Komputasi Statistika
Tugas
Alicia Arifin (20214920001)
March 07, 2023
Email : ali.19arifin@gmail.com
RPubs : https://rpubs.com/aliciaarifin/
Jurusan :
Statistika
Address : ARA Center, Matana University Tower
Jl. CBD Barat Kav, RT.1, Curug Sangereng, Kelapa Dua,
Tangerang, Banten 15810.
1 Library
setwd(getwd())
treatment = read.csv("treatment.csv")2 Exercise
2.1 Exercice 1
Please work out in R by doing a chi-squared test on the treatment (X) and improvement (Y) columns in treatment.csv.
treatment # data## id treatment improvement
## 1 1 treated improved
## 2 2 treated improved
## 3 3 not-treated improved
## 4 4 treated improved
## 5 5 treated not-improved
## 6 6 treated not-improved
## 7 7 not-treated not-improved
## 8 8 treated not-improved
## 9 9 not-treated improved
## 10 10 treated improved
## 11 11 not-treated improved
## 12 12 not-treated not-improved
## 13 13 not-treated not-improved
## 14 14 not-treated not-improved
## 15 15 not-treated improved
## 16 16 not-treated improved
## 17 17 treated improved
## 18 18 treated improved
## 19 19 not-treated not-improved
## 20 20 not-treated not-improved
## 21 21 treated not-improved
## 22 22 not-treated not-improved
## 23 23 treated not-improved
## 24 24 not-treated improved
## 25 25 treated improved
## 26 26 treated improved
## 27 27 not-treated not-improved
## 28 28 not-treated improved
## 29 29 treated not-improved
## 30 30 treated improved
## 31 31 not-treated not-improved
## 32 32 not-treated not-improved
## 33 33 treated improved
## 34 34 not-treated improved
## 35 35 treated not-improved
## 36 36 not-treated improved
## 37 37 treated improved
## 38 38 not-treated not-improved
## 39 39 not-treated improved
## 40 40 treated improved
## 41 41 not-treated improved
## 42 42 not-treated improved
## 43 43 not-treated not-improved
## 44 44 not-treated improved
## 45 45 not-treated improved
## 46 46 treated improved
## 47 47 treated not-improved
## 48 48 not-treated not-improved
## 49 49 treated improved
## 50 50 treated improved
## 51 51 not-treated not-improved
## 52 52 treated improved
## 53 53 not-treated improved
## 54 54 treated improved
## 55 55 treated improved
## 56 56 not-treated improved
## 57 57 treated improved
## 58 58 not-treated not-improved
## 59 59 treated improved
## 60 60 treated improved
## 61 61 treated improved
## 62 62 not-treated improved
## 63 63 treated not-improved
## 64 64 treated not-improved
## 65 65 not-treated improved
## 66 66 not-treated improved
## 67 67 not-treated improved
## 68 68 not-treated not-improved
## 69 69 not-treated not-improved
## 70 70 treated improved
## 71 71 treated not-improved
## 72 72 not-treated not-improved
## 73 73 treated not-improved
## 74 74 not-treated improved
## 75 75 not-treated not-improved
## 76 76 not-treated not-improved
## 77 77 treated not-improved
## 78 78 not-treated improved
## 79 79 treated improved
## 80 80 treated improved
## 81 81 treated improved
## 82 82 not-treated not-improved
## 83 83 treated improved
## 84 84 not-treated not-improved
## 85 85 treated improved
## 86 86 not-treated improved
## 87 87 not-treated not-improved
## 88 88 treated improved
## 89 89 not-treated not-improved
## 90 90 treated improved
## 91 91 not-treated not-improved
## 92 92 not-treated improved
## 93 93 treated not-improved
## 94 94 treated not-improved
## 95 95 not-treated not-improved
## 96 96 treated improved
## 97 97 not-treated improved
## 98 98 treated improved
## 99 99 not-treated not-improved
## 100 100 not-treated improved
## 101 101 treated improved
## 102 102 treated improved
## 103 103 not-treated not-improved
## 104 104 treated improved
## 105 105 not-treated not-improvedtable(treatment$treatment, treatment$improvement)##
## improved not-improved
## not-treated 26 29
## treated 35 15chisq.test(treatment$treatment, treatment$improvement)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: treatment$treatment and treatment$improvement
## X-squared = 4.6626, df = 1, p-value = 0.03083H0 ditolak, p-value <= 0.05. Data yang di atas merupakan identikal.
2.2 Exercice 2
Find out if the cyl and carb variables in
mtcars dataset are dependent or not.
table(mtcars$cyl, mtcars$carb)##
## 1 2 3 4 6 8
## 4 5 6 0 0 0 0
## 6 2 0 0 4 1 0
## 8 0 4 3 6 0 1df2 = (2-1)*(6-1)
alpha = 0.05
chisq.test(mtcars$cyl, mtcars$carb)## Warning in chisq.test(mtcars$cyl, mtcars$carb): Chi-squared approximation may
## be incorrect##
## Pearson's Chi-squared test
##
## data: mtcars$cyl and mtcars$carb
## X-squared = 24.389, df = 10, p-value = 0.006632Asumsi H0 = variabelnya independen
Dari hasil di atas, karena
p-value kurang dari alpha 0.05, H0 ditolak. variabelnya dependen
2.3 Exercise 3
256 visual artists were surveyed to find out their zodiac sign. The results were: Aries (29), Taurus (24), Gemini (22), Cancer (19), Leo (21), Virgo (18), Libra (19), Scorpio (20), Sagittarius (23), Capricorn (18), Aquarius (20), Pisces (23). Test the hypothesis that zodiac signs are evenly distributed across visual artists. (Reference)
zodiac = c(29,24,22,19,21,18,19,20,23,18,20,23)
pert.zodiac = zodiac/256
expected = c(rep(256/12, 12))
zodiak = data.frame(
"zodiak" = c('Aries', 'Taurus' , 'Gemini' , 'Cancer' , 'Leo' , 'Virgo' , 'Libra' , 'Scorpio', 'Sagittarius', 'Capricorn', 'Aquarius', 'Pisces'),
"observed" = zodiac,
'expected' = expected
)
# H0 = semua zodiac terdistribusi dengan baik.
chisq = sum((zodiac-expected)^2 / expected)
pchisq(q = chisq, df = 12-1, lower.tail=F)## [1] 0.9265414H0 diterima, zodiaknya berdistribusi dengan adil atau evenly distributed.