ders2psikometri
Ebrar
2026-03-28
DERS ÖNCESİ SORU PRATİKLERİ
TIMMS 2015 uygulmasına ait Türkiye ve Amerika verilerini kullanarak
TRUSA.RDS R ortamına aktarın.
Eksik verileri kontrol edin.
Kitapçıktaki 35 maddenin toplamını hesaplayarak veri setine yeni bir sütun olarak ekyeyin.
Toplam puanın her iki ülkeye göre betimsel istatistiklerini hesaplayın.
Toplam puanın, Türkiye ve Abd örneklemlerinde farklılaşıp farklılaşmadığını t testi ile test edin.
Veri setinde %5, %10 ve %15 oranında eksik veriler oluşturun
Oluşturulan eksik veri setlerinde önce eksik verinin rastgele olup olmadığını test edin. Daah sonra liste bazında silme yöntemi ile eksk verileri temizleyin ve t testi uygulayın. e seçeneğinde ki t testi sonuçları ile karşılaştırın
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library(expss)## Warning: package 'expss' was built under R version 4.5.2## Zorunlu paket yükleniyor: maditr## Warning: package 'maditr' was built under R version 4.5.2##
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## smc- TRUSA.RDS R ortamına aktarın.
TRUSA <- readRDS("TRUSA.RDS")
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## M042302B M042302C M042100 M042202 M042240 M042093 M042271 M042268
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## M042159 M042164 M042167 M062208 M062208A M062208B M062208C M062208D
## 0 0 0 0 0 0 0 0
## M062153 M062111A M062111B M062237 M062314 M062074 M062183 M062202
## 0 0 0 0 0 0 0 0
## M062246 M062286 M062325 M062106 M062124 CNT
## 0 0 0 0 0 0- Kitapçıktaki 35 maddenin toplamını hesaplayarak veri setine yeni bir sütun olarak ekyeyin.
TRUSA$toplam_puan <- rowSums(TRUSA[, 3:35], na.rm = TRUE)
TRUSA## IDSTUD IDBOOK M042182 M042081 M042049 M042052 M042076 M042302A M042302B
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## 1148 1 1 USA 23
## 1149 1 1 USA 24
## 1150 0 1 USA 12
## 1151 1 0 USA 12- Toplam puanın her iki ülkeye göre betimsel istatistiklerini hesaplayın.
summary(TRUSA$toplam_puan)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 9.00 14.00 14.85 21.00 32.00TRUSA %>%
group_by(CNT) %>%
summarise(
n = sum(!is.na(toplam_puan)),
mean = mean(toplam_puan, na.rm = TRUE),
sd = sd(toplam_puan, na.rm = TRUE),
median = median(toplam_puan, na.rm = TRUE),
min = min(toplam_puan, na.rm = TRUE),
max = max(toplam_puan, na.rm = TRUE))## # A tibble: 2 × 7
## CNT n mean sd median min max
## <chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 TUR 435 12.6 7.07 11 2 30
## 2 USA 716 16.2 7.17 16 1 32- Toplam puanın, Türkiye ve Abd örneklemlerinde farklılaşıp farklılaşmadığını t testi ile test edin.
