library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(skimr)
library(naniar)
## 
## Attaching package: 'naniar'
## The following object is masked from 'package:skimr':
## 
##     n_complete
library(ggplot2)
library(MissMech)
library(mice) 
## 
## Attaching package: 'mice'
## The following object is masked from 'package:stats':
## 
##     filter
## The following objects are masked from 'package:base':
## 
##     cbind, rbind

Bu ödevde, TIMSS 2015 uygulamasına ait bir kitapçığın Türkiye ve Amerika verilerini kullanacaksınız.

  1. Veri seti adı: “TRUSA.RDS”. Bu veri setini R ortamına aktarınız.

  2. Veri setinde eksik veri olup olmadığını kontrol ediniz.

  3. Kitapçıktaki 35 maddenin toplamını hesaplayarak veri setine yeni bir sütun olarak ekleyiniz.

  4. Toplam puanın her iki ülkeye göre betimsel istatistiklerini hesaplayınız.

  5. Toplam puanın, Türkiye ve ABD örneklemlerinde farklılaşıp farklılaşmadığını t testi ile test ediniz.

  6. Veri setinde %5, %10 ve %15 oranında eksik veriler oluşturunuz.

  7. Oluşturulan eksik veri setlerinde önce eksik verinin rasgele olup olmadığını test ediniz. Ardından, liste bazında silme yöntemiyle eksik verileri temizleyerek e seçeneğinde gerçekleştirdiğiniz t testini tekrarlayınız. Tam veri ile elde edilen sonuçlarla karşılaştırınız.

  8. f seçeneğinde oluşturulan veri setlerindeki eksik verileri, belirlediğiniz bir kayıp veri atama yöntemiyle doldurunuz. Daha sonra, e seçeneğinde gerçekleştirdiğiniz t testini tekrar ediniz ve tam veri ile elde edilen sonuçlarla karşılaştırınız.

  9. Eksik veri oranının uygulanan yöntemlerin performansına etkisini açıklayınız.

İyi kodlamalar:)

