test

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

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(effectsize)
library(effsize)
Dataset6_1 <- read_excel("C:/Users/user/Downloads/Dataset6.1.xlsx")
Dataset6_1 %>%
  group_by(Group) %>%
  summarise(
    Mean = mean(Exam_Score, na.rm = TRUE),
    Median = median(Exam_Score, na.rm = TRUE),
    SD = sd(Exam_Score, na.rm = TRUE),
    N = n()
  )

## # A tibble: 2 × 5
##   Group        Mean Median    SD     N
##   <chr>       <dbl>  <dbl> <dbl> <int>
## 1 No Tutoring  71.9   71.5  7.68    40
## 2 Tutoring     78.4   78.7  7.18    40

# Histograms for Each Group
hist(Dataset6_1$Exam_Score[Dataset6_1$Group == "Tutoring"],
     main = "Histogram of Tutoring",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(Dataset6_1$Exam_Score[Dataset6_1$Group == "No Tutoring"],
     main = "Histogram of No  Tutoring",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

#For the tutoring histogram, the data appears symmetrical (normal). The kurtosis also appears bell-shaped (normal).
#For the No tutoring histogram, the data appears symmetrical (normal). The kurtosis also appears bell-shaped (normal).
#Boxplots 
ggboxplot(Dataset6_1, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter")

#The tutoring  boxplot appears normal. There are no dots past the whiskers.

#The No tutoring boxplot appears abnormal. There are several dots past the whiskers. Although some are very close to the whiskers, some are arguably far away.

shapiro.test(Dataset6_1$Exam_Score[Dataset6_1$Group == "Tutoring"])

## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6_1$Exam_Score[Dataset6_1$Group == "Tutoring"]
## W = 0.98859, p-value = 0.953

shapiro.test(Dataset6_1$Exam_Score[Dataset6_1$Group == "No Tutoring"])

## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6_1$Exam_Score[Dataset6_1$Group == "No Tutoring"]
## W = 0.98791, p-value = 0.9398

#The data for Tutoring was abnormal (p < .05).
#The data for No Tutoring was abnormal (p < .05).

#Mann-Whitney U
wilcox.test(Exam_Score ~ Group, data = Dataset6_1)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Exam_Score by Group
## W = 419, p-value = 0.0001833
## alternative hypothesis: true location shift is not equal to 0

# p-value less than .05, the results were SIGNIFICANT
#Independent T-Test
t.test(Exam_Score ~ Group, data = Dataset6_1, var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  Exam_Score by Group
## t = -3.8593, df = 78, p-value = 0.000233
## alternative hypothesis: true difference in means between group No Tutoring and group Tutoring is not equal to 0
## 95 percent confidence interval:
##  -9.724543 -3.105845
## sample estimates:
## mean in group No Tutoring    mean in group Tutoring 
##                  71.94627                  78.36147

# p < .05, this means the results were SIGNIFICANT
#Cohen's D for Independent T-Test
cohens_d_result <- cohens_d(Exam_Score ~ Group, data = Dataset6_1, pooled_sd = TRUE)
print(cohens_d_result)

## Cohen's d |         95% CI
## --------------------------
## -0.86     | [-1.32, -0.40]
## 
## - Estimated using pooled SD.

#Group no tutoring  (M = 71.95, SD = 7.63) was significantly  different from Group tutoring (M = 778.36, SD = 7.18), t(78) =3.86, p = .001. 
#The effect size was large (Cohen's d = 0.86).