -1.3160423 0.9450700 0.9999946
## Male:4th Year-Other:3rd Year     0.029487179 -1.0707321 1.1297065 1.0000000
## Female:4th Year-Other:3rd Year  -0.055512821 -1.1557321 1.0447065 1.0000000
## Other:4th Year-Other:3rd Year    0.045112179 -1.1210257 1.2112501 1.0000000
## Female:4th Year-Male:4th Year   -0.085000000 -1.1782337 1.0082337 1.0000000
## Other:4th Year-Male:4th Year     0.015625000 -1.1439245 1.1751745 1.0000000
## Other:4th Year-Female:4th Year   0.100625000 -1.0589245 1.2601745 1.0000000

Interpretasi: Hasil Two-Way ANOVA untuk Sleep_Duration menunjukkan:

  • Efek utama Gender tidak signifikan (p > 0,05): gender secara mandiri tidak memengaruhi durasi tidur.
  • Efek utama University_Year tidak signifikan (p > 0,05): tahun kuliah secara mandiri tidak memengaruhi durasi tidur.
  • Efek interaksi Gender × University_Year tidak signifikan (p > 0,05): pengaruh gender terhadap durasi tidur tidak bergantung pada tahun kuliah dan sebaliknya.

Karena seluruh efek tidak signifikan, dapat disimpulkan bahwa kombinasi gender dan tahun kuliah tidak memengaruhi durasi tidur mahasiswa. Post-hoc Tukey HSD konsisten mengkonfirmasi tidak ada pasangan kelompok yang berbeda signifikan.

7.2 Model B (Y = Sleep_Quality; F1 = Gender; F2 = University_Year)

anova2B <- aov(Sleep_Quality ~ Gender + University_Year +
                 Gender:University_Year, data = data)
summary(anova2B)
##                         Df Sum Sq Mean Sq F value Pr(>F)
## Gender                   2     21  10.257   1.161  0.314
## University_Year          3      7   2.209   0.250  0.861
## Gender:University_Year   6     56   9.348   1.058  0.387
## Residuals              488   4310   8.832
TukeyHSD(anova2B)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Quality ~ Gender + University_Year + Gender:University_Year, data = data)
## 
## $Gender
##                     diff        lwr       upr     p adj
## Female-Male   0.45206633 -0.2939247 1.1980573 0.3289863
## Other-Male    0.37082244 -0.3987662 1.1404111 0.4943409
## Other-Female -0.08124389 -0.8711086 0.7086208 0.9682834
## 
## $University_Year
##                          diff        lwr       upr     p adj
## 2nd Year-1st Year  0.10732026 -0.8506181 1.0652587 0.9916018
## 3rd Year-1st Year  0.31002069 -0.6461443 1.2661857 0.8373794
## 4th Year-1st Year  0.09119645 -0.9056274 1.0880203 0.9953788
## 3rd Year-2nd Year  0.20270043 -0.7421510 1.1475518 0.9457046
## 4th Year-2nd Year -0.01612381 -1.0021007 0.9698531 0.9999731
## 4th Year-3rd Year -0.21882423 -1.2030782 0.7654298 0.9400700
## 
## $`Gender:University_Year`
##                                          diff        lwr      upr     p adj
## Female:1st Year-Male:1st Year    6.976744e-01 -1.3952293 2.790578 0.9948267
## Other:1st Year-Male:1st Year     1.421085e-14 -2.1614191 2.161419 1.0000000
## Male:2nd Year-Male:1st Year      2.037037e-01 -1.7784623 2.185870 1.0000000
## Female:2nd Year-Male:1st Year    8.157895e-01 -1.3456296 2.977209 0.9854995
## Other:2nd Year-Male:1st Year     2.486900e-14 -2.1464985 2.146499 1.0000000
## Male:3rd Year-Male:1st Year      4.375000e-01 -1.5995287 2.474529 0.9999154
## Female:3rd Year-Male:1st Year    4.888889e-01 -1.5803594 2.558137 0.9997837
## Other:3rd Year-Male:1st Year     7.435897e-01 -1.4029088 2.890088 0.9928254
## Male:4th Year-Male:1st Year     -3.250000e-01 -2.4572273 1.807227 0.9999975
## Female:4th Year-Male:1st Year    2.250000e-01 -1.9072273 2.357227 0.9999999
## Other:4th Year-Male:1st Year     1.281250e+00 -0.9862937 3.548794 0.7858816
## Other:1st Year-Female:1st Year  -6.976744e-01 -2.8707092 1.475360 0.9962654
## Male:2nd Year-Female:1st Year   -4.939707e-01 -2.4887964 1.500855 0.9996592
## Female:2nd Year-Female:1st Year  1.181151e-01 -2.0549197 2.291150 1.0000000
## Other:2nd Year-Female:1st Year  -6.976744e-01 -2.8558690 1.460520 0.9960349
## Male:3rd Year-Female:1st Year   -2.601744e-01 -2.3095240 1.789175 0.9999996
## Female:3rd Year-Female:1st Year -2.087855e-01 -2.2901639 1.872593 1.0000000
## Other:3rd Year-Female:1st Year   4.591532e-02 -2.1122792 2.204110 1.0000000
## Male:4th Year-Female:1st Year   -1.022674e+00 -3.1666756 1.121327 0.9202520
## Female:4th Year-Female:1st Year -4.726744e-01 -2.6166756 1.671327 0.9998904
## Other:4th Year-Female:1st Year   5.835756e-01 -1.6950429 2.862194 0.9995295
## Male:2nd Year-Other:1st Year     2.037037e-01 -1.8628916 2.270299 1.0000000
## Female:2nd Year-Other:1st Year   8.157895e-01 -1.4233100 3.054889 0.9890985
## Other:2nd Year-Other:1st Year    1.065814e-14 -2.2247000 2.224700 1.0000000
## Male:3rd Year-Other:1st Year     4.375000e-01 -1.6817735 2.556773 0.9999430
## Female:3rd Year-Other:1st Year   4.888889e-01 -1.6613721 2.639150 0.9998514
## Other:3rd Year-Other:1st Year    7.435897e-01 -1.4811103 2.968290 0.9947069
## Male:4th Year-Other:1st Year    -3.250000e-01 -2.5359336 1.885934 0.9999983
## Female:4th Year-Other:1st Year   2.250000e-01 -1.9859336 2.435934 1.0000000
## Other:4th Year-Other:1st Year    1.281250e+00 -1.0604563 3.622956 0.8192581
## Female:2nd Year-Male:2nd Year    6.120858e-01 -1.4545095 2.678681 0.9981800
## Other:2nd Year-Male:2nd Year    -2.037037e-01 -2.2546887 1.847281 1.0000000
## Male:3rd Year-Male:2nd Year      2.337963e-01 -1.7023260 2.169919 0.9999998
## Female:3rd Year-Male:2nd Year    2.851852e-01 -1.6848077 2.255178 0.9999985
## Other:3rd Year-Male:2nd Year     5.398860e-01 -1.5110990 2.590871 0.9993896
## Male:4th Year-Male:2nd Year     -5.287037e-01 -2.5647481 1.507341 0.9994634
## Female:4th Year-Male:2nd Year    2.129630e-02 -2.0147481 2.057341 1.0000000
## Other:4th Year-Male:2nd Year     1.077546e+00 -1.0998002 3.254893 0.8992058
## Other:2nd Year-Female:2nd Year  -8.157895e-01 -3.0404895 1.408911 0.9885096
## Male:3rd Year-Female:2nd Year   -3.782895e-01 -2.4975629 1.740984 0.9999870
## Female:3rd Year-Female:2nd Year -3.269006e-01 -2.4771616 1.823360 0.9999975
## Other:3rd Year-Female:2nd Year  -7.219973e-02 -2.2968997 2.152500 1.0000000
## Male:4th Year-Female:2nd Year   -1.140789e+00 -3.3517231 1.070144 0.8702313
## Female:4th Year-Female:2nd Year -5.907895e-01 -2.8017231 1.620144 0.9992968
## Other:4th Year-Female:2nd Year   4.654605e-01 -1.8762458 2.807167 0.9999611
## Male:3rd Year-Other:2nd Year     4.375000e-01 -1.6665541 2.541554 0.9999388
## Female:3rd Year-Other:2nd Year   4.888889e-01 -1.6463736 2.624151 0.9998409
## Other:3rd Year-Other:2nd Year    7.435897e-01 -1.4666169 2.953796 0.9944021
## Male:4th Year-Other:2nd Year    -3.250000e-01 -2.5213495 1.871349 0.9999981
## Female:4th Year-Other:2nd Year   2.250000e-01 -1.9713495 2.421349 1.0000000
## Other:4th Year-Other:2nd Year    1.281250e+00 -1.0466916 3.609192 0.8134351
## Female:3rd Year-Male:3rd Year    5.138889e-02 -1.9737965 2.076574 1.0000000
## Other:3rd Year-Male:3rd Year     3.060897e-01 -1.7979643 2.410144 0.9999984
## Male:4th Year-Male:3rd Year     -7.625000e-01 -2.8519930 1.326993 0.9889552
## Female:4th Year-Male:3rd Year   -2.125000e-01 -2.3019930 1.876993 1.0000000
## Other:4th Year-Male:3rd Year     8.437500e-01 -1.3836570 3.071157 0.9850739
## Other:3rd Year-Female:3rd Year   2.547009e-01 -1.8805617 2.389963 0.9999998
## Male:4th Year-Female:3rd Year   -8.138889e-01 -2.9348046 1.307027 0.9834581
## Female:4th Year-Female:3rd Year -2.638889e-01 -2.3848046 1.857027 0.9999997
## Other:4th Year-Female:3rd Year   7.923611e-01 -1.4645492 3.049271 0.9919743
## Male:4th Year-Other:3rd Year    -1.068590e+00 -3.2649392 1.127760 0.9094391
## Female:4th Year-Other:3rd Year  -5.185897e-01 -2.7149392 1.677760 0.9997850
## Other:4th Year-Other:3rd Year    5.376603e-01 -1.7902813 2.865602 0.9998267
## Female:4th Year-Male:4th Year    5.500000e-01 -1.6324042 2.732404 0.9995966
## Other:4th Year-Male:4th Year     1.606250e+00 -0.7085392 3.921039 0.4931967
## Other:4th Year-Female:4th Year   1.056250e+00 -1.2585392 3.371039 0.9406380

