Research Scenario A

Read the libraries

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)

Import Dataset

Dataset6.1 <- read_excel("/Users/komakechivan/Downloads/Dataset6.1.xlsx")

Descriptive Statistics

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

Normality Check - Histograms

hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "Tutoring"], 
     main="Tutoring Group", col="lightblue")

hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "No Tutoring"], 
     main="No Tutoring Group", col="lightgreen")

Normality Check - Boxplots

ggboxplot(Dataset6.1, x = "Group", y = "Exam_Score", color = "Group")

Shapiro-Wilk Test

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

Conduct Independent T-Test (Assuming Normality)

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

Effect Size (Cohen’s d)

cohens_d(Exam_Score ~ Group, data = Dataset6.1, pooled_sd = TRUE)

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

Interpretation

Students who participated in Tutoring (M = 78.36, SD = 7.18) scored significantly higher on their final exams than students who received No Tutoring (M = 71.95, SD = 7.68), \(t(78) = -3.86, p < .001\). The effect size was large (Cohen’s \(d = 0.86\)).