#a) Veri seti adı: "TRUSA.RDS". Bu veri setini R ortamına aktarınız.
TRUSA <- readRDS("D:/OLC_733/OLC_733/TRUSA.RDS")
TRUSA
##       IDSTUD IDBOOK M042182 M042081 M042049 M042052 M042076 M042302A M042302B
## 1      10210      1       0       0       1       1       1        0        0
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## 1114        1       1       1       1       1       1       1       0       1
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## 1138        1       1       1       1       0       1       0       1       0
## 1139        1       0       0       1       0       1       0       0       0
## 1140        1       1       0       1       0       0       0       0       0
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## 1150        0       0       1       0       0       0       0       0       1
## 1151        0       0       1       0       0       0       0       0       0
##      M062106 M062124 CNT
## 1          0       0 TUR
## 2          0       0 TUR
## 3          0       0 TUR
## 4          0       1 TUR
## 5          0       0 TUR
## 6          1       1 TUR
## 7          1       1 TUR
## 8          1       1 TUR
## 9          1       1 TUR
## 10         0       0 TUR
## 11         0       0 TUR
## 12         1       0 TUR
## 13         0       0 TUR
## 14         1       1 TUR
## 15         1       1 TUR
## 16         1       1 TUR
## 17         1       1 TUR
## 18         1       1 TUR
## 19         1       0 TUR
## 20         0       1 TUR
## 21         0       1 TUR
## 22         0       0 TUR
## 23         0       0 TUR
## 24         0       1 TUR
## 25         1       1 TUR
## 26         1       1 TUR
## 27         1       1 TUR
## 28         0       1 TUR
## 29         0       1 TUR
## 30         0       0 TUR
## 31         0       0 TUR
## 32         1       1 TUR
## 33         0       1 TUR
## 34         0       1 TUR
## 35         0       0 TUR
## 36         0       0 TUR
## 37         0       1 TUR
## 38         0       0 TUR
## 39         1       0 TUR
## 40         1       0 TUR
## 41         1       1 TUR
## 42         1       1 TUR
## 43         1       1 TUR
## 44         0       0 TUR
## 45         0       1 TUR
## 46         1       0 TUR
## 47         1       1 TUR
## 48         0       0 TUR
## 49         0       0 TUR
## 50         0       0 TUR
## 51         0       0 TUR
## 52         1       1 TUR
## 53         0       1 TUR
## 54         1       0 TUR
## 55         1       0 TUR
## 56         1       0 TUR
## 57         0       0 TUR
## 58         1       1 TUR
## 59         1       0 TUR
## 60         0       0 TUR
## 61         0       0 TUR
## 62         0       0 TUR
## 63         1       1 TUR
## 64         1       1 TUR
## 65         0       1 TUR
## 66         1       1 TUR
## 67         1       0 TUR
## 68         1       0 TUR
## 69         0       0 TUR
## 70         0       0 TUR
## 71         0       0 TUR
## 72         1       1 TUR
## 73         0       0 TUR
## 74         0       0 TUR
## 75         1       1 TUR
## 76         1       1 TUR
## 77         1       0 TUR
## 78         1       1 TUR
## 79         0       0 TUR
## 80         1       0 TUR
## 81         1       0 TUR
## 82         0       1 TUR
## 83         1       0 TUR
## 84         0       0 TUR
## 85         0       1 TUR
## 86         0       0 TUR
## 87         0       1 TUR
## 88         1       1 TUR
## 89         1       1 TUR
## 90         0       1 TUR
## 91         0       0 TUR
## 92         0       0 TUR
## 93         1       0 TUR
## 94         0       1 TUR
## 95         0       1 TUR
## 96         0       0 TUR
## 97         0       1 TUR
## 98         0       0 TUR
## 99         1       1 TUR
## 100        0       0 TUR
## 101        0       0 TUR
## 102        0       0 TUR
## 103        1       0 TUR
## 104        1       1 TUR
## 105        1       1 TUR
## 106        0       0 TUR
## 107        1       1 TUR
## 108        0       0 TUR
## 109        0       0 TUR
## 110        0       0 TUR
## 111        0       0 TUR
## 112        0       1 TUR
## 113        0       0 TUR
## 114        0       0 TUR
## 115        1       0 TUR
## 116        0       0 TUR
## 117        1       0 TUR
## 118        0       0 TUR
## 119        0       0 TUR
## 120        0       0 TUR
## 121        1       1 TUR
## 122        0       0 TUR
## 123        1       1 TUR
## 124        0       1 TUR
## 125        0       0 TUR
## 126        1       0 TUR
## 127        1       1 TUR
## 128        1       0 TUR
## 129        1       1 TUR
## 130        1       0 TUR
## 131        1       1 TUR
## 132        1       0 TUR
## 133        0       0 TUR
## 134        1       1 TUR
## 135        0       0 TUR
## 136        0       0 TUR
## 137        1       1 TUR
## 138        0       0 TUR
## 139        0       0 TUR
## 140        1       1 TUR
## 141        1       1 TUR
## 142        1       0 TUR
## 143        1       