Menentukan Nilai Kritis t dengan R
qt(0.975, df = 18) #pengujian hipotesis 2 arah, sehingga 0.975, bukan 0.95
## [1] 2.100922
Menentukan Nilai Kritis F dengan R
qf(0.95, df=1, df2=18)
## [1] 4.413873
Contoh Kasus Uji Kesamaan Rata-Rata dari Dua Populasi yang Tidak
Berhubungan (Independen) dengan Asumsi Varians yang Sama (Contoh
Perhitungan)
data = read.csv("data_independen_1.csv")
data
## X Y
## 1 65 85
## 2 68 75
## 3 70 75
## 4 80 80
## 5 75 75
## 6 72 75
## 7 65 75
## 8 60 80
## 9 88 90
## 10 70 85
t.test(data$Y, data$X, var.equal = TRUE, paired = FALSE)
##
## Two Sample t-test
##
## data: data$Y and data$X
## t = 2.6487, df = 18, p-value = 0.01633
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1.695807 14.704193
## sample estimates:
## mean of x mean of y
## 79.5 71.3
t.test(data$Y, data$X, var.equal = FALSE, paired = FALSE)
##
## Welch Two Sample t-test
##
## data: data$Y and data$X
## t = 2.6487, df = 15.851, p-value = 0.01762
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1.632025 14.767975
## sample estimates:
## mean of x mean of y
## 79.5 71.3
Uji Asumsi Normalitas dalam R
data = read.csv("data_independen_1.csv")
X = data$X
Y = data$Y
library(nortest)
lillie.test(X) #dengan koreksi (lihat p-value)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: X
## D = 0.16556, p-value = 0.6103
suppressWarnings(ks.test(X, "pnorm", mean(X), sd(X))) #tanpa koreksi (lihat p-value)
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: X
## D = 0.16556, p-value = 0.9469
## alternative hypothesis: two-sided
suppressWarnings(ks.test(Y, "pnorm", mean(Y), sd(Y)))
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: Y
## D = 0.29327, p-value = 0.356
## alternative hypothesis: two-sided
library(tseries)
jarque.bera.test(X)
##
## Jarque Bera Test
##
## data: X
## X-squared = 0.92911, df = 2, p-value = 0.6284
jarque.bera.test(Y)
##
## Jarque Bera Test
##
## data: Y
## X-squared = 1.1767, df = 2, p-value = 0.5552
Uji Asumsi Kesamaan Varians dalam R
varians = read.csv("varians3.csv")
varians
## Nilai Jenis
## 1 65 1
## 2 68 1
## 3 70 1
## 4 80 1
## 5 75 1
## 6 72 1
## 7 65 1
## 8 60 1
## 9 88 1
## 10 70 1
## 11 85 2
## 12 75 2
## 13 75 2
## 14 80 2
## 15 75 2
## 16 75 2
## 17 75 2
## 18 80 2
## 19 90 2
## 20 85 2
library(car)
## Loading required package: carData
leveneTest(varians$Nilai, varians$Jenis)
## Warning in leveneTest.default(varians$Nilai, varians$Jenis): varians$Jenis
## coerced to factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.3305 0.5725
## 18
# library(Rcmdr)
# leveneTest(varians$Nilai, varians$Jenis)
library(lawstat)
##
## Attaching package: 'lawstat'
## The following object is masked from 'package:car':
##
## levene.test
## The following object is masked from 'package:tseries':
##
## runs.test
levene.test(varians[, "Nilai"], varians[, "Jenis"], location = "median") #Sesuai Minitab
##
## Modified robust Brown-Forsythe Levene-type test based on the absolute
## deviations from the median
##
## data: varians[, "Nilai"]
## Test Statistic = 0.33053, p-value = 0.5725
levene.test(varians[, "Nilai"], varians[, "Jenis"], location = "mean") #Sesuai SPSS
##
## Classical Levene's test based on the absolute deviations from the mean
## ( none not applied because the location is not set to median )
##
## data: varians[, "Nilai"]
## Test Statistic = 0.62924, p-value = 0.438