t_test_sonuc <- t.test(TRUSA$toplam_puan ~CNT, data= TRUSA )
print(t_test_sonuc)##
## Welch Two Sample t-test
##
## data: TRUSA$toplam_puan by CNT
## t = -8.3364, df = 926.52, p-value = 2.748e-16
## alternative hypothesis: true difference in means between group TUR and group USA is not equal to 0
## 95 percent confidence interval:
## -4.450106 -2.754107
## sample estimates:
## mean in group TUR mean in group USA
## 12.6046 16.2067- Veri setinde %5, %10 ve %15 oranında eksik veriler oluşturun (mvdalab paketi)
TRUSA_5 <- introNAs(TRUSA, percent = 5)
TRUSA_10 <- introNAs(TRUSA, percent = 10)
TRUSA_15 <- introNAs(TRUSA, percent = 10)
TRUSA_5 %>% is.na() %>% colSums()## IDSTUD IDBOOK M042182 M042081 M042049 M042052
## 48 63 50 57 60 66
## M042076 M042302A M042302B M042302C M042100 M042202
## 65 59 61 59 46 56
## M042240 M042093 M042271 M042268 M042159 M042164
## 68 58 71 58 64 44
## M042167 M062208 M062208A M062208B M062208C M062208D
## 59 56 43 48 57 55
## M062153 M062111A M062111B M062237 M062314 M062074
## 55 60 60 62 52 65
## M062183 M062202 M062246 M062286 M062325 M062106
## 61 55 55 60 57 66
## M062124 CNT toplam_puan
## 54 60 51TRUSA_10 %>% is.na() %>% colSums()## IDSTUD IDBOOK M042182 M042081 M042049 M042052
## 92 100 112 119 125 104
## M042076 M042302A M042302B M042302C M042100 M042202
## 116 108 120 126 86 137
## M042240 M042093 M042271 M042268 M042159 M042164
## 109 120 122 112 113 115
## M042167 M062208 M062208A M062208B M062208C M062208D
## 144 113 131 116 111 119
## M062153 M062111A M062111B M062237 M062314 M062074
## 109 126 126 119 108 126
## M062183 M062202 M062246 M062286 M062325 M062106
## 110 101 100 112 119 123
## M062124 CNT toplam_puan
## 125 101 114TRUSA_15 %>% is.na() %>% colSums()## IDSTUD IDBOOK M042182 M042081 M042049 M042052
## 103 129 105 110 123 108
## M042076 M042302A M042302B M042302C M042100 M042202
## 115 123 108 101 112 116
## M042240 M042093 M042271 M042268 M042159 M042164
## 91 120 121 120 129 106
## M042167 M062208 M062208A M062208B M062208C M062208D
## 117 104 100 117 100 124
## M062153 M062111A M062111B M062237 M062314 M062074
## 108 117 122 119 124 120
## M062183 M062202 M062246 M062286 M062325 M062106
## 106 120 107 125 129 127
## M062124 CNT toplam_puan
## 124 116 123- Oluşturulan eksik veri setlerinde önce eksik verinin rastgele olup olmadığını test edin. Daah sonra liste bazında silme yöntemi ile eksk verileri temizleyin ve t testi uygulayın. e seçeneğinde ki t testi sonuçları ile karşılaştırın
TRUSSA_5_lw <- na.omit(TRUSA_5)
TRUSSA_10_lw <- na.omit(TRUSA_10)
TRUSSA_15_lw <- na.omit(TRUSA_15)
#t_test_sonuc_g <- t.test(SUM ~CNT, #data = TRUSA_5_lw, var.equal =)library(stevemisc)## Warning: package 'stevemisc' was built under R version 4.5.3##
## Attaching package: 'stevemisc'## The following object is masked from 'package:lubridate':
##
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##
## tbl_dflibrary(knitr)
library(haven)## Warning: package 'haven' was built under R version 4.5.2##
## Attaching package: 'haven'## The following objects are masked from 'package:expss':
##
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## Attaching package: 'summarytools'## The following object is masked from 'package:tibble':
##
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## Attaching package: 'outliers'## The following object is masked from 'package:psych':
##
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## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
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## method from
## heightDetails.titleGrob ggplot2
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## Attaching package: 'sur'## The following object is masked from 'package:psych':