0 TUR
## 144        1       0 TUR
## 145        0       0 TUR
## 146        0       0 TUR
## 147        1       1 TUR
## 148        0       0 TUR
## 149        1       1 TUR
## 150        0       0 TUR
## 151        1       0 TUR
## 152        0       0 TUR
## 153        1       0 TUR
## 154        1       0 TUR
## 155        1       1 TUR
## 156        0       0 TUR
## 157        1       0 TUR
## 158        1       0 TUR
## 159        0       0 TUR
## 160        1       0 TUR
## 161        1       0 TUR
## 162        0       0 TUR
## 163        0       0 TUR
## 164        0       0 TUR
## 165        0       0 TUR
## 166        0       0 TUR
## 167        0       0 TUR
## 168        0       1 TUR
## 169        0       0 TUR
## 170        0       1 TUR
## 171        1       1 TUR
## 172        1       1 TUR
## 173        1       0 TUR
## 174        1       1 TUR
## 175        0       0 TUR
## 176        1       0 TUR
## 177        0       0 TUR
## 178        0       0 TUR
## 179        0       1 TUR
## 180        1       0 TUR
## 181        0       0 TUR
## 182        1       1 TUR
## 183        1       1 TUR
## 184        1       1 TUR
## 185        1       0 TUR
## 186        0       1 TUR
## 187        0       0 TUR
## 188        1       1 TUR
## 189        0       1 TUR
## 190        0       0 TUR
## 191        1       1 TUR
## 192        0       0 TUR
## 193        0       1 TUR
## 194        0       0 TUR
## 195        1       1 TUR
## 196        0       0 TUR
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## 1037       0       1 USA
## 1038       0       1 USA
## 1039       1       1 USA
## 1040       1       0 USA
## 1041       1       0 USA
## 1042       1       0 USA
## 1043       1       0 USA
## 1044       1       1 USA
## 1045       0       0 USA
## 1046       0       0 USA
## 1047       1       1 USA
## 1048       0       0 USA
## 1049       1       1 USA
## 1050       0       1 USA
## 1051       0       0 USA
## 1052       0       1 USA
## 1053       0       0 USA
## 1054       0       0 USA
## 1055       1       1 USA
## 1056       0       1 USA
## 1057       1       1 USA
## 1058       0       0 USA
## 1059       0       1 USA
## 1060       0       1 USA
## 1061       1       0 USA
## 1062       0       0 USA
## 1063       0       0 USA
## 1064       1       1 USA
## 1065       0       0 USA
## 1066       0       0 USA
## 1067       0       0 USA
## 1068       1       0 USA
## 1069       0       0 USA
## 1070       0       1 USA
## 1071       0       0 USA
## 1072       0       0 USA
## 1073       1       0 USA
## 1074       1       0 USA
## 1075       1       1 USA
## 1076       0       1 USA
## 1077       0       0 USA
## 1078       0       0 USA
## 1079       0       0 USA
## 1080       0       0 USA
## 1081       0       1 USA
## 1082       0       0 USA
## 1083       0       0 USA
## 1084       0       0 USA
## 1085       0       1 USA
## 1086       1       1 USA
## 1087       0       0 USA
## 1088       0       0 USA
## 1089       1       0 USA
## 1090       0       0 USA
## 1091       0       0 USA
## 1092       0       0 USA
## 1093       0       0 USA
## 1094       1       1 USA
## 1095       0       0 USA
## 1096       0       0 USA
## 1097       0       0 USA
## 1098       1       1 USA
## 1099       0       0 USA
## 1100       0       1 USA
## 1101       0       1 USA
## 1102       0       0 USA
## 1103       0       0 USA
## 1104       0       0 USA
## 1105       1       1 USA
## 1106       0       0 USA
## 1107       0       0 USA
## 1108       0       1 USA
## 1109       0       0 USA
## 1110       1       1 USA
## 1111       1       1 USA
## 1112       1       1 USA
## 1113       1       1 USA
## 1114       1       1 USA
## 1115       0       0 USA
## 1116       0       0 USA
## 1117       0       0 USA
## 1118       0       1 USA
## 1119       1       1 USA
## 1120       1       0 USA
## 1121       1       0 USA
## 1122       0       0 USA
## 1123       1       1 USA
## 1124       0       1 USA
## 1125       1       0 USA
## 1126       0       0 USA
## 1127       0       0 USA
## 1128       0       0 USA
## 1129       0       0 USA
## 1130       1       0 USA
## 1131       0       0 USA
## 1132       0       0 USA
## 1133       1       1 USA
## 1134       0       0 USA
## 1135       0       0 USA
## 1136       1       1 USA
## 1137       0       1 USA
## 1138       0       0 USA
## 1139       0       1 USA
## 1140       1       1 USA
## 1141       1       1 USA
## 1142       0       0 USA
## 1143       1       0 USA
## 1144       0       1 USA
## 1145       0       0 USA
## 1146       1       1 USA
## 1147       0       1 USA
## 1148       1       1 USA
## 1149       1       1 USA
## 1150       0       1 USA
## 1151       1       0 USA
#b) Veri setinde eksik veri olup olmadığını kontrol ediniz.
any(is.na(TRUSA))
## [1] FALSE
#c) Kitapçıktaki 35 maddenin toplamını hesaplayarak veri setine yeni bir sütun olarak ekleyiniz.

