#______Kontras Ortogonal dan Polinomial Ortogonal_____#
#_Input data 1_#
Varietas <- factor(rep(LETTERS[1:4], each = 6))
Hasil <- c(25.1, 17.2, 26.4, 16.1, 22.2, 15.9,
40.2, 35.3, 32.0, 36.5, 43.3, 37.1,
18.3, 22.6, 25.9, 15.1, 11.4, 23.7,
28.0, 28.6, 33.2, 31.7, 30.3, 27.6)
data1 <- data.frame(Varietas, Hasil)
head(data1)
## Varietas Hasil
## 1 A 25.1
## 2 A 17.2
## 3 A 26.4
## 4 A 16.1
## 5 A 22.2
## 6 A 15.9
str(data1)
## 'data.frame': 24 obs. of 2 variables:
## $ Varietas: Factor w/ 4 levels "A","B","C","D": 1 1 1 1 1 1 2 2 2 2 ...
## $ Hasil : num 25.1 17.2 26.4 16.1 22.2 15.9 40.2 35.3 32 36.5 ...
#_Kontras Ortogonal_#
anova1 <- aov(Hasil ~ Varietas, data = data1)
contrasts(data1$Varietas) <- cbind(c(3, -1, -1, -1), c(0, 1, -1, 0),
c(0, 1, 1, -2))
contrasts(data1$Varietas)
## [,1] [,2] [,3]
## A 3 0 0
## B -1 1 1
## C -1 -1 1
## D -1 0 -2
anova_1 <- aov(Hasil ~ Varietas, data = data1)
summary(anova_1)
## Df Sum Sq Mean Sq F value Pr(>F)
## Varietas 3 1291.0 430.3 23.46 9.32e-07 ***
## Residuals 20 366.9 18.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(anova_1, split = list (Varietas = list('A vs BCD' = 1, 'B vs C' = 2,
'BC vs D' = 3)))
## Df Sum Sq Mean Sq F value Pr(>F)
## Varietas 3 1291.0 430.3 23.458 9.32e-07 ***
## Varietas: A vs BCD 1 321.3 321.3 17.515 0.000456 ***
## Varietas: B vs C 1 961.2 961.2 52.399 5.27e-07 ***
## Varietas: BC vs D 1 8.4 8.4 0.458 0.506106
## Residuals 20 366.9 18.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#_Input data 2_#
kerapatan <- factor(rep(c(10, 20, 30, 40, 50), each = 3))
hasil <- c(12.2, 11.4, 12.4,
16.0, 15.5, 16.5,
18.6, 20.2, 18.2,
17.6, 19.3, 17.1,
18.0, 16.4, 16.6)
data2 <- data.frame(kerapatan, hasil)
head(data2)
## kerapatan hasil
## 1 10 12.2
## 2 10 11.4
## 3 10 12.4
## 4 20 16.0
## 5 20 15.5
## 6 20 16.5
str(data2)
## 'data.frame': 15 obs. of 2 variables:
## $ kerapatan: Factor w/ 5 levels "10","20","30",..: 1 1 1 2 2 2 3 3 3 4 ...
## $ hasil : num 12.2 11.4 12.4 16 15.5 16.5 18.6 20.2 18.2 17.6 ...
#_Polinomial Ortogonal_#
anova2 <- aov(hasil ~ kerapatan, data = data2)
contrasts(data2$kerapatan) <- cbind(c(-2, -1, 0, 1, 2), c(2, -1, -2, -1, 2),
c(-1, 2, 0, -2, 1), c(1, -4, 6, -4, 1))
contrasts(data2$kerapatan)
## [,1] [,2] [,3] [,4]
## 10 -2 2 -1 1
## 20 -1 -1 2 -4
## 30 0 -2 0 6
## 40 1 -1 -2 -4
## 50 2 2 1 1
anova_2 <- aov(hasil ~ kerapatan, data = data2)
summary(anova_2)
## Df Sum Sq Mean Sq F value Pr(>F)
## kerapatan 4 87.60 21.900 29.28 1.69e-05 ***
## Residuals 10 7.48 0.748
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(anova_2, split = list (kerapatan = list('Linear' = 1, 'Kuadratik' = 2,
'Kubik' = 3, 'Kuartik' = 4)))
## Df Sum Sq Mean Sq F value Pr(>F)
## kerapatan 4 87.60 21.90 29.278 1.69e-05 ***
## kerapatan: Linear 1 43.20 43.20 57.754 1.84e-05 ***
## kerapatan: Kuadratik 1 42.00 42.00 56.150 2.08e-05 ***
## kerapatan: Kubik 1 0.30 0.30 0.401 0.541
## kerapatan: Kuartik 1 2.10 2.10 2.807 0.125
## Residuals 10 7.48 0.75
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#atau#
contrasts(data2$kerapatan) <- contr.poly(5)
summary.aov(anova_2, split = list (kerapatan = list('Linear' = 1, 'Kuadratik' = 2,
'Kubik' = 3, 'Kuartik' = 4)))
## Df Sum Sq Mean Sq F value Pr(>F)
## kerapatan 4 87.60 21.90 29.278 1.69e-05 ***
## kerapatan: Linear 1 43.20 43.20 57.754 1.84e-05 ***
## kerapatan: Kuadratik 1 42.00 42.00 56.150 2.08e-05 ***
## kerapatan: Kubik 1 0.30 0.30 0.401 0.541
## kerapatan: Kuartik 1 2.10 2.10 2.807 0.125
## Residuals 10 7.48 0.75
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1