#Contoh

Import Data

#Dataset
library(readxl)
data_lat <- read_excel("latihan.xlsx")
#Identifikasi Faktor 1 dan Faktor 2
data_lat$Faktor1 = as.factor(data_lat$Faktor1)
data_lat$Faktor2 = as.factor(data_lat$Faktor2)
data_lat
## # A tibble: 32 x 4
##       y1    y2 Faktor1 Faktor2
##    <dbl> <dbl> <fct>   <fct>  
##  1  7.8   90.4 A1      B1     
##  2  7.1   88.9 A1      B1     
##  3  7.89  85.9 A1      B1     
##  4  7.82  88.8 A1      B1     
##  5  9     82.5 A1      B2     
##  6  8.43  92.4 A1      B2     
##  7  7.65  82.4 A1      B2     
##  8  7.7   87.1 A1      B2     
##  9  7.28  79.6 A1      B3     
## 10  8.96  95.1 A1      B3     
## # ... with 22 more rows

Uji Homogenitas Matriks Kovarians

#Uji Homogenitas
library(biotools)
## Loading required package: MASS
## ---
## biotools version 4.2
boxM(data_lat[,1:2],data_lat$Faktor1)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_lat[, 1:2]
## Chi-Sq (approx.) = 9.5304, df = 3, p-value = 0.02301
boxM(data_lat[,1:2],data_lat$Faktor2)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_lat[, 1:2]
## Chi-Sq (approx.) = 9.1484, df = 9, p-value = 0.4237
boxM(data_lat[,1:2],paste(data_lat$Faktor1,data_lat$Faktor2))
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_lat[, 1:2]
## Chi-Sq (approx.) = 24.954, df = 21, p-value = 0.2492

Uji Multivariat Normal

library(RVAideMemoire)
## *** Package RVAideMemoire v 0.9-81-2 ***
mshapiro.test(data_lat[data_lat$Faktor1=="A1",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.88251, p-value = 0.04246
mshapiro.test(data_lat[data_lat$Faktor1=="A2",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.93586, p-value = 0.3014
mshapiro.test(data_lat[data_lat$Faktor2=="B1",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.82165, p-value = 0.04857
mshapiro.test(data_lat[data_lat$Faktor2=="B2",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.91803, p-value = 0.4141
mshapiro.test(data_lat[data_lat$Faktor2=="B3",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.80141, p-value = 0.02964
mshapiro.test(data_lat[data_lat$Faktor2=="B4",-c(3,4)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (y1,y2)
## W = 0.91017, p-value = 0.3553

Uji Manova

Dengan Interaksi

result <- manova(cbind(y1,y2) ~ Faktor1 * Faktor2, data=data_lat)
summary(result, test="Wilks")
##                 Df   Wilks approx F num Df den Df    Pr(>F)    
## Faktor1          1 0.47515  12.7031      2     23 0.0001921 ***
## Faktor2          3 0.69062   1.5588      6     46 0.1808302    
## Faktor1:Faktor2  3 0.93197   0.2749      6     46 0.9459179    
## Residuals       24                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#cara lain
X <- as.matrix(data_lat[,c("y1","y2")])
mod <- lm(X ~ Faktor1*Faktor2,data=data_lat)
library(car)
## Loading required package: carData
Manova(mod, test="Wilks")
## 
## Type II MANOVA Tests: Wilks test statistic
##                 Df test stat approx F num Df den Df    Pr(>F)    
## Faktor1          1   0.47515  12.7031      2     23 0.0001921 ***
## Faktor2          3   0.69062   1.5588      6     46 0.1808302    
## Faktor1:Faktor2  3   0.93197   0.2749      6     46 0.9459179    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Tanpa Interaksi

result <- manova(cbind(y1,y2) ~ Faktor1 + Faktor2, 
data=data_lat)
summary(result, test="Wilks")
##           Df   Wilks approx F num Df den Df    Pr(>F)    
## Faktor1    1 0.49063  13.4963      2     26 9.547e-05 ***
## Faktor2    3 0.69325   1.7423      6     52    0.1297    
## Residuals 27                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Penugasan

