Educational Performance Analysis

Project Overview

This project analyzes factors influencing student exam performance using nonparametric statistical methods. Based on the research paper "Simplifying Statistical Decision Making: A Research Scholar's Guide to Parametric and Non-Parametric Methods" by Pirani (2024) doi:10.56815/IJMRR.V3I3.2024/184-192 , we implement a comprehensive analysis following the CRISP-DM methodology.

Table of Contents

• Business Understanding
• Data Understanding
• Data Preparation
• Statistical Method Selection
• Modeling
• Evaluation
• Dependencies
• Installation
• Usage

Business Understanding

The goal is to identify key factors affecting student exam performance to help educators and administrators prioritize interventions and resource allocation.

Target Variable

• Exam_Score: Final exam performance

Features

Numeric Variables

• Hours_Studied: Study hours allocated
• Attendance: Class attendance percentage
• Sleep_Hours: Average daily sleep
• Previous_Scores: Prior assessment scores
• Tutoring_Sessions: Extra tutoring count
• Physical_Activity: Weekly physical activity hours

Categorical Variables

• Parental Involvement
• Access to Resources
• Motivation Level
• Family Income
• Extracurricular Activities
• School Type
• Gender
• And others...

Data Preparation

Outlier Treatment

• Used IQR method (1.5 × IQR rule)
• Implemented boxplot visualization
• Treated outliers by replacing with NA values

Missing Value Treatment

• Utilized KNN imputation (k=5)
• Visualized missing data patterns
• Handled both numeric and categorical variables

Statistical Method Selection

Normality Testing

1. Visual inspection:

   • Histograms with density plots
   • Q-Q plots

2. Statistical testing using Jarque-Bera test:

   • H0: Data follows normal distribution
   • H1: Data does not follow normal distribution
   • Results: p-values < 0.05 for most variables:
     • Hours_Studied: p = 0.003
     • Attendance: p = 0.001
     • Sleep_Hours: p = 0.002
     • Previous_Scores: p = 0.004
     • Exam_Score: p = 0.001
     • Only Physical_Activity showed p > 0.05 (p = 0.067)

Choice of Nonparametric Methods

Based on normality test results (p < 0.05), we rejected the null hypothesis of normality and selected nonparametric methods for analysis:

1. Spearman correlation instead of Pearson
2. Kruskal-Wallis test instead of ANOVA
3. Dunn's test for post-hoc analysis

Modeling

Implemented nonparametric methods:

1. Correlation Analysis:

   • Spearman correlation for numeric variables
   • Correlation matrix visualization

2. Categorical Analysis:

   • Kruskal-Wallis tests for variables with >2 groups
   • Dunn's test with Bonferroni correction for pairwise comparisons
   • Selection criteria: p < 0.05 for statistical significance

Key Findings

1. Strongest predictors of exam performance:

   • Attendance (ρ = 0.69)
   • Hours studied (ρ = 0.49)
   • Parental involvement (Kruskal-Wallis p < 0.001)

2. Moderate impact factors:

   • Previous scores (ρ = 0.19)
   • Family income (Kruskal-Wallis p < 0.001)
   • Access to resources (Kruskal-Wallis p < 0.001)

3. Non-significant factors:

   • Gender (Kruskal-Wallis p = 0.4548)
   • School type (Kruskal-Wallis p = 0.3271)

Dependencies

library(ggplot2)      # Visualization
library(gridExtra)    # Multiple plot arrangement
library(dplyr)        # Data manipulation
library(tidyr)        # Data reshaping
library(rstatix)      # Statistical tests
library(corrplot)     # Correlation visualization
library(tseries)      # Jarque-Bera test
library(VIM)          # KNN imputation

Installation

1. Clone this repository
2. Install R and RStudio
3. Install required packages:

install.packages(c("ggplot2", "gridExtra", "dplyr", "tidyr", 
                  "rstatix", "corrplot", "tseries", "VIM"))