# 1. Pendahuluan
Tujuan Praktikum:
1. Memahami konsep uji vektor nilai tengah untuk dua populasi.
2. Mampu melakukan uji hipotesis dan membentuk selang kepercayaan untuk:
Sampel Berpasangan (Paired Samples)
Sampel Saling Bebas (Independent Samples) dengan asumsi ragam sama.
3. Mampu menginterpretasikan hasil output R dalam konteks masalah.
# membangkitkan data dengan set seed 34
library(readxl)## Warning: package 'readxl' was built under R version 4.4.3dataset <- read_excel("C:/Users/LENOVO/Downloads/Latihan Data Pertemuan 4.xlsx", sheet = 1)
dataset## # A tibble: 15 × 4
## `Kata Formal` `Kata Kerja Formal` `Kata Informal` `Kata Kerja Informal`
## <dbl> <dbl> <dbl> <dbl>
## 1 137 15 148 20
## 2 164 25 159 24
## 3 224 27 144 19
## 4 208 33 103 18
## 5 178 24 121 17
## 6 128 20 89 11
## 7 154 18 119 17
## 8 158 16 123 13
## 9 102 21 76 16
## 10 214 25 217 29
## 11 209 24 148 22
## 12 151 16 151 21
## 13 123 13 83 7
## 14 161 22 135 20
## 15 175 23 178 15set.seed(34)
# Banyak baris data
n <- 15
# Bangkitkan data acak
dataset2 <- data.frame(
`Jumlah Gol` = sample(100:230, n, replace = TRUE),
`Gol Jarak Jauh` = sample(10:35, n, replace = TRUE),
`Jumlah Poin` = sample(70:220, n, replace = TRUE),
`Poin Jarak Jauh` = sample(7:30, n, replace = TRUE)
)
# Tampilkan data
print(dataset2)## Jumlah.Gol Gol.Jarak.Jauh Jumlah.Poin Poin.Jarak.Jauh
## 1 109 13 173 17
## 2 149 22 91 19
## 3 107 29 181 30
## 4 185 34 144 27
## 5 199 22 177 23
## 6 128 27 128 30
## 7 110 14 106 30
## 8 225 18 216 9
## 9 198 31 116 13
## 10 160 13 214 12
## 11 166 18 82 14
## 12 132 34 188 17
## 13 190 21 191 20
## 14 145 31 187 18
## 15 108 29 151 18d_Gol = dataset2[,1]-dataset2[,3]
d_Gol_Jarak_Jauh = dataset2[,2]-dataset2[,4]
X = data.frame(d_Gol,d_Gol_Jarak_Jauh)xbar = apply(X, 2, mean)
xbar## d_Gol d_Gol_Jarak_Jauh
## -2.266667 3.933333cov_m = cov(X)
cov_m## d_Gol d_Gol_Jarak_Jauh
## d_Gol 2754.78095 50.40952
## d_Gol_Jarak_Jauh 50.40952 79.35238library(MVTests)## Warning: package 'MVTests' was built under R version 4.4.3##
## Attaching package: 'MVTests'## The following object is masked from 'package:datasets':
##
## irismean0 = c(0,0)
result = OneSampleHT2(X,mu0=mean0,alpha=0.05)