TRUSA <- TRUSA %>%
  mutate(Toplam_puan= rowSums(select(.,starts_with("M0")),na.rm = TRUE))
#d) Toplam puanın her iki ülkeye göre betimsel istatistiklerini hesaplayınız.
 TRUSA %>% 
filter(CNT %in% c("TUR","USA")) %>% 
        group_by(CNT) %>% 
          skim(Toplam_puan)
Data summary
Name Piped data
Number of rows 1151
Number of columns 39
_______________________
Column type frequency:
numeric 1
________________________
Group variables CNT

Variable type: numeric

skim_variable CNT n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
Toplam_puan TUR 0 1 13.45 7.57 2 7 11 19.00 32 ▇▆▃▃▂
Toplam_puan USA 0 1 17.05 7.53 1 11 17 22.25 34 ▃▇▇▆▃
#e) Toplam puanın, Türkiye ve ABD örneklemlerinde farklılaşıp farklılaşmadığını t testi ile test ediniz.

Tt_TRUSA <- TRUSA %>% 
  filter(CNT %in% c("TUR","USA"))

ttest <- t.test(Toplam_puan ~ CNT, data = Tt_TRUSA, var.equal = TRUE)

print(ttest)
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.8348, df = 1149, p-value = 1.064e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.493049 -2.693382
## sample estimates:
## mean in group TUR mean in group USA 
##          13.45287          17.04609
# TUR grubu ile ABD grubu arasındaki gerçek ortalama farkı 0'a eşit değildir
#f) Veri setinde %5, %10 ve %15 oranında eksik veriler oluşturunuz.

set.seed(123)  # Rastgelelik için aynı sonuçları almak adına seed kullanılır

# Fonksiyon: Belirtilen oranda eksik veri ekler
eksik_veri_ekle <- function(veri, oran) {
  veri_kopya <- veri  # Orijinal veri setini korumak için kopyasını al
  n <- nrow(veri_kopya) * ncol(veri_kopya)  # Toplam hücre sayısı
  eksik_sayisi <- round(n * oran)  # Eksik olacak hücre sayısını hesapla
  
  # Satır ve sütun indekslerini rastgele seç
  satir_index <- sample(1:nrow(veri_kopya), eksik_sayisi, replace = TRUE)
  sutun_index <- sample(1:ncol(veri_kopya), eksik_sayisi, replace = TRUE)
  
  # Seçilen satır ve sütunlarda eksik veri oluştur
  for (i in 1:eksik_sayisi) {
    veri_kopya[satir_index[i], sutun_index[i]] <- NA
  }
  
  return(veri_kopya)
}

# %5, %10 ve %15 eksik veri içeren veri setlerini oluştur
veri_5 <- eksik_veri_ekle(TRUSA, 0.05)
veri_10 <- eksik_veri_ekle(TRUSA, 0.10)
veri_15 <- eksik_veri_ekle(TRUSA, 0.15)

