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/JT/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 Group 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 Group Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

For the Tutoring histogram, the data appears symmetrical distributed skewed. The kurtosis, appears bell-shaped (normal). For the no tutoring the histogram,appears symmetrical (normal). The kurtosis also appears bell-shaped (normal). We do not 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 dots past the whiskers. The No Tutoring boxplot appears normal. The dots are not very far away from the whiskers. Although some are very close to the whiskers.

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 clear we must continue with 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

If p < .05, (less than .05), this means the results were SIGNIFICANT.

cohens_d_result <- cohens_d(Exam_Score ~ Group, data = Dataset6.1, pooled_sd = TRUE) print(cohens_d_result) The effect size is -0.86 which means the difference between tutoring and no tutoring is large. No Tutoring (M = 71.9, SD = 7.68) was significantly different from Tutoring (M = 78.4, SD = 7.18), t(78) = -3.85, p = .000233 The effect size was large (Cohen’s d = -0.86).