Anmul uts - Anova
Aulia
2026-10-23
Preprocessing Data
Memuat Library
# Memuat paket untuk manipulasi data, grafik, uji statistik, dan tabel
# install.packages(c("dplyr", "ggplot2", "car", "knitr"))
library(dplyr)
library(ggplot2)
library(car)
library(knitr)Import Data
# Membaca data, merapikan nama kolom, dan mengubah faktor ke tipe kategori
data <- read.csv("Sleep_health_and_lifestyle_dataset.csv",
check.names = FALSE,
stringsAsFactors = FALSE)
names(data) <- make.names(names(data))
data$Sleep.Disorder <- factor(data$Sleep.Disorder,
levels = c("None", "Insomnia", "Sleep Apnea"))
data$Gender <- as.factor(data$Gender)
str(data)## 'data.frame': 374 obs. of 13 variables:
## $ Person.ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Gender : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
## $ Age : int 27 28 28 28 28 28 29 29 29 29 ...
## $ Occupation : chr "Software Engineer" "Doctor" "Doctor" "Sales Representative" ...
## $ Sleep.Duration : num 6.1 6.2 6.2 5.9 5.9 5.9 6.3 7.8 7.8 7.8 ...
## $ Quality.of.Sleep : int 6 6 6 4 4 4 6 7 7 7 ...
## $ Physical.Activity.Level: int 42 60 60 30 30 30 40 75 75 75 ...
## $ Stress.Level : int 6 8 8 8 8 8 7 6 6 6 ...
## $ BMI.Category : chr "Overweight" "Normal" "Normal" "Obese" ...
## $ Blood.Pressure : chr "126/83" "125/80" "125/80" "140/90" ...
## $ Heart.Rate : int 77 75 75 85 85 85 82 70 70 70 ...
## $ Daily.Steps : int 4200 10000 10000 3000 3000 3000 3500 8000 8000 8000 ...
## $ Sleep.Disorder : Factor w/ 3 levels "None","Insomnia",..: 1 1 1 3 3 2 2 1 1 1 ...head(data)## Person.ID Gender Age Occupation Sleep.Duration Quality.of.Sleep
## 1 1 Male 27 Software Engineer 6.1 6
## 2 2 Male 28 Doctor 6.2 6
## 3 3 Male 28 Doctor 6.2 6
## 4 4 Male 28 Sales Representative 5.9 4
## 5 5 Male 28 Sales Representative 5.9 4
## 6 6 Male 28 Software Engineer 5.9 4
## Physical.Activity.Level Stress.Level BMI.Category Blood.Pressure Heart.Rate
## 1 42 6 Overweight 126/83 77
## 2 60 8 Normal 125/80 75
## 3 60 8 Normal 125/80 75
## 4 30 8 Obese 140/90 85
## 5 30 8 Obese 140/90 85
## 6 30 8 Obese 140/90 85
## Daily.Steps Sleep.Disorder
## 1 4200 None
## 2 10000 None
## 3 10000 None
## 4 3000 Sleep Apnea
## 5 3000 Sleep Apnea
## 6 3000 InsomniaPemeriksaan Data Kosong dan Duplikat
colSums(is.na(data)) # data kosong## Person.ID Gender Age
## 0 0 0
## Occupation Sleep.Duration Quality.of.Sleep
## 0 0 0
## Physical.Activity.Level Stress.Level BMI.Category
## 0 0 0
## Blood.Pressure Heart.Rate Daily.Steps
## 0 0 0
## Sleep.Disorder
## 0sum(duplicated(data)) # data duplikat## [1] 0Pemilihan Variabel
# Memilih variabel respons dan dua faktor sesuai rumusan masalah
data_anova <- data %>%
dplyr::select(Quality.of.Sleep, Sleep.Disorder, Gender)
head(data_anova)## Quality.of.Sleep Sleep.Disorder Gender
## 1 6 None Male
## 2 6 None Male
## 3 6 None Male
## 4 4 Sleep Apnea Male
## 5 4 Sleep Apnea Male
## 6 4 Insomnia Malesummary(data_anova)## Quality.of.Sleep Sleep.Disorder Gender
## Min. :4.000 None :219 Female:185
## 1st Qu.:6.000 Insomnia : 77 Male :189
## Median :7.000 Sleep Apnea: 78
## Mean :7.313
## 3rd Qu.:8.000
## Max. :9.000Eksplorasi Data (EDA)
# Jumlah data pada tiap kombinasi Sleep Disorder dan Gender
table(data_anova$Sleep.Disorder, data_anova$Gender)##