Interpretasi: Hasil Two-Way ANOVA untuk Sleep_Quality menunjukkan bahwa efek utama Gender, efek utama University_Year, maupun efek interaksi Gender × University_Year semuanya tidak signifikan (p > 0,05). Hal ini mengindikasikan bahwa kualitas tidur mahasiswa tidak dipengaruhi oleh gender, tahun kuliah, maupun kombinasi keduanya. Tidak adanya efek interaksi berarti pola kualitas tidur antar gender konsisten di semua angkatan, karena tidak ada angkatan tertentu yang membuat perbedaan gender dalam kualitas tidur menjadi lebih atau kurang menonjol.

8. Uji Asumsi MANOVA / MANCOVA

8.1 Normalitas Multivariat (Mardia’s Test)

mvn_result <- mvn(
  data     = data[, c("Sleep_Duration", "Sleep_Quality")],
  mvn_test = "mardia"
)
print(mvn_result$multivariateNormality)
## NULL

Interpretasi: Mardia’s Test menguji normalitas multivariat melalui dua komponen: skewness multivariat dan kurtosis multivariat. Berdasarkan hasil:

  • Jika p-value skewness < 0,05: data memiliki kemiringan multivariat yang signifikan, mengindikasikan pelanggaran normalitas multivariat.
  • Jika p-value kurtosis > 0,05: komponen kurtosis tidak melanggar asumsi normalitas.

Karena Sleep_Quality berdistribusi mendekati seragam (uniform), kemungkinan besar uji skewness akan signifikan. Meski demikian, dengan n = 500 yang besar dan menggunakan Pillai’s Trace sebagai statistik uji (yang paling robust terhadap pelanggaran normalitas multivariat), analisis MANOVA dan MANCOVA tetap dapat dilanjutkan secara valid.

8.2 Homogenitas Matriks Kovarians (Box’s M Test)

boxM(cbind(Sleep_Duration, Sleep_Quality) ~ Gender,
     data = data)
## 
##  Box's M-test for Homogeneity of Covariance Matrices 
## 
## data:  data 
## Chi-Sq (approx.) = 4.6693, df = 6, p-value = 0.5869
boxM(cbind(Sleep_Duration, Sleep_Quality) ~ University_Year,
     data = data)
## 
##  Box's M-test for Homogeneity of Covariance Matrices 
## 
## data:  data 
## Chi-Sq (approx.) = 3.7791, df = 9, p-value = 0.9253

Interpretasi: Box’s M Test menguji kesamaan matriks kovarians variabel dependen (Sleep_Duration dan Sleep_Quality) di seluruh kelompok faktor (H₀: Σ₁ = Σ₂ = … = Σₖ).

  • Box’s M untuk Gender: jika p > 0,05, matriks kovarians homogen antar kelompok gender maka asumsi terpenuhi.
  • Box’s M untuk University_Year: jika p > 0,05, matriks kovarians homogen antar angkatan maka asumsi terpenuhi.

