# LATIHAN 1 - ANOVA DUA JALUR
tinggi <- c(25,28,26,27, 20,22,21,23, 30,32,31,29,
30,32,31,33, 25,27,26,28, 35,37,36,34,
28,30,29,31, 23,25,24,26, 33,35,34,32)
pupuk <- factor(rep(c("Organik","Anorganik","Campuran"), each=12))
tanah <- factor(rep(rep(c("Lempung","Pasir","Humus"), each=4), 3))
model <- aov(tinggi ~ pupuk * tanah)
summary(model)
## Df Sum Sq Mean Sq F value Pr(>F)
## pupuk 2 152 76.00 45.6 2.20e-09 ***
## tanah 2 488 244.00 146.4 3.22e-15 ***
## pupuk:tanah 4 0 0.00 0.0 1
## Residuals 27 45 1.67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
interaction.plot(tanah, pupuk, tinggi, type="b",
col=c("red","blue","green"))
# LATIHAN 2 - MANOVA
pendapatan <- c(3,4,3.5,4.5,3.8, 6,7,6.5,7.5,6.8, 10,12,11,13,11.5)
kepuasan <- c(6,7,6.5,7,6.8, 8,9,8.5,9,8.8, 9,10,9.5,10,9.8)
pendidikan <- factor(rep(c("SMA","S1","S2"), each=5))
Y <- cbind(pendapatan, kepuasan)
model_manova <- manova(Y ~ pendidikan)
summary(model_manova, test="Wilks")
## Df Wilks approx F num Df den Df Pr(>F)
## pendidikan 2 0.0080673 55.735 4 22 3.38e-11 ***
## Residuals 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(model_manova, test="Pillai")
## Df Pillai approx F num Df den Df Pr(>F)
## pendidikan 2 1.759 43.784 4 24 1.085e-10 ***
## Residuals 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Matriks W, T, B dan Wilks' Lambda
W <- crossprod(resid(model_manova))
T <- crossprod(scale(Y, scale=FALSE))
B <- T - W
W; B
## pendapatan kepuasan
## pendapatan 7.504 3.514
## kepuasan 3.514 2.136
## pendapatan kepuasan
## pendapatan 152.292 56.60000
## kepuasan 56.600 23.33333
det(W) / det(T)
## [1] 0.008067319
library(heplots)
## Warning: package 'heplots' was built under R version 4.5.3
boxM(Y, pendidikan)
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: Y by pendidikan
## Chi-Sq (approx.) = 7.1899, df = 6, p-value = 0.3036