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library(tidyverse)

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library(lsr)

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library(car) # Levene testi için

## Warning: package 'car' was built under R version 4.5.3

## Zorunlu paket yükleniyor: carData

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## 
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set.seed(1923) # Tekrarlanabilirlik için

deney_grubu <- rnorm(50, mean = 45, sd = 8) # İlaç verilen grup (deney grubu)
kontrol_grubu <- rnorm(50, mean = 52, sd = 8) # Plasebo verilan grup (kontrol grubu)

fare_verisi <- data.frame(grup = rep(c("Deney","Kontrol"),each = 50)) %>%
  mutate(süre = round(c(deney_grubu, kontrol_grubu),2))

fare_istatistik <- fare_verisi %>% 
  group_by(grup) %>% 
  summarise(N= n(),
            Ortalama = mean(süre),
            Standart_Sapma = sd(süre)
            )

print(fare_istatistik)

## # A tibble: 2 × 4
##   grup        N Ortalama Standart_Sapma
##   <chr>   <int>    <dbl>          <dbl>
## 1 Deney      50     45.2           8.81
## 2 Kontrol    50     52.4           7.92

# Her grup için ayrı ayrı normallik testi
fare_verisi %>% 
  group_by(grup) %>% 
  summarise(shapiro_p =
              shapiro.test(süre)$p.value)

## # A tibble: 2 × 2
##   grup    shapiro_p
##   <chr>       <dbl>
## 1 Deney       0.409
## 2 Kontrol     0.810

leveneTest(süre ~ grup, data = fare_verisi)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.5295 0.4686
##       98

# Bağımsız örneklem t-testi
sonuc <- t.test(süre ~ grup, data = fare_verisi, var.equal 
                = TRUE)
print(sonuc)

## 
##  Two Sample t-test
## 
## data:  süre by grup
## t = -4.3425, df = 98, p-value = 3.436e-05
## alternative hypothesis: true difference in means between group Deney and group Kontrol is not equal to 0
## 95 percent confidence interval:
##  -10.601619  -3.951181
## sample estimates:
##   mean in group Deney mean in group Kontrol 
##               45.1614               52.4378

# Cohen's d (Etki Büyüklüğü)
cohensD(süre ~ grup, data = fare_verisi)

## [1] 0.8685009

Yapılan bağımsız örneklem t-testi sonucunda, ilaç verilen deney grubunun labirent tamamlama sürelerinin (X = 45.16, SS = 8.81), kontrol grubuna göre (X = 52.44, SS = 7.92) anlamlı derecede daha düşük (hızlı) olduğu saptanmıştır, t(98) = -4.34, p.001, d = 0.87 . Bu bulgu, İlaç-X’in mekansal bellek ve öğrenme üzerinde geliştirici bir etkisi olduğunu desteklemektedir.