Komputasi Statistika

1 Import Data

treatment<- read.csv("treatment.csv")
treatment

##      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-improved

2 Soal 1

Please work out in R by doing a chi-squared test on the treatment (X) and improvement (Y) columns in treatment.csv.

table(treatment$treatment, treatment$improvement)

##              
##               improved not-improved
##   not-treated       26           29
##   treated           35           15

chisq.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 = 0.03083

dari hasil diatas di simpulkan bahwa H0 ditolak, karena p-value ≤ 0.05.

3 Soal 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 1

df2 = (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 = 0.006632

Asumsi H0 merupakan variabelnya independen. Dari hasil di atas, karena p-value > alpha 0.05, H0 diterima. maka variable tersebut independent.

4 Soal 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)
n <- sum(zodiac)
expected_counts <- rep(n/length(zodiac), length(zodiac)) / n


chisq_result <- chisq.test(zodiac, p = expected_counts)


chisq_result

## 
##  Chi-squared test for given probabilities
## 
## data:  zodiac
## X-squared = 5.0938, df = 11, p-value = 0.9265

berdasarkan hasil diatas kita dapat hasilnya adalah 0.9265 dan H0 diterima artinya bahwa data zodiac tersebut berdistribusi secara merata.