8.3 Uji Dependensi antar Variabel Dependen

cor.test(data$Sleep_Duration, data$Sleep_Quality)
## 
##  Pearson's product-moment correlation
## 
## data:  data$Sleep_Duration and data$Sleep_Quality
## t = -0.34904, df = 498, p-value = 0.7272
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.10318811  0.07215051
## sample estimates:
##         cor 
## -0.01563903

Interpretasi: Uji korelasi Pearson antara Sleep_Duration dan Sleep_Quality menghasilkan r ≈ -0,016 dengan p-value > 0,05. Ini berarti tidak terdapat korelasi yang signifikan antara durasi dan kualitas tidur. Meskipun dalam teori MANOVA lebih kuat ketika variabel dependen saling berkorelasi, analisis tetap dapat dilakukan karena MANOVA masih valid bahkan dengan korelasi rendah. Rendahnya korelasi ini mengindikasikan bahwa Sleep_Duration dan Sleep_Quality mengukur aspek tidur yang berbeda dan independen pada populasi mahasiswa ini, sehingga analisis multivariatnya tetap bermakna untuk menangkap gambaran tidur yang lebih komprehensif.

8.4 Uji Asumsi MANCOVA — Homogenitas Kemiringan Regresi

kovariat <- c("Screen_Time", "Age", "Study_Hours", "Caffeine_Intake",
              "Physical_Activity", "Weekday_Sleep_Start",
              "Weekend_Sleep_Start", "Weekday_Sleep_End",
              "Weekend_Sleep_End")
One-Way MANCOVA: University_Year × tiap Kovariat
for (kov in kovariat) {
  fit <- manova(as.formula(paste0(
    "cbind(Sleep_Duration, Sleep_Quality) ~ University_Year * ", kov)),
    data = data)
  res  <- summary(fit, test = "Pillai")
  pval <- res$stats[paste0("University_Year:", kov), "Pr(>F)"]
  cat(sprintf("University_Year x %-25s p = %.4f %s\n", kov, pval,
              ifelse(!is.na(pval) & pval < 0.05, "<-- SIGNIFIKAN", "")))
}
## University_Year x Screen_Time               p = 0.9041 
## University_Year x Age                       p = 0.0661 
## University_Year x Study_Hours               p = 0.7644 
## University_Year x Caffeine_Intake           p = 0.0090 <-- SIGNIFIKAN
## University_Year x Physical_Activity         p = 0.1811 
## University_Year x Weekday_Sleep_Start       p = 0.4681 
## University_Year x Weekend_Sleep_Start       p = 0.0548 
## University_Year x Weekday_Sleep_End         p = 0.6559 
## University_Year x Weekend_Sleep_End         p = 0.8561
One-Way MANCOVA: Gender × tiap Kovariat
for (kov in kovariat) {
  fit <- manova(as.formula(paste0(
    "cbind(Sleep_Duration, Sleep_Quality) ~ Gender * ", kov)),
    data = data)
  res  <- summary(fit, test = "Pillai")
  pval <- res$stats[paste0("Gender:", kov), "Pr(>F)"]
  cat(sprintf("Gender x %-25s p = %.4f %s\n", kov, pval,
              ifelse(!is.na(pval) & pval < 0.05, "<-- SIGNIFIKAN", "")))
}
## Gender x Screen_Time               p = 0.1742 
## Gender x Age                       p = 0.5503 
## Gender x Study_Hours               p = 0.9800 
## Gender x Caffeine_Intake           p = 0.0073 <-- SIGNIFIKAN
## Gender x Physical_Activity         p = 0.1909 
## Gender x Weekday_Sleep_Start       p = 0.9035 
## Gender x Weekend_Sleep_Start       p = 0.5944 
## Gender x Weekday_Sleep_End         p = 0.7027 
## Gender x Weekend_Sleep_End         p = 0.8219
Two-Way MANCOVA: Gender × tiap Kovariat
for (kov in kovariat) {
  fit <- manova(as.formula(paste0(
    "cbind(Sleep_Duration, Sleep_Quality) ~ Gender + University_Year +",
    " Gender:University_Year + ", kov, " + Gender:", kov)),
    data = data)
  res  <- summary(fit, test = "Pillai")
  pval <- res$stats[paste0("Gender:", kov), "Pr(>F)"]
  cat(sprintf("Gender x %-25s p = %.4f %s\n", kov, pval,
              ifelse(!is.na(pval) & pval < 0.05, "<-- SIGNIFIKAN", "")))
}
## Gender x Screen_Time               p = 0.2056 
## Gender x Age                       p = 0.5477 
## Gender x Study_Hours               p = 0.9749 
## Gender x Caffeine_Intake           p = 0.0123 <-- SIGNIFIKAN
## Gender x Physical_Activity         p = 0.1954 
## Gender x Weekday_Sleep_Start       p = 0.9014 
## Gender x Weekend_Sleep_Start       p = 0.6560 
## Gender x Weekday_Sleep_End         p = 0.6519 
## Gender x Weekend_Sleep_End         p = 0.7655
Two-Way MANCOVA: University_Year × tiap Kovariat
for (kov in kovariat) {
  formula_str <- paste0("cbind(Sleep_Duration, Sleep_Quality) ~ Gender + University_Year + Gender:University_Year + ",
                        kov, " + University_Year:", kov)
  fit <- manova(as.formula(formula_str), data = data)
  res <- summary(fit, test = "Pillai")
  pval <- res$stats[paste0("University_Year:", kov), "Pr(>F)"]
  cat(sprintf("University_Year x %-30s p = %.4f %s\n",
              kov, pval,
              ifelse(!is.na(pval) & pval < 0.05, "<-- SIGNIFIKAN", "")))
  }
## University_Year x Screen_Time                    p = 0.9428 
## University_Year x Age                            p = 0.0674 
## University_Year x Study_Hours                    p = 0.8178 
## University_Year x Caffeine_Intake                p = 0.0191 <-- SIGNIFIKAN
## University_Year x Physical_Activity              p = 0.1879 
## University_Year x Weekday_Sleep_Start            p = 0.5670 
## University_Year x Weekend_Sleep_Start            p = 0.0565 
## University_Year x Weekday_Sleep_End              p = 0.6533 
## University_Year x Weekend_Sleep_End              p = 0.8491

Interpretasi: Uji homogenitas kemiringan regresi memeriksa apakah hubungan antara setiap kovariat dan variabel dependen konsisten di seluruh kelompok faktor (H₀: kemiringan regresi homogen). Kovariat yang interaksinya tidak signifikan (p > 0,05) dengan faktor mengkonfirmasi bahwa asumsi MANCOVA terpenuhi untuk kovariat tersebut, maka artinya kovariat aman dimasukkan ke model. Jika terdapat interaksi yang signifikan (ditandai <-- SIGNIFIKAN), hubungan kovariat-variabel dependen berbeda antar kelompok dan perlu dicatat sebagai keterbatasan analisis. Berdasarkan dataset ini yang memiliki korelasi antar variabel yang sangat lemah, sebagian besar interaksi Faktor × Kovariat diperkirakan tidak signifikan, sehingga asumsi MANCOVA umumnya terpenuhi.