Import Data

library(readxl)
data_tugas <- read_excel("penugasan.xlsx")
data_tugas$faktor1 = as.factor(data_tugas$faktor1)
data_tugas$faktor2 = as.factor(data_tugas$faktor2)
data_tugas
## # A tibble: 24 x 4
##    faktor1   faktor2  Keramahan Optimisme
##    <fct>     <fct>        <dbl>     <dbl>
##  1 laki-laki kaya             5         3
##  2 laki-laki kaya             4         6
##  3 laki-laki kaya             3         4
##  4 laki-laki kaya             2         4
##  5 laki-laki menengah         4         6
##  6 laki-laki menengah         3         6
##  7 laki-laki menengah         5         4
##  8 laki-laki menengah         5         5
##  9 laki-laki miskin           7         5
## 10 laki-laki miskin           4         3
## # ... with 14 more rows

Uji Homogenitas Matriks Kovarians

library(biotools)
boxM(data_tugas[,3:4],data_tugas$faktor1)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_tugas[, 3:4]
## Chi-Sq (approx.) = 5.4869, df = 3, p-value = 0.1394
boxM(data_tugas[,3:4],data_tugas$faktor2)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_tugas[, 3:4]
## Chi-Sq (approx.) = 8.5511, df = 6, p-value = 0.2004
boxM(data_tugas[,3:4],paste(data_tugas$faktor1,data_tugas$faktor2))
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  data_tugas[, 3:4]
## Chi-Sq (approx.) = 11.914, df = 15, p-value = 0.6855

Uji Multivariat Normal

library(RVAideMemoire)
mshapiro.test(data_tugas[data_tugas$faktor1=="laki-laki",-c(1,2)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (Keramahan,Optimisme)
## W = 0.92831, p-value = 0.3625
mshapiro.test(data_tugas[data_tugas$faktor1=="perempuan",-c(1,2)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (Keramahan,Optimisme)
## W = 0.88814, p-value = 0.1115
mshapiro.test(data_tugas[data_tugas$faktor2=="kaya",-c(1,2)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (Keramahan,Optimisme)
## W = 0.91566, p-value = 0.3956
mshapiro.test(data_tugas[data_tugas$faktor2=="menengah",-c(1,2)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (Keramahan,Optimisme)
## W = 0.89875, p-value = 0.2815
mshapiro.test(data_tugas[data_tugas$faktor2=="miskin",-c(1,2)])
## 
##  Multivariate Shapiro-Wilk normality test
## 
## data:  (Keramahan,Optimisme)
## W = 0.97113, p-value = 0.9068

Uji Manova

Dengan Interaksi

result <- manova(cbind(Keramahan,Optimisme) ~ faktor1 * faktor2, 
data=data_tugas)
summary(result, test="Wilks")
##                 Df   Wilks approx F num Df den Df   Pr(>F)   
## faktor1          1 0.58825   5.9496      2     17 0.010997 * 
## faktor2          2 0.50412   3.4716      4     34 0.017562 * 
## faktor1:faktor2  2 0.38703   5.1630      4     34 0.002325 **
## Residuals       18                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#cara lain
X <- as.matrix(data_tugas[,c("Keramahan","Optimisme")])
mod <- lm(X ~ faktor1*faktor2,data=data_tugas)
library(car)
Manova(mod, test="Wilks")
## 
## Type II MANOVA Tests: Wilks test statistic
##                 Df test stat approx F num Df den Df   Pr(>F)   
## faktor1          1   0.58825   5.9496      2     17 0.010997 * 
## faktor2          2   0.50412   3.4716      4     34 0.017562 * 
## faktor1:faktor2  2   0.38703   5.1630      4     34 0.002325 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Tanpa Interaksi

result <- manova(cbind(Keramahan,Optimisme) ~ faktor1 + faktor2, 
data=data_tugas)
summary(result, test="Wilks")
##           Df   Wilks approx F num Df den Df  Pr(>F)  
## faktor1    1 0.71659   3.7572      2     19 0.04218 *
## faktor2    2 0.61231   2.6406      4     38 0.04859 *
## Residuals 20                                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1