6.1 Markdown

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/Admin/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

hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "Tutoring"],
     main = "Histogram of Tutoring Scores",
     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 Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

#For the Tutoring histogram, the data appears slightly negatively skewed. The kurtosis looks roughly bell-shaped, but it may be a bit flatter than a perfect normal curve.
#For the No Tutoring histogram, the data appears roughly symmetrical (close to normal), though there may be a slight negative skew due to a small left tail. The kurtosis looks like a normal bell-shape overall.
#Since the Tutoring group looked a bit skewed, we may need to use a Mann–Whitney U test.

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.
#We may need to use a Mann-Whitney U 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

#The data for Tutoring was normal (p > .05).
#The data for No Tutoring was normal (p > .05).
#After conducting all three normality tests, it is suggested that we continue with the 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

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.

#The Tutoring Group (M = 78.4, SD = 7.18) was significantly different from No Tutoring Group (M = 71.9, SD = 7.68), t(78) = -3.86, p < .001. The effect size was large (Cohen's d = -.86).