Step 1: Open the installed packages

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)

Step 3:Import and name dataset

dataset6.1 <- read_excel("/Users/sarva/Desktop/Dataset6.1.xlsx")

Step 4:Calculate descriptive statistics for each group

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

Group No Tutoring, Mean =71.9, Median = 71.4, SD = 7.6

Group Tutoring, Mean = 78.3, Median = 78.7, SD = 7.1

Step 5: Create Histograms for each group

hist(dataset6.1$Exam_Score[dataset6.1$Group =="Tutoring"],
     main =  "Tutored",
     xlab = "Score",
     ylab = "frequency",
     col = "black",
     border = "yellow",
     breaks = 10
     )

hist(dataset6.1$Exam_Score[dataset6.1$Group =="No Tutoring"],
     main =  "Not Tutored",
     xlab = "Score",
     ylab = "frequency",
     col = "black",
     border = "yellow",
     breaks = 10
)

# Group Tutored = Skewness= normal , Kurtosis = Mesokurtic # Group Not Tutored = Skewness= normal , Kurtosis = Mesokurtic

Step 6: Creating Box Plots for each group

ggboxplot(dataset6.1, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter")

# Data appears to have certain outliers on the no tutoring group, after visual inspection data appears to be normal. Step 7: Shapiro Wilk test of normality

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

Group Tutoring,p-Value < 0.5,

Group Not tutored, P-Value <0.5

Step 8 : Conducting inferrential 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

Step 10: Calculating the effect size

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 1 (M = 71.4. SD = 7.6) was significantly different from Group 2 (M = 78.7, SD = ), t(df) = x.xx, p = .xxx. The effect size was large (Cohen’s d = .0.86)