# ============================================================
# BAB 7 - UJI KESAMAAN VARIANS POPULASI (UJI LEVENE)
# ============================================================
# --- CONTOH KASUS 1 ---
# 1. Menghitung Nilai F Tabel (alpha = 0.05, df1 = 2, df2 = 15)
qf(0.95, df1 = 2, df2 = 15)
## [1] 3.68232
# 2. Input Data Kasus 1
Nilai <- c(70, 80, 87, 77, 80, 80, 85, 70, 77, 85, 60, 80, 70, 87, 90, 77, 76, 87)
Kelas <- as.factor(c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3))
varians <- data.frame(Nilai, Kelas)
varians
## Nilai Kelas
## 1 70 1
## 2 80 1
## 3 87 1
## 4 77 1
## 5 80 1
## 6 80 2
## 7 85 2
## 8 70 2
## 9 77 2
## 10 85 2
## 11 60 2
## 12 80 2
## 13 70 3
## 14 87 3
## 15 90 3
## 16 77 3
## 17 76 3
## 18 87 3
# 3. Uji Levene (Package car)
library(car)
## Loading required package: carData
leveneTest(Nilai ~ Kelas, data = varians)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.4267 0.6604
## 15
# 4. Uji Levene dengan Median & Mean (Package lawstat)
library(lawstat)
##
## Attaching package: 'lawstat'
## The following object is masked from 'package:car':
##
## levene.test
leveneTest(varians$Nilai, varians$Kelas, location = "median", correction.method = "zero.correction")
## Levene's Test for Homogeneity of Variance (center = median: "median")
## Df F value Pr(>F)
## group 2 0.4267 0.6604
## 15
leveneTest(varians$Nilai, varians$Kelas, location = "mean", correction.method = "zero.correction")
## Levene's Test for Homogeneity of Variance (center = median: "mean")
## Df F value Pr(>F)
## group 2 0.4267 0.6604
## 15
# --- CONTOH KASUS 2 ---
# 1. Input Data Kasus 2
Nilai2 <- c(30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70)
Kelas2 <- as.factor(c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2))
simpan <- data.frame(Nilai = Nilai2, Kelas = Kelas2)
simpan
## Nilai Kelas
## 1 30 1
## 2 40 1
## 3 50 1
## 4 60 1
## 5 70 1
## 6 80 1
## 7 90 2
## 8 10 2
## 9 20 2
## 10 30 2
## 11 40 2
## 12 50 2
## 13 60 2
## 14 70 2
# 2. Ringkasan Statistik per Kelas
library(doBy)
summaryBy(Nilai ~ Kelas, data = simpan, FUN = function(x){ c(ratarata = mean(x), varians = var(x), jumlah = sum(x)) })
## Kelas Nilai.ratarata Nilai.varians Nilai.jumlah
## 1 1 55.00 350.0 330
## 2 2 46.25 712.5 370
# 3. Menghitung Nilai F Tabel Kasus 2 (alpha = 0.05, df1 = 1, df2 = 12)
qf(0.95, df1 = 1, df2 = 12)
## [1] 4.747225
# 4. Uji Levene Kasus 2 (Mean)
leveneTest(simpan$Nilai, simpan$Kelas, location = "mean", correction.method = "zero.correction")
## Levene's Test for Homogeneity of Variance (center = median: "mean")
## Df F value Pr(>F)
## group 1 0.8991 0.3617
## 12