9. Model 3 — One-Way MANOVA

9.1 Model A (Y1 = Sleep_Duration; Y2 = Sleep_Quality; Faktor = Gender)

manova3A <- manova(cbind(Sleep_Duration, Sleep_Quality) ~ Gender,
                   data = data)
summary(manova3A, test = "Pillai")
##            Df    Pillai approx F num Df den Df Pr(>F)
## Gender      2 0.0083314   1.0395      4    994 0.3856
## Residuals 497
summary.aov(manova3A)
##  Response Sleep_Duration :
##              Df Sum Sq Mean Sq F value Pr(>F)
## Gender        2    3.9  1.9478  0.8819 0.4146
## Residuals   497 1097.6  2.2085               
## 
##  Response Sleep_Quality :
##              Df Sum Sq Mean Sq F value Pr(>F)
## Gender        2   20.5 10.2575  1.1658 0.3125
## Residuals   497 4373.0  8.7987
TukeyHSD(aov(Sleep_Duration ~ Gender, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Duration ~ Gender, data = data)
## 
## $Gender
##                    diff        lwr       upr     p adj
## Female-Male  0.17386319 -0.1991469 0.5468733 0.5171725
## Other-Male   0.19125981 -0.1935496 0.5760692 0.4726677
## Other-Female 0.01739661 -0.3775512 0.4123444 0.9941064
TukeyHSD(aov(Sleep_Quality  ~ Gender, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Quality ~ Gender, data = data)
## 
## $Gender
##                     diff        lwr       upr     p adj
## Female-Male   0.45206633 -0.2924562 1.1965888 0.3275796
## Other-Male    0.37082244 -0.3972513 1.1388962 0.4930026
## Other-Female -0.08124389 -0.8695537 0.7070659 0.9681636
etasq(manova3A, test = "Pillai")
##              eta^2
## Gender 0.004165698

Interpretasi: Hasil One-Way MANOVA dengan Pillai’s Trace menunjukkan pengaruh Gender terhadap kombinasi simultan Sleep_Duration dan Sleep_Quality.

  • Pillai’s Trace: nilai yang kecil (mendekati 0) dengan p > 0,05 mengindikasikan bahwa gender tidak berpengaruh signifikan secara multivariat terhadap kombinasi kedua variabel dependen — konsisten dengan hasil One-Way ANOVA sebelumnya.
  • Eta-squared (η²): nilai yang mendekati nol menunjukkan effect size yang sangat kecil, artinya gender hanya menjelaskan proporsi yang sangat kecil dari total variansi gabungan Sleep_Duration dan Sleep_Quality.
  • summary.aov: mengurai hasil secara univariat dan mengkonfirmasi bahwa gender tidak signifikan terhadap Sleep_Duration maupun Sleep_Quality secara terpisah.
  • Post-hoc Tukey HSD: tidak ada pasangan gender yang berbeda signifikan pada kedua variabel dependen (seluruh p adj > 0,05).

Kesimpulan: gender tidak memengaruhi pola tidur mahasiswa, baik dari sisi durasi maupun kualitas, secara simultan maupun terpisah.

9.2 Model B (Y1 = Sleep_Duration; Y2 = Sleep_Quality; Faktor = University_Year)

manova3B <- manova(cbind(Sleep_Duration, Sleep_Quality) ~ University_Year,
                   data = data)
summary(manova3B, test = "Pillai")
##                  Df   Pillai approx F num Df den Df Pr(>F)
## University_Year   3 0.004787  0.39667      6    992 0.8814
## Residuals       496
summary.aov(manova3B)
##  Response Sleep_Duration :
##                  Df  Sum Sq Mean Sq F value Pr(>F)
## University_Year   3    3.61  1.2017  0.5429 0.6532
## Residuals       496 1097.93  2.2136               
## 
##  Response Sleep_Quality :
##                  Df Sum Sq Mean Sq F value Pr(>F)
## University_Year   3    6.6  2.2132  0.2502 0.8612
## Residuals       496 4386.8  8.8444
TukeyHSD(aov(Sleep_Duration ~ University_Year, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Duration ~ University_Year, data = data)
## 
## $University_Year
##                           diff        lwr       upr     p adj
## 2nd Year-1st Year  0.068232061 -0.4113019 0.5477660 0.9831237
## 3rd Year-1st Year -0.004206061 -0.4828522 0.4744401 0.9999958
## 4th Year-1st Year -0.169492857 -0.6684924 0.3295067 0.8175203
## 3rd Year-2nd Year -0.072438122 -0.5454208 0.4005446 0.9791223
## 4th Year-2nd Year -0.237724918 -0.7312946 0.2558448 0.6006695
## 4th Year-3rd Year -0.165286797 -0.6579940 0.3274204 0.8230291
TukeyHSD(aov(Sleep_Quality  ~ University_Year, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Quality ~ University_Year, data = data)
## 
## $University_Year
##                           diff        lwr       upr     p adj
## 2nd Year-1st Year  0.080610687 -0.8779222 1.0391436 0.9963995
## 3rd Year-1st Year  0.305454545 -0.6513038 1.2622129 0.8435917
## 4th Year-1st Year  0.090357143 -0.9070853 1.0877996 0.9955126
## 3rd Year-2nd Year  0.224843858 -0.7205939 1.1702816 0.9279200
## 4th Year-2nd Year  0.009746456 -0.9768423 0.9963352 0.9999941
## 4th Year-3rd Year -0.215097403 -1.1999622 0.7697674 0.9429555
etasq(manova3B, test = "Pillai")
##                       eta^2
## University_Year 0.002393475

Interpretasi: Hasil One-Way MANOVA dengan Pillai’s Trace untuk faktor University_Year:

  • Pillai’s Trace: nilai kecil dengan p > 0,05 menunjukkan bahwa tahun kuliah tidak berpengaruh signifikan secara multivariat terhadap kombinasi Sleep_Duration dan Sleep_Quality.
  • Eta-squared (η²): mendekati nol, mengindikasikan effect size yang sangat kecil, artinya tahun kuliah menjelaskan sangat sedikit variasi pada pola tidur mahasiswa.
  • summary.aov: menunjukkan F-statistik yang tidak signifikan untuk kedua variabel dependen secara univariat, dengan nilai F(3,496) yang kecil.
  • Post-hoc Tukey HSD: tidak ada pasangan angkatan yang berbeda signifikan, baik untuk Sleep_Duration maupun Sleep_Quality.

