Exam Scores Difference between Tutoring and Non Tutoring Groups

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)

1. Data Source

Dataset6.1 <- read_excel("/Users/alexiaprudencio/Desktop/Applied Analytics 1/Assingment 6/Dataset6.1.xlsx")

2. 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

3. Histograms for Each Group

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

hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "No Tutoring"],
     main = "Histogram of No Tutoring Group Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightyellow",
     border = "darkgoldenrod1",
     breaks = 10)

The data on the Tutoring Group Scores appears normally distributed. The data looks symmetrical with most data in the middle. The data also appear to have a proper bell curve. The data on the No Tutoring Group Scores appears symetrical and normaly distributed as well. The kurtosis also appears bell-shaped (normal). We may need to use a Independent t-test.

4. Boxplots for Each Group

ggboxplot(Dataset6.1, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter")

The Tutoring Group boxplot appears normal. There are no dots past the whiskers; it follows a normal distribution. The No Tutoring Group boxplot also appears normal with most the data points within the reach of the whiskers. There are some outside, but does not disrupt the normality of the data. We may need to use a Independent t-test.

5. 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

The data for the Tutoring Group is normal, p-value = 0.953 > .05. The data for the No Tutoring Group is also normal, p-value = 0.9398 > .05. Since both p-values pass the Shapiro-Wilk Test of Normality. We need to use the Independent t-test to compare the exam scores between the two groups.

6. Conduct Inferential Test - 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

The p-value = 0.000233 < .05, this means the results were significant, which means we can calculate the Effect Size to see how big the difference is.

7. Calculation of the Effect Size - Cohen’s D

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 size of the effect, the difference between the group averages is ± 0.80 to 1.29 = large

8. Report the Results No Tutoring Group (M=71.95,SD=7.68) was significantly different from Tutoring Group (M=78.36,SD=7.18), t(78)=−3.86,p=.0002. The effect size was large (Cohen’s d=−0.86).