Orthogonal kontras dan polinomial
Rohim Firdaus dan M. Ainur Rohim
2024-10-11
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#_Input data_#
Suplemen <- factor(rep(LETTERS[1:6], each = 4))
Bobot_Badan <- c(6.78, 6.51, 6.92, 7.08,
6.88, 6.13, 7.21, 7.84,
9.80, 9.72, 10.14, 9.53,
7.50, 7.89, 6.40, 8.22,
6.87, 6.99, 7.11, 6.54,
7.13, 8.00, 9.62, 7.09)
data_contoh <- data.frame(Suplemen, Bobot_Badan)
data_contoh## Suplemen Bobot_Badan
## 1 A 6.78
## 2 A 6.51
## 3 A 6.92
## 4 A 7.08
## 5 B 6.88
## 6 B 6.13
## 7 B 7.21
## 8 B 7.84
## 9 C 9.80
## 10 C 9.72
## 11 C 10.14
## 12 C 9.53
## 13 D 7.50
## 14 D 7.89
## 15 D 6.40
## 16 D 8.22
## 17 E 6.87
## 18 E 6.99
## 19 E 7.11
## 20 E 6.54
## 21 F 7.13
## 22 F 8.00
## 23 F 9.62
## 24 F 7.09str(data_contoh)## 'data.frame': 24 obs. of 2 variables:
## $ Suplemen : Factor w/ 6 levels "A","B","C","D",..: 1 1 1 1 2 2 2 2 3 3 ...
## $ Bobot_Badan: num 6.78 6.51 6.92 7.08 6.88 6.13 7.21 7.84 9.8 9.72 ...anova_contoh <- aov(Bobot_Badan ~ Suplemen, data = data_contoh)
summary(anova_contoh)## Df Sum Sq Mean Sq F value Pr(>F)
## Suplemen 5 25.654 5.131 11.33 4.72e-05 ***
## Residuals 18 8.154 0.453
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova_contoh <- aov(Bobot_Badan ~ Suplemen, data = data_contoh)
contrasts(data_contoh$Suplemen) <- cbind(c(2, 2, -1, -1, -1, -1), c(1,-1, 0, 0, 0, 0),
c(0, 0, 1, 1, -1, -1), c(0, 0, 1, -1, 0, 0),
c(0, 0, 0, 0, 1, -1))
contrasts(data_contoh$Suplemen)## [,1] [,2] [,3] [,4] [,5]
## A 2 1 0 0 0
## B 2 -1 0 0 0
## C -1 0 1 1 0
## D -1 0 1 -1 0
## E -1 0 -1 0 1
## F -1 0 -1 0 -1summary.aov(anova_contoh, split = list (Suplemen = list('Kontras1' = 1, 'Kontras2' = 2,
'Kontras3' = 3, 'Kontras4' = 4, 'Kontras5' = 5)))## Df Sum Sq Mean Sq F value Pr(>F)
## Suplemen 5 25.654 5.131 11.326 4.72e-05 ***
## Suplemen: Kontras1 1 2.012 2.012 4.442 0.0493 *
## Suplemen: Kontras2 1 20.110 20.110 44.391 2.99e-06 ***
## Suplemen: Kontras3 1 0.239 0.239 0.528 0.4766
## Suplemen: Kontras4 1 0.704 0.704 1.554 0.2286
## Suplemen: Kontras5 1 2.588 2.588 5.712 0.0280 *
## Residuals 18 8.154 0.453
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qf(0.05, 1, 18, lower.tail = FALSE)## [1] 4.413873#kontras polynomial orthogonal#
#_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)
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
## 7 30 18.6
## 8 30 20.2
## 9 30 18.2
## 10 40 17.6
## 11 40 19.3
## 12 40 17.1
## 13 50 18.0
## 14 50 16.4
## 15 50 16.6str(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 1anova_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 ' ' 1summary.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 ' ' 1qf(0.05, 1, 10, lower.tail = FALSE)## [1] 4.964603summary(lm(hasil~kerapatan,data2))##
## Call:
## lm(formula = hasil ~ kerapatan, data = data2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90 -0.55 -0.40 0.45 1.30
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.40000 0.22331 73.441 5.35e-15 ***
## kerapatan1 1.20000 0.15790 7.600 1.84e-05 ***
## kerapatan2 -1.00000 0.13345 -7.493 2.08e-05 ***
## kerapatan3 0.10000 0.15790 0.633 0.541
## kerapatan4 0.10000 0.05968 1.676 0.125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8649 on 10 degrees of freedom
## Multiple R-squared: 0.9213, Adjusted R-squared: 0.8899
## F-statistic: 29.28 on 4 and 10 DF, p-value: 1.69e-05# Plot hasil regresi polinomial ortogonal
plot(data2$kerapatan, data2$hasil, main="Hasil Gandum vs Kerapatan Tanaman",
xlab="Kerapatan Tanaman", ylab="Rata-rata Hasil", pch=19)
lines(sort(data2$kerapatan), predict(anova_2)[order(data2$kerapatan)], col="blue", lwd=2)