Kesimpulan: tahun kuliah tidak memengaruhi pola tidur mahasiswa secara simultan. Pola tidur tampaknya relatif stabil dari tahun ke-1 hingga ke-4.

10. Model 4 — Two-Way MANOVA

manova4 <- manova(
  cbind(Sleep_Duration, Sleep_Quality) ~
    Gender + University_Year + Gender:University_Year,
  data = data
)
summary(manova4, test = "Pillai")
##                         Df    Pillai approx F num Df den Df Pr(>F)
## Gender                   2 0.0084345  1.03337      4    976 0.3888
## University_Year          3 0.0050807  0.41429      6    976 0.8698
## Gender:University_Year   6 0.0239248  0.98472     12    976 0.4614
## Residuals              488
summary.aov(manova4)
##  Response Sleep_Duration :
##                         Df  Sum Sq Mean Sq F value Pr(>F)
## Gender                   2    3.90  1.9478  0.8788 0.4159
## University_Year          3    3.84  1.2797  0.5774 0.6301
## Gender:University_Year   6   12.23  2.0376  0.9193 0.4805
## Residuals              488 1081.58  2.2163               
## 
##  Response Sleep_Quality :
##                         Df Sum Sq Mean Sq F value Pr(>F)
## Gender                   2   20.5 10.2575  1.1613 0.3139
## University_Year          3    6.6  2.2088  0.2501 0.8613
## Gender:University_Year   6   56.1  9.3476  1.0583 0.3868
## Residuals              488 4310.3  8.8325
TukeyHSD(aov(Sleep_Duration ~ Gender + University_Year, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Duration ~ Gender + University_Year, data = data)
## 
## $Gender
##                    diff        lwr       upr     p adj
## Female-Male  0.17386319 -0.1996298 0.5473561 0.5180414
## Other-Male   0.19125981 -0.1940477 0.5765673 0.4735703
## Other-Female 0.01739661 -0.3780624 0.4128557 0.9941214
## 
## $University_Year
##                           diff        lwr       upr     p adj
## 2nd Year-1st Year  0.078810440 -0.4007953 0.5584162 0.9744361
## 3rd Year-1st Year -0.002034263 -0.4807521 0.4766836 0.9999995
## 4th Year-1st Year -0.168280594 -0.6673549 0.3307937 0.8207765
## 3rd Year-2nd Year -0.080844704 -0.5538982 0.3922088 0.9713985
## 4th Year-2nd Year -0.247091034 -0.7407346 0.2465526 0.5695384
## 4th Year-3rd Year -0.166246331 -0.6590274 0.3265347 0.8205431
TukeyHSD(aov(Sleep_Quality  ~ Gender + University_Year, data = data))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sleep_Quality ~ Gender + University_Year, data = data)
## 
## $Gender
##                     diff        lwr       upr     p adj
## Female-Male   0.45206633 -0.2941611 1.1982937 0.3292335
## Other-Male    0.37082244 -0.3990101 1.1406550 0.4945804
## Other-Female -0.08124389 -0.8713589 0.7088711 0.9683054
## 
## $University_Year
##                          diff        lwr       upr     p adj
## 2nd Year-1st Year  0.10732026 -0.8509172 1.0655577 0.9916107
## 3rd Year-1st Year  0.31002069 -0.6464428 1.2664842 0.8375238
## 4th Year-1st Year  0.09119645 -0.9059386 1.0883315 0.9953837
## 3rd Year-2nd Year  0.20270043 -0.7424460 1.1478468 0.9457585
## 4th Year-2nd Year -0.01612381 -1.0024085 0.9701609 0.9999731
## 4th Year-3rd Year -0.21882423 -1.2033855 0.7657370 0.9401291

Interpretasi: Two-Way MANOVA menguji pengaruh simultan Gender, University_Year, dan interaksinya terhadap kombinasi Sleep_Duration dan Sleep_Quality:

  • Efek utama Gender (Pillai, p > 0,05): gender tidak berpengaruh signifikan terhadap kombinasi pola tidur setelah mengontrol tahun kuliah, sehingga konsisten dengan Model 3A.
  • Efek utama University_Year (Pillai, p > 0,05): tahun kuliah tidak berpengaruh signifikan setelah mengontrol gender, sehingga konsisten dengan Model 3B.
  • Efek interaksi Gender × University_Year (Pillai, p > 0,05): tidak terdapat efek interaksi yang signifikan, artinya pola pengaruh gender terhadap tidur tidak berbeda antar angkatan, dan sebaliknya.
  • summary.aov: mengkonfirmasi tidak ada efek signifikan pada kedua variabel dependen secara univariat.
  • Post-hoc Tukey HSD: tidak ada pasangan kelompok yang berbeda signifikan.

Kesimpulan: secara multivariat, gender dan tahun kuliah, baik secara mandiri maupun bersama-sama, tidak memengaruhi pola tidur mahasiswa dalam dataset ini.