# Eksik verilerin durumunu kontrol etmek için:
print(colSums(is.na(veri_5)))  # %5 eksik veri içeren veri setindeki eksik değerler
##      IDSTUD      IDBOOK     M042182     M042081     M042049     M042052 
##          82          57          47          58          40          44 
##     M042076    M042302A    M042302B    M042302C     M042100     M042202 
##          59          47          55          64          49          56 
##     M042240     M042093     M042271     M042268     M042159     M042164 
##          56          66          50          65          62          62 
##     M042167     M062208    M062208A    M062208B    M062208C    M062208D 
##          51          65          58          51          59          60 
##     M062153    M062111A    M062111B     M062237     M062314     M062074 
##          52          61          49          51          48          58 
##     M062183     M062202     M062246     M062286     M062325     M062106 
##          53          63          49          67          61          57 
##     M062124         CNT Toplam_puan 
##          54          50          56
print(colSums(is.na(veri_10))) # %10 eksik veri içeren veri setindeki eksik değerler
##      IDSTUD      IDBOOK     M042182     M042081     M042049     M042052 
##         101         113         116         112         109         109 
##     M042076    M042302A    M042302B    M042302C     M042100     M042202 
##         122         107         103          99         109         100 
##     M042240     M042093     M042271     M042268     M042159     M042164 
##         104         118         107         107          96         125 
##     M042167     M062208    M062208A    M062208B    M062208C    M062208D 
##         110         108          97         121         111         111 
##     M062153    M062111A    M062111B     M062237     M062314     M062074 
##         117         108         120         114         112         112 
##     M062183     M062202     M062246     M062286     M062325     M062106 
##         105         115          99         102          99         105 
##     M062124         CNT Toplam_puan 
##         108         109         117
print(colSums(is.na(veri_15))) # %15 eksik veri içeren veri setindeki eksik değerler
##      IDSTUD      IDBOOK     M042182     M042081     M042049     M042052 
##         154         141         157         169         179         167 
##     M042076    M042302A    M042302B    M042302C     M042100     M042202 
##         154         173         147         176         146         163 
##     M042240     M042093     M042271     M042268     M042159     M042164 
##         159         163         174         177         151         161 
##     M042167     M062208    M062208A    M062208B    M062208C    M062208D 
##         153         157         157         152         179         154 
##     M062153    M062111A    M062111B     M062237     M062314     M062074 
##         153         167         163         150         155         148 
##     M062183     M062202     M062246     M062286     M062325     M062106 
##         159         140         166         168         145         166 
##     M062124         CNT Toplam_puan 
##         158         171         153
#g) Oluşturulan eksik veri setlerinde önce eksik verinin rasgele olup olmadığını test ediniz. Ardından, liste bazında silme yöntemiyle eksik verileri temizleyerek e seçeneğinde gerçekleştirdiğiniz t testini tekrarlayınız. Tam veri ile elde edilen sonuçlarla karşılaştırınız.


# SADECE SAYISAL VE EKSİK VERİ İÇEREN SÜTUNLARI SEÇİLMESİ
veri_5_num <- veri_5 %>%
  select(where(is.numeric)) %>%
  select(where(~ any(is.na(.)) & !all(is.na(.))))  
veri_10_num <- veri_10 %>%
  select(where(is.numeric)) %>%
  select(where(~ any(is.na(.)) & !all(is.na(.))))

veri_15_num <- veri_15 %>%
  select(where(is.numeric)) %>%
  select(where(~ any(is.na(.)) & !all(is.na(.))))

mcar_test(data=veri_5_num[,c(3:35)])
## Warning in norm::prelim.norm(data): NAs introduced by coercion to integer range
## # A tibble: 1 × 4
##   statistic    df p.value missing.patterns
##       <dbl> <dbl>   <dbl>            <int>
## 1     1297. 15662       1              516
mcar_test(data=veri_10_num[,c(3:35)])
## Warning in norm::prelim.norm(data): NAs introduced by coercion to integer range
## # A tibble: 1 × 4
##   statistic    df p.value missing.patterns
##       <dbl> <dbl>   <dbl>            <int>
## 1     3404. 28121       1              956
mcar_test(data=veri_15_num[,c(3:35)])
## Warning in norm::prelim.norm(data): NAs introduced by coercion to integer range
## # A tibble: 1 × 4
##   statistic    df p.value missing.patterns
##       <dbl> <dbl>   <dbl>            <int>
## 1     6191. 31536       1             1115
# Eksik verileri içeren satırları temizleme (Liste Bazında Silme)
veri_5_clean <- na.omit(veri_5)
veri_10_clean <- na.omit(veri_10)
veri_15_clean <- na.omit(veri_15)




