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)

# Import dataset
data <- read_excel("C:/Users/Admin/Downloads/Dataset6.1.xlsx")

# Check Data
head(data)

## # A tibble: 6 × 2
##   Group    Exam_Score
##   <chr>         <dbl>
## 1 Tutoring       73.5
## 2 Tutoring       76.2
## 3 Tutoring       90.5
## 4 Tutoring       78.6
## 5 Tutoring       79.0
## 6 Tutoring       91.7

str(data)

## tibble [80 × 2] (S3: tbl_df/tbl/data.frame)
##  $ Group     : chr [1:80] "Tutoring" "Tutoring" "Tutoring" "Tutoring" ...
##  $ Exam_Score: num [1:80] 73.5 76.2 90.5 78.6 79 ...

library(dplyr)

# Calculate Descriptive Statistics for Each Group
data %>%
  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

#  Create Histograms for Each Group
hist(data$Exam_Score[data$Group=="Tutoring"],
     main = "Histogram of Tutoring Scores",
     xlab = "Exam Score",
     ylab = "Frequency",
     col = "Lightblue",
     border = "Black",
     breaks = 10)

hist(data$Exam_Score[data$Group=="No Tutoring"],
     main = "Histogram of No Tutoring Scores",
     xlab = "Exam Score",
     ylab = "Frequency",
     col = "lightgreen",
     border = "Black",
     breaks = 10)

# Boxplots 
ggboxplot(data,
          x = "Group",
          y = "Exam_Score",
          color = "Group",
          add = "jitter")

The Tutoring boxplot appears normal. There are no dots past the whiskers. The No Tutoring boxplot appears mostly normal. Although there are a few points near the whiskers, there are no extreme outliers. We may proceed with the Independent t-test.

Shapiro-Wilk Test of Normality

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

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

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

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

Both test are normal will use independent t-test

Independent T-Test

t.test(Exam_Score ~ Group, data = data, 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

cohens_d(Exam_Score ~ Group, data = data)

Interpretation

Students in the Tutoring group (M = 78.36, SD = 7.18) scored significantly higher than students in the No Tutoring group (M = 71.94, SD = 7.68), t(78) = −3.86, p < .001. The effect size was large (Cohen’s d = 0.86).

RQ-1

Ismail Khan Mohammed

2026-02-18

Shapiro-Wilk Test of Normality

Independent T-Test

Interpretation