##
## skewlibrary(moments)## Warning: package 'moments' was built under R version 4.5.2library(corrplot)## Warning: package 'corrplot' was built under R version 4.5.2## corrplot 0.95 loadedlibrary(olsrr)## Warning: package 'olsrr' was built under R version 4.5.3##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversscreen <- read_sav("SCREEN.sav")
screen <- expss::drop_var_labs(screen)
head(screen) ## # A tibble: 6 × 8
## SUBNO TIMEDRS ATTDRUG ATTHOUSE INCOME EMPLMNT MSTATUS RACE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 8 27 5 1 2 1
## 2 2 3 7 20 6 0 2 1
## 3 3 0 8 23 3 0 2 1
## 4 4 13 9 28 8 1 2 1
## 5 5 15 7 24 1 1 2 1
## 6 6 3 8 25 4 0 2 1EKSİK VERİLERİN DÜZENLENMESİ
screen <- screen %>%
mutate(INCOME= ifelse(is.na(INCOME), mean(INCOME, na.rm= TRUE), INCOME)) %>%
na.omit()
summary(screen)## SUBNO TIMEDRS ATTDRUG ATTHOUSE
## Min. : 1.0 Min. : 0.000 Min. : 5.00 Min. : 2.00
## 1st Qu.:136.8 1st Qu.: 2.000 1st Qu.: 7.00 1st Qu.:21.00
## Median :313.5 Median : 4.000 Median : 8.00 Median :24.00
## Mean :317.3 Mean : 7.914 Mean : 7.69 Mean :23.54
## 3rd Qu.:483.2 3rd Qu.:10.000 3rd Qu.: 9.00 3rd Qu.:27.00
## Max. :758.0 Max. :81.000 Max. :10.00 Max. :35.00
## INCOME EMPLMNT MSTATUS RACE
## Min. : 1.000 Min. :0.000 Min. :1.00 Min. :1.000
## 1st Qu.: 3.000 1st Qu.:0.000 1st Qu.:2.00 1st Qu.:1.000
## Median : 4.000 Median :0.000 Median :2.00 Median :1.000
## Mean : 4.208 Mean :0.472 Mean :1.78 Mean :1.086
## 3rd Qu.: 6.000 3rd Qu.:1.000 3rd Qu.:2.00 3rd Qu.:1.000
## Max. :10.000 Max. :1.000 Max. :2.00 Max. :2.000race değişkeninin frekans tablosu
table(screen$RACE)##
## 1 2
## 424 40library(summarytools)
freq(screen$RACE,
round.digits = 2,report.nas = FALSE,
style = "rmarkdown")## setting plain.ascii to FALSE## ### Frequencies
## #### screen$RACE
## **Type:** Numeric
##
## | | Freq | % | % Cum. |
## |----------:|-----:|-------:|-------:|
## | **1** | 424 | 91.38 | 91.38 |
## | **2** | 40 | 8.62 | 100.00 |
## | **Total** | 464 | 100.00 | 100.00 |İkili kategorili değişkenlerden race değişkeninin kategorilere dağılımları incelendiğinde kategoriler arasında yaklaşık 10.1:1 (91/9) oranı olduğu görülmektedir. Bu oran oldukça yüksektir. Değişken araştırma için önemli değilse çıkarılabilir, aksi halde değişkenle ilgili sonuçlar yorumlanırken bu durum göz önüne alınmalıdır.
library(knitr)
freq(screen$MSTATUS, report.nas = FALSE) %>%
kable(format = 'markdown',
caption = "Frekans Tablosu", digits = 2)| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 1 | 102 | 21.98 | 21.98 | 21.98 | 21.98 |
| 2 | 362 | 78.02 | 100.00 | 78.02 | 100.00 |
| 0 | NA | NA | 0.00 | 100.00 | |
| Total | 464 | 100.00 | 100.00 | 100.00 | 100.00 |
İki kategorili değişkenlerden mstatus değişkeninin kategoriler dağımlıları incelendiğinde kategoriler arasında yaklaşık 3.5:1 (78/22) oranı olduğu görülmektedir. Bu oran kabul edilebilir bir orandır.
SÜREKLİ DEĞİŞKENLERDE UÇ DEĞERLER
Sürekli değişke ler için tek değişkenli uç değerleri belirlemenin bir yolu, değişkene ait bütün değerlerin ortalama 0, standart sapma 1 olacak şekilde standart değerlere (z puanlarına) dönüştürülmesidir. Tek değişkenli uç değerler çok büyük z puanlarına sahiptirler.
outliers paketinde scores() fonksiyonu ile z değerleri hesaplanabilir.
library(outliers)
z.scores <- screen %>%
select(2:5) %>%
scores(type = "z") %>%
round(2)
head(z.scores)## TIMEDRS ATTDRUG ATTHOUSE INCOME
## 1 -0.63 0.27 0.77 0.34
## 2 -0.45 -0.60 -0.79 0.76
## 3 -0.72 0.27 -0.12 -0.51
## 4 0.46 1.13 0.99 1.61
## 5 0.65 -0.60 0.10 -1.36
## 6 -0.45 0.27 0.33 -0.09summarytools paketinde descr() fonksiyonu ile z değerlerinin minumum ve maksimum değerleri incelenebilir.
summarytools::descr(z.scores,
stats = c("min", "max"),
transpose = TRUE,
heading = FALSE)##
## Min Max
## -------------- ------- ------
## ATTDRUG -2.33 2.00
## ATTHOUSE -4.80 2.56
## INCOME -1.36 2.46
## TIMEDRS -0.72 6.67timedrs değişkeni için z puanlarının maksimum değerin 4.0’ten büyük olduğu, atthouse değişkeni z puanlarının içinse minumum değerin 4.0’ ten küçük olduğu görülmektedir. Diğer değişkenler için değerler beklenen sınırlar içerisindedir.
