Input data

library(car)
## Warning: package 'car' was built under R version 4.3.3
## Loading required package: carData
padi <- read.table(header=T,text =
               "
Varietas Y1 Y2
v1 5 7.2
v1 5.1 7.1
v1 5.2 7.3
v1 5.1 7.2
v2 5.5 7.5
v2 5.4 7.6
v2 5.6 7.7
v2 5.4 7.6
v3 7.1 8.7
v3 7.2 8.6
v3 7.3 8.7
v3 7.4 8.5
v4 8.5 9.1
v4 8.6 9.2
v4 8.6 9.2
v4 8.7 9.1
")
padi
##    Varietas  Y1  Y2
## 1        v1 5.0 7.2
## 2        v1 5.1 7.1
## 3        v1 5.2 7.3
## 4        v1 5.1 7.2
## 5        v2 5.5 7.5
## 6        v2 5.4 7.6
## 7        v2 5.6 7.7
## 8        v2 5.4 7.6
## 9        v3 7.1 8.7
## 10       v3 7.2 8.6
## 11       v3 7.3 8.7
## 12       v3 7.4 8.5
## 13       v4 8.5 9.1
## 14       v4 8.6 9.2
## 15       v4 8.6 9.2
## 16       v4 8.7 9.1

Manova

mod1 = Manova(lm(cbind(Y1,Y2)~Varietas,data=padi),type="III")
summary(mod1,multivariate=TRUE)
## 
## Type III MANOVA Tests:
## 
## Sum of squares and products for error:
##         Y1      Y2
## Y1  0.1175 -0.0050
## Y2 -0.0050  0.0775
## 
## ------------------------------------------
##  
## Term: (Intercept) 
## 
## Sum of squares and products for the hypothesis:
##        Y1     Y2
## Y1 104.04 146.88
## Y2 146.88 207.36
## 
## Multivariate Tests: (Intercept)
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1     1.000 20529.32      2     11 < 2.22e-16 ***
## Wilks             1     0.000 20529.32      2     11 < 2.22e-16 ***
## Hotelling-Lawley  1  3732.603 20529.32      2     11 < 2.22e-16 ***
## Roy               1  3732.603 20529.32      2     11 < 2.22e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: Varietas 
## 
## Sum of squares and products for the hypothesis:
##          Y1        Y2
## Y1 31.75187 17.410625
## Y2 17.41062  9.721875
## 
## Multivariate Tests: Varietas
##                  Df test stat  approx F num Df den Df     Pr(>F)    
## Pillai            3    1.5938   15.6960      6     24 2.9583e-07 ***
## Wilks             3    0.0010  113.9501      6     22 1.9895e-15 ***
## Hotelling-Lawley  3  415.9336  693.2226      6     20 < 2.22e-16 ***
## Roy               3  414.4569 1657.8276      3     12 5.6971e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Dapat dilihat dari multivariate test: Varietas baris wilks Pada taraf 5% H0 ditolak karena nilai p value wilks 1.9895e-15<0.05 Kesimpulan: Cukup bukti untuk menyatakan bahwa terdapat perbedaan respon akibat adanya perbedaan varietas