# %5 Eksik Veri İçin t-Testi
t_test_5 <- t.test(Toplam_puan ~ CNT, data = veri_5_clean, var.equal = TRUE)

# %10 Eksik Veri İçin t-Testi
t_test_10 <- t.test(Toplam_puan ~ CNT, data = veri_10_clean, var.equal = TRUE)

# %15 Eksik Veri İçin t-Testi
#t_test_15 <- t.test(Toplam_puan ~ CNT, data = veri_15_clean, var.equal = TRUE)

# Tam Veri İçin t-Testi
t_test_tam <- t.test(Toplam_puan ~ CNT, data = TRUSA, var.equal = TRUE)

# Sonuçları Karşılaştırma
list(
  "Tam Veri t-Testi" = t_test_tam,
  "%5 Eksik Veri t-Testi" = t_test_5,
  "%10 Eksik Veri t-Testi" = t_test_10
)
## $`Tam Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.8348, df = 1149, p-value = 1.064e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.493049 -2.693382
## sample estimates:
## mean in group TUR mean in group USA 
##          13.45287          17.04609 
## 
## 
## $`%5 Eksik Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -3.2496, df = 150, p-value = 0.001426
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -6.856304 -1.671232
## sample estimates:
## mean in group TUR mean in group USA 
##          13.61667          17.88043 
## 
## 
## $`%10 Eksik Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -2.5343, df = 24, p-value = 0.0182
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -11.158975  -1.141679
## sample estimates:
## mean in group TUR mean in group USA 
##          10.55556          16.70588
#h) f seçeneğinde oluşturulan veri setlerindeki eksik verileri, belirlediğiniz bir kayıp veri atama yöntemiyle doldurunuz. Daha sonra, e seçeneğinde gerçekleştirdiğiniz t testini tekrar ediniz ve tam veri ile elde edilen sonuçlarla karşılaştırınız.


set.seed(123)  # Rastgelelik için seed ayarla

# Eksik veri ekleme fonksiyonunu kullanarak eksik verili setler oluşturduk
veri_5 <- eksik_veri_ekle(TRUSA, 0.05)
veri_10 <- eksik_veri_ekle(TRUSA, 0.10)
veri_15 <- eksik_veri_ekle(TRUSA, 0.15)

#  Eksik verileri Multiple Imputation ile doldurma
impute_5 <- mice(veri_5, m = 5, method = "pmm", maxit = 10, seed = 123)
## 
##  iter imp variable
##   1   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
## Warning: Number of logged events: 125
impute_10 <- mice(veri_10, m = 5, method = "pmm", maxit = 10, seed = 123)
## 
##  iter imp variable
##   1   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
## Warning: Number of logged events: 66
impute_15 <- mice(veri_15, m = 5, method = "pmm", maxit = 10, seed = 123)
## 
##  iter imp variable
##   1   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   1   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   2   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   3   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   4   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   5   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   6   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   7   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   8   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   9   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   1  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   2  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   3  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   4  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
##   10   5  IDSTUD  M042182  M042081  M042049  M042052  M042076  M042302A  M042302B  M042302C  M042100  M042202  M042240  M042093  M042271  M042268  M042159  M042164  M042167  M062208  M062208A  M062208B  M062208C  M062208D  M062153  M062111A  M062111B  M062237  M062314  M062074  M062183  M062202  M062246  M062286  M062325  M062106  M062124  Toplam_puan
## Warning: Number of logged events: 6
# Tamamlanan veri setlerini oluştur
veri_5_t <- complete(impute_5)
veri_10_t <- complete(impute_10)
veri_15_t <- complete(impute_15)