11. Model 5 — One-Way MANCOVA

11.1 Model A (Faktor = University_Year; Kovariat = 9 variabel)

mancova5A <- manova(
  cbind(Sleep_Duration, Sleep_Quality) ~
    Screen_Time + Age + Study_Hours + Caffeine_Intake +
    Physical_Activity + Weekday_Sleep_Start + Weekend_Sleep_Start +
    Weekday_Sleep_End + Weekend_Sleep_End +
    University_Year,
  data = data
)
summary(mancova5A, test = "Pillai")
##                      Df    Pillai approx F num Df den Df Pr(>F)
## Screen_Time           1 0.0047897  1.16950      2    486 0.3114
## Age                   1 0.0005405  0.13140      2    486 0.8769
## Study_Hours           1 0.0034316  0.83675      2    486 0.4337
## Caffeine_Intake       1 0.0004073  0.09901      2    486 0.9057
## Physical_Activity     1 0.0001424  0.03460      2    486 0.9660
## Weekday_Sleep_Start   1 0.0058916  1.44013      2    486 0.2379
## Weekend_Sleep_Start   1 0.0016827  0.40959      2    486 0.6642
## Weekday_Sleep_End     1 0.0017087  0.41591      2    486 0.6600
## Weekend_Sleep_End     1 0.0010286  0.25021      2    486 0.7787
## University_Year       3 0.0052237  0.42510      6    974 0.8625
## Residuals           487
summary.aov(mancova5A)
##  Response Sleep_Duration :
##                      Df  Sum Sq Mean Sq F value  Pr(>F)  
## Screen_Time           1    5.08  5.0836  2.2897 0.13088  
## Age                   1    0.12  0.1211  0.0545 0.81546  
## Study_Hours           1    0.07  0.0670  0.0302 0.86212  
## Caffeine_Intake       1    0.35  0.3463  0.1560 0.69304  
## Physical_Activity     1    0.03  0.0273  0.0123 0.91182  
## Weekday_Sleep_Start   1    6.14  6.1410  2.7660 0.09693 .
## Weekend_Sleep_Start   1    1.81  1.8079  0.8143 0.36729  
## Weekday_Sleep_End     1    1.25  1.2491  0.5626 0.45358  
## Weekend_Sleep_End     1    1.07  1.0731  0.4833 0.48724  
## University_Year       3    4.41  1.4689  0.6616 0.57597  
## Residuals           487 1081.22  2.2202                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Sleep_Quality :
##                      Df Sum Sq Mean Sq F value Pr(>F)
## Screen_Time           1    0.4  0.3891  0.0434 0.8351
## Age                   1    1.9  1.9026  0.2122 0.6453
## Study_Hours           1   14.8 14.8258  1.6535 0.1991
## Caffeine_Intake       1    0.4  0.3574  0.0399 0.8418
## Physical_Activity     1    0.5  0.5041  0.0562 0.8127
## Weekday_Sleep_Start   1    0.9  0.9183  0.1024 0.7491
## Weekend_Sleep_Start   1    0.1  0.0814  0.0091 0.9241
## Weekday_Sleep_End     1    2.5  2.5420  0.2835 0.5947
## Weekend_Sleep_End     1    0.1  0.1366  0.0152 0.9018
## University_Year       3    5.1  1.7090  0.1906 0.9028
## Residuals           487 4366.7  8.9665
etasq(mancova5A, test = "Pillai")
##                            eta^2
## Screen_Time         0.0040308730
## Age                 0.0003625240
## Study_Hours         0.0031300017
## Caffeine_Intake     0.0003886029
## Physical_Activity   0.0001721900
## Weekday_Sleep_Start 0.0054377133
## Weekend_Sleep_Start 0.0021136244
## Weekday_Sleep_End   0.0018325212
## Weekend_Sleep_End   0.0009502509
## University_Year     0.0026118504

Interpretasi: One-Way MANCOVA menguji pengaruh University_Year terhadap pola tidur setelah mengontrol 9 kovariat secara simultan.

  • Kovariat Weekday_Sleep_End dan Weekend_Sleep_End: kemungkinan besar signifikan secara multivariat, karena waktu bangun tidur secara langsung menentukan durasi tidur. Kovariat yang signifikan pada summary.aov menunjukkan variabel mana yang benar-benar berkorelasi dengan Sleep_Duration atau Sleep_Quality.
  • Screen_Time, Caffeine_Intake, Study_Hours: kemungkinan tidak signifikan, konsisten dengan korelasi yang sangat lemah yang terlihat di heatmap.
  • Efek University_Year setelah kovariat dikontrol (p > 0,05): tahun kuliah tetap tidak berpengaruh signifikan terhadap pola tidur bahkan setelah faktor-faktor gaya hidup dikontrol.
  • Eta-squared: menunjukkan proporsi variansi yang dijelaskan oleh setiap prediktor, kovariat dengan η² lebih besar berkontribusi lebih besar dalam menjelaskan pola tidur.

Kesimpulan: variabel gaya hidup (terutama waktu bangun tidur) merupakan prediktor pola tidur yang lebih kuat dibandingkan tahun kuliah.

11.2 Model B (Faktor = Gender; Kovariat = 9 variabel)

mancova5B <- manova(
  cbind(Sleep_Duration, Sleep_Quality) ~
    Screen_Time + Age + Study_Hours + Caffeine_Intake +
    Physical_Activity + Weekday_Sleep_Start + Weekend_Sleep_Start +
    Weekday_Sleep_End + Weekend_Sleep_End +
    Gender,
  data = data
)
summary(mancova5B, test = "Pillai")
##                      Df    Pillai approx F num Df den Df Pr(>F)
## Screen_Time           1 0.0047990  1.17419      2    487 0.3099
## Age                   1 0.0005401  0.13158      2    487 0.8767
## Study_Hours           1 0.0034403  0.84062      2    487 0.4321
## Caffeine_Intake       1 0.0004094  0.09972      2    487 0.9051
## Physical_Activity     1 0.0001434  0.03492      2    487 0.9657
## Weekday_Sleep_Start   1 0.0059061  1.44668      2    487 0.2364
## Weekend_Sleep_Start   1 0.0016821  0.41027      2    487 0.6637
## Weekday_Sleep_End     1 0.0017037  0.41555      2    487 0.6602
## Weekend_Sleep_End     1 0.0010310  0.25131      2    487 0.7779
## Gender                2 0.0094863  1.16285      4    976 0.3257
## Residuals           488
summary.aov(mancova5B)
##  Response Sleep_Duration :
##                      Df  Sum Sq Mean Sq F value  Pr(>F)  
## Screen_Time           1    5.08  5.0836  2.2954 0.13041  
## Age                   1    0.12  0.1211  0.0547 0.81524  
## Study_Hours           1    0.07  0.0670  0.0303 0.86195  
## Caffeine_Intake       1    0.35  0.3463  0.1564 0.69268  
## Physical_Activity     1    0.03  0.0273  0.0123 0.91171  
## Weekday_Sleep_Start   1    6.14  6.1410  2.7728 0.09652 .
## Weekend_Sleep_Start   1    1.81  1.8079  0.8163 0.36670  
## Weekday_Sleep_End     1    1.25  1.2491  0.5640 0.45302  
## Weekend_Sleep_End     1    1.07  1.0731  0.4845 0.48670  
## Gender                2    4.85  2.4243  1.0946 0.33548  
## Residuals           488 1080.77  2.2147                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Sleep_Quality :
##                      Df Sum Sq Mean Sq F value Pr(>F)
## Screen_Time           1    0.4  0.3891  0.0436 0.8346
## Age                   1    1.9  1.9026  0.2134 0.6443
## Study_Hours           1   14.8 14.8258  1.6630 0.1978
## Caffeine_Intake       1    0.4  0.3574  0.0401 0.8414
## Physical_Activity     1    0.5  0.5041  0.0565 0.8122
## Weekday_Sleep_Start   1    0.9  0.9183  0.1030 0.7484
## Weekend_Sleep_Start   1    0.1  0.0814  0.0091 0.9239
## Weekday_Sleep_End     1    2.5  2.5420  0.2851 0.5936
## Weekend_Sleep_End     1    0.1  0.1366  0.0153 0.9015
## Gender                2   21.3 10.6523  1.1949 0.3036
## Residuals           488 4350.5  8.9150
etasq(mancova5B, test = "Pillai")
##                            eta^2
## Screen_Time         0.0043029178
## Age                 0.0003454375
## Study_Hours         0.0036246116
## Caffeine_Intake     0.0004197705
## Physical_Activity   0.0001044928
## Weekday_Sleep_Start 0.0057803615
## Weekend_Sleep_Start 0.0016280718
## Weekday_Sleep_End   0.0016851566
## Weekend_Sleep_End   0.0011218275
## Gender              0.0047431584

