assignment 6.1

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)

fourarms<-read_excel("D:/Vedant Work/SLU/Spring Sem (Jan to May 2026)/Applied Analytics/Assignment 6/Assignment 6.1/fourarms.xlsx")

fourarms%>%
  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

hist(fourarms$Exam_Score[fourarms$Group=="Tutoring"],
    main="Historgram of Tutored student scores",
    xlab="Exam Score",
    ylab="Frequency",
    col="lightblue",
    border="black",
    breaks=10)

hist(fourarms$Exam_Score[fourarms$Group=="No Tutoring"],
     main="Histogram of not tutored student scores",
     xlab="Exam Score",
     ylab="Frequency",
     col="lightgreen",
     border="black",
     breaks=10)

ggboxplot(fourarms, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter",
          title = "Boxplot of Exam Scores by Group")

Step 7: Conduct Independent T-Test

t_test_result <- t.test(Exam_Score ~ Group, 
                        data = fourarms, 
                        var.equal = TRUE)  # assumes equal variances

t_test_result

## 
##  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

Step 8: Calculate Effect Size (Cohen’s D) for Independent T-Test Only run if t-test was significant (p < 0.05)

cohens_d_result <- cohens_d(Exam_Score ~ Group, 
                            data = fourarms, 
                            pooled_sd = TRUE)

Print the Cohen’s d result

print(cohens_d_result)

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

Students who did not attend tutoring (Nottutored; M = 71.95, SD = 7.XX) were significantly different from students who attended tutoring (Tutored; M = 78.36, SD = 7.XX) in exam scores, t(78) = −3.86, p < .001. The effect size was large (Cohen’s d = 0.86).