summary(result)## One Sample Hotelling T Square Test
##
## Hotelling T Sqaure Statistic = 3.049613
## F value = 1.416 , df1 = 2 , df2 = 13 , p-value: 0.278
##
## Descriptive Statistics
##
## d_Gol d_Gol_Jarak_Jauh
## N 15.000000 15.000000
## Means -2.266667 3.933333
## Sd 52.486007 8.907995
##
##
## Detection important variable(s)
##
## Lower Upper Mu0 Important Variables?
## d_Gol -41.065157 36.53182 0 FALSE
## d_Gol_Jarak_Jauh -2.651598 10.51827 0 FALSEresult$CI## Lower Upper Mu0 Important Variables?
## d_Gol -41.065157 36.53182 0 FALSE
## d_Gol_Jarak_Jauh -2.651598 10.51827 0 FALSEbon = function(mu,S,n,alpha,k){
p = length(mu)
lower = mu[k] - sqrt(S[k,k]/n) * abs(qt(alpha/(2*p), df=n-1))
upper = mu[k] + sqrt(S[k,k]/n) * abs(qt(alpha/(2*p), df=n-1))
c(lower = lower,upper = upper)
}
n = nrow(X)#Gol
bon(xbar, cov_m,n,0.05,1)## lower.d_Gol upper.d_Gol
## -36.27592 31.74259#Jarak Jauh
bon(xbar, cov_m,n,0.05,2)## lower.d_Gol_Jarak_Jauh upper.d_Gol_Jarak_Jauh
## -1.838763 9.705430library(readxl)
dataset <- read_excel("C:/Users/LENOVO/Downloads/Latihan Data Pertemuan 4.xlsx", sheet = 2)
dataset## # A tibble: 20 × 4
## `CAT TWK` `CAT TIU` `MANUAL TWK` `MANUAL TIU`
## <dbl> <dbl> <dbl> <dbl>
## 1 54 77 58 84
## 2 76 58 49 60
## 3 55 58 83 69
## 4 79 63 55 60
## 5 84 37 85 89
## 6 60 45 90 68
## 7 73 60 42 36
## 8 81 56 85 57
## 9 65 80 80 46
## 10 54 42 89 51
## 11 67 42 40 65
## 12 51 64 71 64
## 13 56 62 81 82
## 14 50 41 40 50
## 15 58 43 80 77
## 16 82 46 75 35
## 17 61 48 41 55
## 18 60 43 54 61
## 19 45 56 48 50
## 20 80 38 69 43set.seed(34)
n <- 20
# Bangkitkan data acak
Digital_Sistolik <- round(rnorm(n, mean=120, sd=15))
Digital_Diastolik <- round(rnorm(n, mean=80, sd=10))
Manual_Sistolik <- pmin(pmax(round(rnorm(n, mean=122, sd=12)), 0), 250)
Manual_Diastolik <- pmin(pmax(round(rnorm(n, mean=82, sd=8)), 0), 150)
dataset_kesehatan <- data.frame(
Digital_Sistolik,
Digital_Diastolik,
Manual_Sistolik,
Manual_Diastolik
)
dataset_kesehatan## Digital_Sistolik Digital_Diastolik Manual_Sistolik Manual_Diastolik
## 1 118 65 114 74
## 2 138 105 115 93
## 3 109 69 94 72
## 4 111 66 100 68
## 5 116 84 121 76
## 6 113 88 133 84
## 7 130 71 124 89
## 8 107 75 145 87
## 9 136 78 112 87
## 10 120 92 131 78
## 11 114 72 135 86
## 12 131 92 109 76
## 13 117 68 113 78
## 14 136 80 121 101
## 15 126 87 110 79
## 16 140 75 134 73
## 17 120 82 110 82
## 18 113 81 137 70
## 19 92 81 122 71
## 20 116 80 137 88# Memisahkan Data dari Populasi 1 dan 2
data_cat = dataset_kesehatan[,1:2]
data_man = dataset_kesehatan[,3:4]xbar1 = apply(data_cat, 2, mean)
xbar1## Digital_Sistolik Digital_Diastolik
## 120.15 79.55xbar2 = apply(data_man, 2, mean)
xbar2## Manual_Sistolik Manual_Diastolik
## 120.85 80.60cov_m1 = cov(data_cat)
cov_m1## Digital_Sistolik Digital_Diastolik
## Digital_Sistolik 148.76579 38.01842
## Digital_Diastolik 38.01842 101.52368cov_m2 = cov(data_man)
cov_m2## Manual_Sistolik Manual_Diastolik
## Manual_Sistolik 183.81842 31.51579
## Manual_Diastolik 31.51579 74.56842n1 = nrow(data_cat)
n2 = nrow(data_man)
# S Gabungan
s_gab = ((n1-1)*cov_m1+(n2-1)*cov_m2)/(n1+n2-2)
s_gab## Digital_Sistolik Digital_Diastolik