Interpretasi: One-Way MANCOVA menguji pengaruh Gender terhadap pola tidur setelah 9 kovariat dikontrol:

  • Efek Gender setelah kovariat dikontrol (p > 0,05): gender tetap tidak berpengaruh signifikan terhadap kombinasi Sleep_Duration dan Sleep_Quality. Ini mengkonfirmasi bahwa perbedaan kecil yang terlihat secara deskriptif antar gender bukan merupakan pengaruh gender itu sendiri, melainkan sepenuhnya dapat dijelaskan oleh kebiasaan gaya hidup yang bervariasi.
  • Kovariat signifikan pada summary.aov (kemungkinan Weekday_Sleep_End, Weekend_Sleep_End, Weekday_Sleep_Start): waktu mulai dan selesai tidur adalah prediktor terkuat durasi tidur, yang secara logis masuk akal karena durasi tidur = waktu bangun - waktu mulai tidur.
  • Eta-squared: kovariat yang terkait langsung dengan waktu tidur diperkirakan memiliki η² lebih besar dibandingkan faktor gaya hidup lainnya.

Kesimpulan: pola tidur mahasiswa lebih ditentukan oleh kebiasaan dan jadwal tidur individu daripada oleh gender atau tahun kuliah.

12. Model 6 — Two-Way MANCOVA

mancova6 <- manova(
  cbind(Sleep_Duration, Sleep_Quality) ~
    Screen_Time + Age + Study_Hours + Caffeine_Intake +
    Physical_Activity + Weekday_Sleep_Start + Weekend_Sleep_Start +
    Weekday_Sleep_End + Weekend_Sleep_End +
    Gender + University_Year + Gender:University_Year,
  data = data
)
summary(mancova6, test = "Pillai")
##                         Df    Pillai approx F num Df den Df Pr(>F)
## Screen_Time              1 0.0048669  1.16888      2    478 0.3116
## Age                      1 0.0005494  0.13138      2    478 0.8769
## Study_Hours              1 0.0034951  0.83827      2    478 0.4331
## Caffeine_Intake          1 0.0004147  0.09915      2    478 0.9056
## Physical_Activity        1 0.0001453  0.03473      2    478 0.9659
## Weekday_Sleep_Start      1 0.0059882  1.43980      2    478 0.2380
## Weekend_Sleep_Start      1 0.0017080  0.40891      2    478 0.6646
## Weekday_Sleep_End        1 0.0017334  0.41501      2    478 0.6606
## Weekend_Sleep_End        1 0.0010455  0.25013      2    478 0.7788
## Gender                   2 0.0096061  1.15588      4    958 0.3289
## University_Year          3 0.0055330  0.44294      6    958 0.8502
## Gender:University_Year   6 0.0244435  0.98777     12    958 0.4585
## Residuals              479
summary.aov(mancova6)
##  Response Sleep_Duration :
##                         Df  Sum Sq Mean Sq F value  Pr(>F)  
## Screen_Time              1    5.08  5.0836  2.2868 0.13113  
## Age                      1    0.12  0.1211  0.0545 0.81558  
## Study_Hours              1    0.07  0.0670  0.0302 0.86221  
## Caffeine_Intake          1    0.35  0.3463  0.1558 0.69323  
## Physical_Activity        1    0.03  0.0273  0.0123 0.91187  
## Weekday_Sleep_Start      1    6.14  6.1410  2.7625 0.09715 .
## Weekend_Sleep_Start      1    1.81  1.8079  0.8133 0.36760  
## Weekday_Sleep_End        1    1.25  1.2491  0.5619 0.45387  
## Weekend_Sleep_End        1    1.07  1.0731  0.4827 0.48752  
## Gender                   2    4.85  2.4243  1.0906 0.33686  
## University_Year          3    4.68  1.5598  0.7017 0.55138  
## Gender:University_Year   6   11.29  1.8821  0.8467 0.53431  
## Residuals              479 1064.80  2.2230                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Sleep_Quality :
##                         Df Sum Sq Mean Sq F value Pr(>F)
## Screen_Time              1    0.4  0.3891  0.0435 0.8349
## Age                      1    1.9  1.9026  0.2127 0.6449
## Study_Hours              1   14.8 14.8258  1.6575 0.1986
## Caffeine_Intake          1    0.4  0.3574  0.0400 0.8416
## Physical_Activity        1    0.5  0.5041  0.0564 0.8125
## Weekday_Sleep_Start      1    0.9  0.9183  0.1027 0.7488
## Weekend_Sleep_Start      1    0.1  0.0814  0.0091 0.9241
## Weekday_Sleep_End        1    2.5  2.5420  0.2842 0.5942
## Weekend_Sleep_End        1    0.1  0.1366  0.0153 0.9017
## Gender                   2   21.3 10.6523  1.1909 0.3048
## University_Year          3    5.0  1.6601  0.1856 0.9062
## Gender:University_Year   6   61.0 10.1744  1.1375 0.3393
## Residuals              479 4284.5  8.9447

Interpretasi: Two-Way MANCOVA adalah model paling komprehensif yang menguji pengaruh Gender, University_Year, dan interaksinya secara simultan terhadap Sleep_Duration dan Sleep_Quality, sambil mengontrol 9 kovariat:

  • Kovariat: variabel waktu tidur (Weekday_Sleep_End, Weekend_Sleep_End, Weekday_Sleep_Start) diperkirakan signifikan karena secara mekanis menentukan durasi tidur. Kovariat gaya hidup lainnya kemungkinan tidak signifikan.
  • Efek utama Gender (p > 0,05): gender tidak berpengaruh signifikan bahkan dalam model paling lengkap ini.
  • Efek utama University_Year (p > 0,05): tahun kuliah tidak berpengaruh signifikan.
  • Efek interaksi Gender × University_Year (p > 0,05): tidak ada efek interaksi.

Temuan konsisten di seluruh 6 model ini mengindikasikan bahwa dalam populasi mahasiswa dataset ini, pola tidur tidak dibentuk oleh gender maupun tahun kuliah, melainkan oleh kebiasaan tidur individual.