İnteraktif Tablo Oluşturma
library(DT)## Warning: package 'DT' was built under R version 4.5.3DT::datatable(z.scores)Tek değişkenli uç değerleri saptamak için grafiksel yöntemlerden de yararlanılabilir ( Örneğin, histogramlar, kutu grafikleri, normal olasılık grafikleri gibi).
timedrs değişkeninin incelenmesi
ggplot(screen, aes(x= TIMEDRS)) +
geom_histogram(bins= 30L, fill = "skyblue")
grafik üzerinde ortalamanın gösterilmesi
library(ggpmisc)
ggplot(screen, aes(x = TIMEDRS)) + geom_histogram() +
geom_vline(xintercept = 7.914, color ="red",
linetype = "dashed") +
annotate("text", label = "Ort = 7.913", x=10, y=100, color = "black")## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
İnteraktif Grafik 2
library(plotly)
plot_ly(x = screen$TIMEDRS, type= "histogram", histnorm = "probability")timedrs değişkeninin mstatus değişkenine göre incelenmesi
ggplot(screen, aes(x= factor(MSTATUS),
y=TIMEDRS, fill = factor(MSTATUS)))+
geom_boxplot() +
theme_minimal()
attdrug değişkeninin incelenmesi
ggplot(screen) + aes(x = ATTDRUG) +
geom_histogram(bins = 6, fill ="skyblue") +
theme_minimal()
atthouse değişkeninin incelenmesi
ggplot(screen) +
aes(x= ATTHOUSE) +
geom_histogram(bins=10, fill= "darkgreen")
plot_ly(y= screen$ATTHOUSE, type = 'box')Veri setinde potansiyel tek değişkenli uç değerler tespit edildiğinde, önce uç değerin nedeni tespit edilmelidir. Veri grişinde hata varsa veya kayıp veri kodlanırken hata yapıldıysa düzeltilmelidir.
Bunun dışındaki nedenler için değişkenin dönüştürülmesinin uygun olup olmayacağına karar verilmelidir.
Dönüşümler hem dağılımların normalliğini geliştirir hemde tek değişkenli uç değerleri dağılımın merkezine çeker ve etkisini azaltır.
Dönüşüme karar verilirse çok değişkenli uç değerler incelenmeden dönüşüm yapılmamalıdır çünkü çok değişkenli uç değerlerin belirlenmesinde kullanılan istatistikler normal dağılım gerektirir.
UÇ DEĞERLERİN BELİRLENMESİ
Veri setinde timedrs ve atthouse uç değere sahip değişkenlerdir.
timedrs değişkeninin veri girişinde hata bulunmadığı görülmüş, uç değerlere sahip bireylerin veri setinde kalmasına karar verilmiştir.
atthouse değikeninde bulunan uç değerlerin evren için beklenen değerler mi yoksa veri girişinde hata mı olduğuna karar verilmelidir.
Her iki durum içinde 260. ve 296. satırda yer alan 2 birey veri setinden çıkarılmalıdır.
screen[c(260,298),]## # A tibble: 2 × 8
## SUBNO TIMEDRS ATTDRUG ATTHOUSE INCOME EMPLMNT MSTATUS RACE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 346 2 8 2 1 0 1 1
## 2 407 2 8 2 4 0 1 1screen2 <- screen[-c(260,298),]MAHALANOBİS UZAKLIĞI
Çok değişkenli uç değerleri belirlemenin bir yoludur. Z puanının çok boyutlu versiyonudur.Bir gözlemin, dağılımın kovaryansı verildiğinde, dağılımın ağırlık merkezinden uzaklığını ölçer.