# Orijinal tam veri ile eksik verisi doldurulmuş setleri karşılaştırmak için t testini uygula

# %5 Eksik Veri İçin t-Testi
t_test_5 <- t.test(Toplam_puan ~ CNT, data = veri_5_t, var.equal = TRUE)

# %10 Eksik Veri İçin t-Testi
t_test_10 <- t.test(Toplam_puan ~ CNT, data = veri_10_t, var.equal = TRUE)

# %15 Eksik Veri İçin t-Testi
t_test_15 <- t.test(Toplam_puan ~ CNT, data = veri_15_t, var.equal = TRUE)

# Tam Veri İçin t-Testi
t_test_tam <- t.test(Toplam_puan ~ CNT, data = TRUSA, var.equal = TRUE)

# Sonuçları Karşılaştırma
list(
  "Tam Veri t-Testi" = t_test_tam,
  "%5 Eksik Veri t-Testi" = t_test_5,
  "%10 Eksik Veri t-Testi" = t_test_10,
  "%15 Eksik Veri t-Testi" = t_test_15
)
## $`Tam Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.8348, df = 1149, p-value = 1.064e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.493049 -2.693382
## sample estimates:
## mean in group TUR mean in group USA 
##          13.45287          17.04609 
## 
## 
## $`%5 Eksik Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.5954, df = 1099, p-value = 6.54e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.459271 -2.628331
## sample estimates:
## mean in group TUR mean in group USA 
##          13.38571          16.92952 
## 
## 
## $`%10 Eksik Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.5056, df = 1040, p-value = 1.31e-13
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.549583 -2.663754
## sample estimates:
## mean in group TUR mean in group USA 
##          13.41176          17.01843 
## 
## 
## $`%15 Eksik Veri t-Testi`
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -6.7788, df = 978, p-value = 2.092e-11
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.392021 -2.420011
## sample estimates:
## mean in group TUR mean in group USA 
##          13.67598          17.08199
# Sonuçları Yazdır
cat("Tam Veri T-Testi Sonuçları:\n")
## Tam Veri T-Testi Sonuçları:
print(t_test_tam)
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.8348, df = 1149, p-value = 1.064e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.493049 -2.693382
## sample estimates:
## mean in group TUR mean in group USA 
##          13.45287          17.04609
cat("\n%5 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:\n")
## 
## %5 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:
print(t_test_5)
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.5954, df = 1099, p-value = 6.54e-14
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.459271 -2.628331
## sample estimates:
## mean in group TUR mean in group USA 
##          13.38571          16.92952
cat("\n%10 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:\n")
## 
## %10 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:
print(t_test_10)
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -7.5056, df = 1040, p-value = 1.31e-13
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.549583 -2.663754
## sample estimates:
## mean in group TUR mean in group USA 
##          13.41176          17.01843
cat("\n%15 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:\n")
## 
## %15 Eksik Veri ile Doldurulmuş Setin T-Testi Sonuçları:
print(t_test_15)
## 
##  Two Sample t-test
## 
## data:  Toplam_puan by CNT
## t = -6.7788, df = 978, p-value = 2.092e-11
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
##  -4.392021 -2.420011
## sample estimates:
## mean in group TUR mean in group USA 
##          13.67598          17.08199

#i) Eksik veri oranının uygulanan yöntemlerin performansına etkisini açıklayınız. * t Değeri Küçülmesi

Çoklu veri atama yöntemi ile eksik veri oranı arttıkça t değeri azaldığı gözlenmiştir. Bu, iki ülke arasındaki farkın daha az belirgin hale geldiğini gösteriyor. Örneğin: Tam veri için t = -7.8348 %15 eksik veri için t = -6.7788 Eksik veri, değişkenler arasındaki farkı tespit etme gücünü düşürüyor.

*p-Değeri Artması

p değeri eksik veri oranına bağlı olarak arttığı görülmektedir. Tam veri için p = 1.064e-14, %15 eksik veri için p = 2.092e-11 *Anlamlılık düzeyi hala oldukça güçlü olsa da, eksik veri oranı arttıkça testin anlamlılığı azaldığı söylenebilir.

*Güven Aralığı Genişlemesi

Eksik veri oranı arttıkça %95 güven aralıkları genişlediği gözlenmiştir. Tam veri: (-4.493, -2.693) *%15 eksik veri: (-4.392, -2.420)