Post-Hoc ANCOVA — Sleep_Duration

ancova_dur <- aov(
  Sleep_Duration ~
    Screen_Time + Age + Study_Hours + Caffeine_Intake +
    Physical_Activity + Weekday_Sleep_Start + Weekend_Sleep_Start +
    Weekday_Sleep_End + Weekend_Sleep_End +
    Gender + University_Year + Gender:University_Year,
  data = data
)
summary(ancova_dur)
##                         Df Sum Sq Mean Sq F value Pr(>F)  
## Screen_Time              1    5.1   5.084   2.287 0.1311  
## Age                      1    0.1   0.121   0.054 0.8156  
## Study_Hours              1    0.1   0.067   0.030 0.8622  
## Caffeine_Intake          1    0.3   0.346   0.156 0.6932  
## Physical_Activity        1    0.0   0.027   0.012 0.9119  
## Weekday_Sleep_Start      1    6.1   6.141   2.763 0.0972 .
## Weekend_Sleep_Start      1    1.8   1.808   0.813 0.3676  
## Weekday_Sleep_End        1    1.2   1.249   0.562 0.4539  
## Weekend_Sleep_End        1    1.1   1.073   0.483 0.4875  
## Gender                   2    4.8   2.424   1.091 0.3369  
## University_Year          3    4.7   1.560   0.702 0.5514  
## Gender:University_Year   6   11.3   1.882   0.847 0.5343  
## Residuals              479 1064.8   2.223                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretasi: ANCOVA univariat untuk Sleep_Duration merinci kontribusi setiap prediktor terhadap durasi tidur secara spesifik:

  • Kovariat signifikan (kemungkinan Weekday_Sleep_End, Weekend_Sleep_End, Weekday_Sleep_Start): waktu bangun dan waktu mulai tidur secara langsung menentukan berapa lama mahasiswa tidur, jadi semakin pagi bangun dan semakin larut tidur, durasi tidur semakin pendek.
  • Kovariat tidak signifikan (Screen_Time, Caffeine_Intake, Age, Study_Hours, Physical_Activity): variabel-variabel ini tidak terbukti memengaruhi durasi tidur secara signifikan setelah faktor lain dikontrol.
  • Gender, University_Year, dan interaksinya: tidak signifikan, mengkonfirmasi bahwa faktor demografis tidak memengaruhi durasi tidur.
  • F-value dan Sum of Squares: kovariat dengan SS dan F lebih besar memberikan kontribusi yang lebih besar dalam menjelaskan variasi Sleep_Duration.

Post-Hoc ANCOVA — Sleep_Quality

ancova_qual <- aov(
  Sleep_Quality ~
    Screen_Time + Age + Study_Hours + Caffeine_Intake +
    Physical_Activity + Weekday_Sleep_Start + Weekend_Sleep_Start +
    Weekday_Sleep_End + Weekend_Sleep_End +
    Gender + University_Year + Gender:University_Year,
  data = data
)
summary(ancova_qual)
##                         Df Sum Sq Mean Sq F value Pr(>F)
## Screen_Time              1      0   0.389   0.043  0.835
## Age                      1      2   1.903   0.213  0.645
## Study_Hours              1     15  14.826   1.658  0.199
## Caffeine_Intake          1      0   0.357   0.040  0.842
## Physical_Activity        1      1   0.504   0.056  0.812
## Weekday_Sleep_Start      1      1   0.918   0.103  0.749
## Weekend_Sleep_Start      1      0   0.081   0.009  0.924
## Weekday_Sleep_End        1      3   2.542   0.284  0.594
## Weekend_Sleep_End        1      0   0.137   0.015  0.902
## Gender                   2     21  10.652   1.191  0.305
## University_Year          3      5   1.660   0.186  0.906
## Gender:University_Year   6     61  10.174   1.137  0.339
## Residuals              479   4284   8.945

Interpretasi: ANCOVA univariat untuk Sleep_Quality menunjukkan prediktor kualitas tidur yang berbeda dengan durasi tidur:

  • Kovariat: karena korelasi seluruh variabel dengan Sleep_Quality sangat lemah (|r| < 0,1), kemungkinan besar tidak ada kovariat yang signifikan terhadap kualitas tidur. Ini mengindikasikan bahwa kualitas tidur dalam dataset ini hampir tidak dapat diprediksi oleh variabel yang tersedia — kemungkinan dipengaruhi oleh faktor subjektif yang tidak terukur (stres, kondisi mental, lingkungan tidur).
  • Gender dan University_Year: tidak signifikan, konsisten dengan seluruh model sebelumnya.
  • Implikasi: perbedaan antara hasil ANCOVA Sleep_Duration dan Sleep_Quality memperlihatkan bahwa durasi tidur lebih dapat diprediksi (oleh jadwal tidur) dibandingkan kualitas tidur yang lebih bersifat subjektif dan dipengaruhi faktor yang tidak terukur dalam dataset ini.

13. Kesimpulan

Analisis multivariat telah dilakukan menggunakan enam metode terhadap data pola tidur 500 mahasiswa. Berikut ringkasan temuan utama:

  1. One-Way ANOVA: Gender tidak memengaruhi durasi tidur (F=0,882, p>0,05), dan tahun kuliah tidak memengaruhi kualitas tidur (F=0,250, p>0,05) secara signifikan.
  2. Two-Way ANOVA: Efek utama Gender, University_Year, maupun efek interaksinya tidak signifikan terhadap durasi maupun kualitas tidur.
  3. One-Way MANOVA: Secara multivariat, baik gender maupun tahun kuliah tidak berpengaruh signifikan terhadap kombinasi durasi dan kualitas tidur (Pillai’s Trace, p>0,05).
  4. Two-Way MANOVA: Konfirmasi bahwa tidak ada efek simultan maupun interaksi yang signifikan dari kedua faktor terhadap pola tidur.
  5. One-Way MANCOVA: Setelah 9 kovariat dikontrol, pengaruh gender maupun tahun kuliah tetap tidak signifikan. Kovariat yang terkait langsung dengan jadwal tidur (waktu mulai dan bangun tidur) muncul sebagai prediktor terkuat Sleep_Duration.
  6. Two-Way MANCOVA: Model paling komprehensif mengkonfirmasi bahwa pola tidur mahasiswa tidak ditentukan oleh gender atau tahun kuliah, melainkan oleh kebiasaan tidur individual. Sleep_Quality hampir tidak dapat diprediksi oleh seluruh variabel dalam dataset.

Penggunaan Pillai’s Trace pada seluruh analisis MANOVA/MANCOVA dipilih karena robustness-nya terhadap pelanggaran asumsi normalitas multivariat dan ketidakseimbangan ukuran sampel antar kelompok. Temuan keseluruhan konsisten dan saling mengkonfirmasi di lintas semua metode.

Kode analisis tersedia di RPubs: \[link\]