Ki kare dağılımı gösterir ve ki kare dağılımı kullanılarak değerlendirilebilir. Mahalanobis uzaklığının gözlenme olasılığı 0.0001 veya daha küçükse gözlem uç değerdir.
Bu yöntem eşit aralık veya eşit oran düzeyinde ölçülen değişkenler için veya sürekli değişken olarak ele alınan sıralama ölçeğinde ölçülen değişkenler için geçerli olup sınıflama düzeyinde ölçülen değişkenler için geçerli değildir.
Mahalanobis UZaklığı Hesaplama
veri <- screen2[,1:5]
md <- mahalanobis(veri, center = colMeans(veri), cov = cov(veri))
head(md,20)## [1] 3.785517 4.541493 3.501077 7.281365 5.457240 2.896550 5.807898
## [8] 3.879478 4.751166 7.415405 10.602100 5.249121 6.073732 3.271885
## [15] 12.316463 4.440749 4.836160 6.362806 4.126524 10.797545alpha <- .001
cutoff <- (qchisq(p=1 - alpha, df= ncol(veri)))
cutoff## [1] 20.51501Mahalanobİs Uzaklığı değerleri ki kare ile değerlendirilir. 20.515 değerinden büyük değerler 0.001 alfa düzeyinde istatistiksel olarak anlamlı olarak değerlendirilir.
ucdegerler <- which(md > cutoff)
veri[ucdegerler, ]## # A tibble: 9 × 5
## SUBNO TIMEDRS ATTDRUG ATTHOUSE INCOME
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 48 60 7 24 1
## 2 235 60 10 29 4
## 3 276 57 9 24 2
## 4 291 52 8 19 1
## 5 330 58 7 29 4
## 6 370 57 8 23 4
## 7 398 75 9 33 9
## 8 502 56 8 19 3
## 9 548 81 8 24 9data_temiz <- veri[-ucdegerler, ]ÇOK DEĞİŞKENLİ NORMALLİK SAYILTISI
Çok değişkenli normallik sayıltısını test etmek için doğrudan bir test bulunmadığından, genellikle her bir değişken ayrı ayrı test edilir ve eğer her bir değişken normal dağılım gösteriyorsa çok değişkenli normal oldukları varsayılır.
Çok değişkenli normallik her bir değişkenin ve değişkenlerin bütün doğrusal kombinasyonlarının normal dağıldığı sayıltısıdır.
Normalliğin iki bileşeni vardır: Çarpıklık ve Basıklık
Bir değişkene ait dağılım normal olduğunda, değişkenin çarpıklık ve basıklık değerleri sıfıra eşittir.
Kural olarak eğer değişkenin çarpıklık ve basıklık değerleri -1.0 ile +1.0 arasındaysa, değişkenin normale oldukça yakın olduğu söylenebilir.
Sayıltının karşılanması durumunda analizin artıkları normal dağılır.
Çok değişkenli normallik sayıltısı farklı çok değişkenli istatistikler için farklı ele alınır.
library(sur)
attach(screen)
skew(screen$TIMEDRS)## [1] 3.234045skew((data_temiz$TIMEDRS))## [1] 2.35295ÖĞRENME GÜNLÜĞÜ
AŞAMA 2 Uç Değerlerin Saptanması -Tek Değişkenli (Univariate) Uç Değerler Standartlaştırılmış Z puanı + - 3,29’u aşan durumlar, büyük örneklemler için uç değer olarak kabul edilebilir.
-Çok Değişkenli (Multivariate) Uç Değerler İki veya daha fazla değişkenin alışılmadık kombinasyonuna sahip durumları saptamak için Mahalanobis uzaklığı (p< .001) hesaplanır.
- UÇ Değerlerin Etkisi Azaltılır Logaritmik dönüşümler gibi dönüşümler kullanılır.
AŞAMA 3 İSTATİSTİKSEL VARSAYıMLARIN TEST EDİLMESİ -Normallik Kontrolü ÇArpıklık ve Basıklık, incelenir. Histogram Grafikleri kullanılır.
_Doğrusallık Kontrolü Saçılım diyagramı incelenir.
Liste bazında silme işlemi veriyi çok büyük ölçüde küçülttüğü için kullanılması önerilmemektedir.