## Digital_Sistolik 166.29211 34.76711
## Digital_Diastolik 34.76711 88.04605library(Hotelling)## Loading required package: corpcort2_homogen = hotelling.test(data_cat,data_man,var.equal=TRUE)
t2_homogen## Test stat: 0.13056
## Numerator df: 2
## Denominator df: 37
## P-value: 0.9385T.ci = function(mu1, mu2, S_gab, n1, n2, avec=rep(1,length(mu)), level=0.95){
p = length(mu1)
mu = mu1-mu2
cval = qf(level, p, n1+n2-p-1) * p * (n1+n2-2) / (n1+n2-p-1)
zhat = crossprod(avec, mu)
zvar = crossprod(avec, S_gab %*% avec)* (1/n1+1/n2)
const = sqrt(cval * zvar)
c(lower = zhat - const, upper = zhat + const)
}#TWK
T.ci(xbar1, xbar2, s_gab, n1,n2, avec=c(1,0),level=0.95)## lower upper
## -11.239304 9.839304#TIU
T.ci(xbar1, xbar2, s_gab, n1,n2, avec=c(0,1),level=0.95)## lower upper
## -8.718864 6.618864bon = function(mu1, mu2 ,S, n1, n2, alpha, k){
p = length(mu1)
mu = mu1-mu2
lower = mu[k] - sqrt((S[k,k]) *(1/n1+1/n2))* abs(qt(alpha/(2*p), df=n1+n2-2))
upper = mu[k] + sqrt((S[k,k]) *(1/n1+1/n2))* abs(qt(alpha/(2*p), df=n1+n2-2))
ci = c(lower = lower,upper = upper)
names(ci)= c("lower","upper")
ci
}#TWK
bon(xbar1, xbar2, s_gab, n1, n2,0.05,1)## lower upper
## -10.216665 8.816665#TIU
bon(xbar1, xbar2, s_gab, n1, n2,0.05,2)## lower upper
## -7.974747 5.874747library(readxl)
dataset <- read_excel("C:/Users/LENOVO/Downloads/Latihan Data Pertemuan 4.xlsx", sheet = 2)
dataset## # A tibble: 20 × 4
## `CAT TWK` `CAT TIU` `MANUAL TWK` `MANUAL TIU`
## <dbl> <dbl> <dbl> <dbl>
## 1 54 77 58 84
## 2 76 58 49 60
## 3 55 58 83 69
## 4 79 63 55 60
## 5 84 37 85 89
## 6 60 45 90 68
## 7 73 60 42 36
## 8 81 56 85 57
## 9 65 80 80 46
## 10 54 42 89 51
## 11 67 42 40 65
## 12 51 64 71 64
## 13 56 62 81 82
## 14 50 41 40 50
## 15 58 43 80 77
## 16 82 46 75 35
## 17 61 48 41 55
## 18 60 43 54 61
## 19 45 56 48 50
## 20 80 38 69 43# Memisahkan Data dari Populasi 1 dan 2
data_cat = dataset[,1:2]
data_man = dataset[,3:4]xbar1 = apply(data_cat, 2, mean)
xbar1## CAT TWK CAT TIU
## 64.55 52.95xbar2 = apply(data_man, 2, mean)
xbar2## MANUAL TWK MANUAL TIU
## 65.75 60.10cov_m1 = cov(data_cat)
cov_m1## CAT TWK CAT TIU
## CAT TWK 151.10263 -26.28684
## CAT TIU -26.28684 154.15526cov_m2 = cov(data_man)
cov_m2## MANUAL TWK MANUAL TIU
## MANUAL TWK 333.77632 81.86842
## MANUAL TIU 81.86842 230.41053n1 = nrow(data_cat)
n2 = nrow(data_man)library(Hotelling)
t2_not_homogen = hotelling.test(data_cat,data_man,var.equal=FALSE)
t2_not_homogen## Test stat: 2.6599
## Numerator df: 2
## Denominator df: 34.1358976944273
## P-value: 0.287T.ci = function(mu1, mu2, S1, S2, n1, n2, avec=rep(1,length(mu)), level=0.95){
p = length(mu1)
mu = mu1-mu2
cval = qchisq(level, p)
zhat = crossprod(avec, mu)
zvar = crossprod(avec, S1 %*% avec)/n1 + crossprod(avec, S2 %*% avec)/n2
const = sqrt(cval * zvar)
c(lower = zhat - const, upper = zhat + const)
}
#TWK
T.ci(xbar1, xbar2, cov_m1, cov_m2, n1,n2, avec=c(1,0),level=0.95)## lower upper
## -13.25225 10.85225#TWK
T.ci(xbar1, xbar2, cov_m1, cov_m2, n1,n2, avec=c(1,0),level=0.95)## lower upper
## -13.25225 10.85225#TIU
T.ci(xbar1, xbar2, cov_m1, cov_m2, n1,n2, avec=c(0,1),level=0.95)## lower upper
## -17.883388 3.583388