Research Scenario 6.1

Peer Tutoring Program

Research Question

Do students who participate in a peer tutoring program have different final exam scores compared to students who do not participate?

Hypotheses

Null Hypothesis (H₀):
There is no difference in final exam scores between students who participated in tutoring and those who did not.

Alternative Hypothesis (H₁):
There is a difference in final exam scores between students who participated in tutoring and those who did not.

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Install Required Packages

install.packages(“readxl”) install.packages(“ggpubr”) install.packages(“dplyr”) install.packages(“effectsize”) install.packages(“effsize”)

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Open 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)

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Import Dataset

Dataset6_1<- read_excel('/Users/sharathnallaganti/Desktop/3rd sem/applied analytics/Dataset6.1.xlsx')

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Descriptive Statistics

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

Students in the Tutoring group had a mean score of 78.36 (SD = 7.18).
Students in the No Tutoring group had a mean score of 71.95 (SD = 7.68).

This suggests that students who participated in tutoring performed better on average.

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Histograms (Check Normality)

hist(Dataset6_1$Exam_Score[Dataset6_1$Group == "Tutoring"],
     main = "Histogram of Tutoring Group",
     xlab = "Exam Score",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(Dataset6_1$Exam_Score[Dataset6_1$Group == "No Tutoring"],
     main = "Histogram of No Tutoring Group",
     xlab = "Exam Score",
     col = "lightgreen",
     border = "black",
     breaks = 10)

Both histograms appear approximately symmetrical and bell-shaped, suggesting normal distributions.

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Boxplots

ggboxplot(Dataset6_1, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter")

Interpretation

There were no extreme outliers far from the whiskers.
The distributions appear reasonably normal.

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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

Tutoring group: p = 0.953 (> .05)
No Tutoring group: p = 0.940 (> .05)

Since both p-values are greater than .05, the data are normally distributed.

Therefore, we proceed with the Independent Samples t-test.

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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

t(78) = -3.86
p = 0.000233
95% CI [-9.72, -3.11]

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Effect Size (Cohen’s d)

cohens_d(Exam_Score ~ Group, data = Dataset6_1, pooled_sd = TRUE)

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

Cohen’s d = 0.86 (Large effect)

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Final Statistical Conclusion

Students in the Tutoring group (M = 78.36, SD = 7.18) scored significantly higher than students in the No Tutoring group (M = 71.95, SD = 7.68),
t(78) = -3.86, p < .001.

The effect size was large (Cohen’s d = 0.86).

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Final Interpretation

There is strong statistical evidence that the peer tutoring program improves final exam performance.

The difference between groups was not only statistically significant but also practically meaningful, with a large effect size.