## Female Male
## None 82 137
## Insomnia 36 41
## Sleep Apnea 67 11# Rata-rata dan simpangan baku kualitas tidur per kelompok
data_anova %>%
group_by(Sleep.Disorder, Gender) %>%
summarise(
n = n(),
rata_rata = mean(Quality.of.Sleep),
sd = sd(Quality.of.Sleep),
.groups = "drop"
) %>%
kable(digits = 2, caption = "Statistik deskriptif per kelompok")| Sleep.Disorder | Gender | n | rata_rata | sd |
|---|---|---|---|---|
| None | Female | 82 | 8.28 | 0.84 |
| None | Male | 137 | 7.23 | 0.83 |
| Insomnia | Female | 36 | 6.94 | 0.63 |
| Insomnia | Male | 41 | 6.17 | 0.77 |
| Sleep Apnea | Female | 67 | 7.30 | 1.61 |
| Sleep Apnea | Male | 11 | 6.64 | 1.80 |
# Boxplot kualitas tidur per Sleep Disorder, dibedakan menurut Gender
ggplot(data_anova, aes(x = Sleep.Disorder, y = Quality.of.Sleep, fill = Gender)) +
geom_boxplot(alpha = 0.7) +
labs(
title = "Kualitas Tidur Berdasarkan Sleep Disorder dan Gender",
x = "Sleep Disorder",
y = "Kualitas Tidur",
fill = "Gender"
) +
theme_minimal()
# Interaction plot: rata-rata kualitas tidur per kombinasi faktor
ggplot(data_anova, aes(x = Sleep.Disorder, y = Quality.of.Sleep,
color = Gender, group = Gender)) +
stat_summary(fun = mean, geom = "point", size = 3) +
stat_summary(fun = mean, geom = "line", linewidth = 1) +
labs(
title = "Interaction Plot: Sleep Disorder x Gender",
x = "Sleep Disorder",
y = "Rata-rata Kualitas Tidur",
color = "Gender"
) +
theme_minimal()
Model ANOVA Dua Jalur
Ukuran sel tidak seimbang, sehingga digunakan Type II sum of squares.
# Model ANOVA dua jalur dengan interaksi, lalu tabel ANOVA Type II
model <- aov(Quality.of.Sleep ~ Sleep.Disorder * Gender, data = data_anova)
anova_tab <- Anova(model, type = 2)
anova_tab## Anova Table (Type II tests)
##
## Response: Quality.of.Sleep
## Sum Sq Df F value Pr(>F)
## Sleep.Disorder 93.84 2 43.8984 < 2.2e-16 ***
## Gender 70.00 1 65.4858 8.618e-15 ***
## Sleep.Disorder:Gender 1.84 2 0.8628 0.4228
## Residuals 393.34 368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Uji Asumsi
Normalitas Residual dengan Shapiro-Wilk
# H0: residual berdistribusi normal
res <- residuals(model)
shapiro.test(res)##
## Shapiro-Wilk normality test
##
## data: res
## W = 0.94481, p-value = 1.384e-10Homogenitas Varians
# Uji Levene. H0: varians sama di semua kelompok
leveneTest(Quality.of.Sleep ~ Sleep.Disorder * Gender, data = data_anova)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 5 17.927 6.475e-16 ***
## 368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Uji Lanjut (Tukey HSD)
# Perbandingan berpasangan antar kelompok Sleep Disorder
tukey <- TukeyHSD(model, which = "Sleep.Disorder")
tukey## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Quality.of.Sleep ~ Sleep.Disorder * Gender, data = data_anova)
##
## $Sleep.Disorder
## diff lwr upr p adj
## Insomnia-None -1.0931032 -1.4154371 -0.77076941 0.0000000
## Sleep Apnea-None -0.4204426 -0.7412440 -0.09964112 0.0062031
## Sleep Apnea-Insomnia 0.6726607 0.2818192 1.06350215 0.0001843plot(tukey, las = 1)