Are you a statistics master's student grappling with a challenging R programming assignment? Fear not! In this blog post, we'll delve into a complex statistical analysis question designed to push your R programming skills to the limit. Follow along as we break down the problem step by step, providing a thorough and insightful answer.

The Challenge: Comparative Analysis of Multiple Groups
Question: Comparative Analysis of Multiple Groups

You are given a dataset (data.csv) that contains the test scores of students from three different schools (School A, School B, and School C) in three different subjects (Mathematics, Physics, and Chemistry). The dataset has the following structure:

R
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# Sample Data
set.seed(123)
data <- data.frame(
School = rep(c("A", "B", "C"), each = 30),
Subject = rep(c("Math", "Physics", "Chemistry"), each = 30),
Score = round(rnorm(90, mean = 70, sd = 10), 2)
)
Your task is to perform a comprehensive statistical analysis to compare the average scores of students across the three schools for each subject. Specifically, answer the following questions:

Descriptive Statistics:

Compute summary statistics (mean, median, standard deviation, minimum, maximum) for each school and subject.
Visualize the distribution of scores using appropriate plots (e.g., boxplots, histograms).
Statistical Testing:

Conduct a one-way analysis of variance (ANOVA) to test if there are significant differences in scores among the three schools for each subject.
If ANOVA indicates significant differences, perform post-hoc tests (e.g., Tukey's HSD) to identify which pairs of schools differ significantly.
Effect Size:

Calculate effect size measures (e.g., eta-squared) to quantify the practical significance of observed differences.
Multivariate Analysis:

Explore potential interactions between schools and subjects using a two-way ANOVA.
Visualization:

Create visualizations (e.g., interaction plots) to illustrate any significant interactions.

# Set seed for reproducibility
set.seed(123)

# Generate sample data
data <- data.frame(
School = rep(c("A", "B", "C"), each = 30),
Subject = rep(c("Math", "Physics", "Chemistry"), each = 30),
Score = round(rnorm(90, mean = 70, sd = 10), 2)
)

# Load necessary libraries
library(tidyverse)
library(rstatix)
library(effsize)
library(multcomp)

# 1. Descriptive Statistics

# Summary statistics
summary_stats <- data %>%
group_by(School, Subject) %>%
summarise(
Mean = mean(Score),
Median = median(Score),
SD = sd(Score),
Min = min(Score),
Max = max(Score)
)

# Visualize distribution of scores
ggplot(data, aes(x = School, y = Score, fill = Subject)) +
geom_boxplot() +
labs(title = "Distribution of Scores by School and Subject",
x = "School", y = "Score") +
theme_minimal()

# 2. Statistical Testing

# One-way ANOVA for each subject
anova_results <- data %>%
anova_test(Score ~ School + Subject)

# Post-hoc tests using Tukey's HSD if ANOVA is significant
posthoc_results <- anova_results %>%
group_by(Subject) %>%
tukey_hsd(Score)

# 3. Effect Size

# Eta-squared for each subject
effect_size <- anova_results %>%
group_by(Subject) %>%
effect_size(Score)

# 4. Multivariate Analysis

# Two-way ANOVA
interaction_anova <- data %>%
anova_test(Score ~ School * Subject)

# 5. Visualization of Interactions

# Interaction plot
interaction_plot <- data %>%
ggplot(aes(x = School, y = Score, color = Subject)) +
geom_point(position = position_dodge(width = 0.5), size = 3) +
labs(title = "Interaction Plot of Scores by School and Subject",
x = "School", y = "Score") +
theme_minimal() +
facet_wrap(~Subject, scales = "free_y")

# Print results and plots
cat("1. Descriptive Statistics:\n")
print(summary_stats)

cat("\n2. Statistical Testing (ANOVA):\n")
print(anova_results)

cat("\nPost-hoc Tests (Tukey's HSD):\n")
print(posthoc_results)

cat("\n3. Effect Size (Eta-squared):\n")
print(effect_size)

cat("\n4. Multivariate Analysis (Two-way ANOVA):\n")
print(interaction_anova)

cat("\n5. Visualization of Interactions:\n")
print(interaction_plot)

Please note that the dataset is randomly generated, so your results may vary each time you run the code. Ensure you have the required libraries installed (tidyverse, rstatix, effsize, multcomp) before running the code.

Conclusion: Empowering You to Excel in Your R Homework
Whether you're facing a similar assignment or simply looking to enhance your statistical analysis skills in R, this blog post equips you with the tools and knowledge needed. By breaking down a challenging question and providing a thorough answer, we aim to help with your R homework but also gain a deeper understanding of statistical analysis techniques.

Remember, practice makes perfect, and with R programming, the journey to mastery is both challenging and rewarding. Happy coding!