library(agricolae)
## Warning: package 'agricolae' was built under R version 4.4.2

Input Data

tekanan <- factor(rep(c("A","B","C","D"), each=3))
logam <- factor(c(1,2,4, 2,3,4, 1,2,3, 1,3,4))
nilai <- c(79,83,86, 75,78,84, 86,88,90, 92,94,80)

Data Frame

data_frame <- data.frame(tekanan, logam, nilai)
print(data_frame)
##    tekanan logam nilai
## 1        A     1    79
## 2        A     2    83
## 3        A     4    86
## 4        B     2    75
## 5        B     3    78
## 6        B     4    84
## 7        C     1    86
## 8        C     2    88
## 9        C     3    90
## 10       D     1    92
## 11       D     3    94
## 12       D     4    80

Parameter Rancangan

t <- 4
b <-4
r <- 3
k<- 3
N <- 12
lambda <- 2
total <- 1024
nilai_perlakuan <- c(257, 246, 262, 250)
nilai_blok <- c(248, 237, 264, 266)

Nilai Hilang setiap sel

Baris13 <- (3 * (248 + 262) - 1024) / 8
Baris11 <- (3 * (237 + 257) - 1024) / 8
Baris34 <- (3 * (264 + 250) - 1024) / 8
Baris42 <- (3 * (266 + 246) - 1024) / 8
print(Baris13)
## [1] 63.25
print(Baris11)
## [1] 57.25
print(Baris34)
## [1] 64.75
print(Baris42)
## [1] 64

Analisis ragam

JKT <- sum(nilai^2) - (sum(nilai)^2)/((t-1)*(b-1))
print(JKT)
## [1] -28238.44
total_logam <- tapply(nilai, logam, sum)
Q <- sum(total_logam^2/r)
JKP <- (Q - (sum(nilai)^2)/((t-1)*(b-1))) / k
print(JKP)
## [1] -9522.148
total_tekanan <- tapply(nilai, tekanan, sum)
B <- sum(total_tekanan^2/k)
JKB <- (B - (sum(nilai)^2)/((t-1)*(b-1))) / r
print(JKB)
## [1] -9475.926
JKG <- JKT-JKP-JKB
print(JKG)
## [1] -9240.37

Derajat Bebas

db_total <- (t-1)*(b-1)
db_perlakuan <- t-1
db_blok <- b-1
db_galat <- (t-1)*(b-1)-t
KTP <- JKP/db_perlakuan
KTB <- JKB/db_blok
KTG <- JKG/db_galat
print(KTP)
## [1] -3174.049
print(KTB)
## [1] -3158.642
print(KTG)
## [1] -1848.074

F-Hitung

F_perlakuan <- KTP/KTG
F_blok <- KTB/KTG
print(F_perlakuan)
## [1] 1.71749
print(F_blok)
## [1] 1.709153

F-Tabel

qf(0.05, db_perlakuan, db_galat, lower.tail = TRUE)
## [1] 0.1109452

KESIMPULAN : F-Hitung perlakuan > F-Tabel, maka tolak H0, sehingga terdapat pengaruh signifikan antara jenis logam terhadap hasil pengujian

F-Hitung blok > F-Tabel, maka tolak H0, sehingga terdapat pengaruh signifikan antara tekanan terhadap hasil pengujian.