🩺 mHealth Analysis Project

Overview

This project analyzes multi-subject wearable sensor data from mHealth logs to explore how physical activity levels affect acceleration and heart rate.
It includes data cleaning, feature engineering, statistical testing, and visual analytics.

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This project is not Open Sourced , No external PR's will be accepted

📁 Project Structure

Data-Analytics-Assignment-4/
│
├── CONTRIBUTORS.md        
├── LICENSE                              
├── README.md        
├── RULES.md
└── DA IA/                     
    ├── DA_IA_4.ipynb                    <-- Main Project
    ├── activity_summary_statistics.csv
    ├── mHealth_subject1.log
    ├── mHealth_subject10.log
    ├── mHealth_subject2.log
    ├── mHealth_subject3.log
    ├── mHealth_subject4.log
    ├── mHealth_subject5.log
    ├── mHealth_subject6.log
    ├── mHealth_subject7.log
    ├── mHealth_subject8.log
    ├── mHealth_subject9.log
    ├── pairwise_comparisons.csv
    └─── .ipynb_checkpoints
        ├── Untitled0-checkpoint.ipynb

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Usage Instructions

Step-by-Step Execution

1. Setup Phase (Blocks 1-2)

• Run Block 1 to import libraries
• Run Block 2 to load all subject data files
• Expected Output: Confirmation of loaded subjects and total samples

2. Data Exploration (Block 3)

• Displays basic dataset information
• Shows first few rows and data types
• Expected Output: DataFrame preview and statistics

3. Data Cleaning (Blocks 4-6)

• Block 4: Check and impute missing values
• Block 5: Remove null class (label 0)
• Block 6: Detect and remove outliers using IQR method
• Expected Output: Cleaning summary statistics

4. Feature Engineering (Block 7)

• Creates acceleration magnitude features
• Estimates heart rate from ECG
• Adds activity name labels
• Expected Output: New feature confirmation

5. Exploratory Data Analysis (Blocks 8-12)

• Block 8: Activity distribution visualization
• Block 9: Descriptive statistics by activity
• Block 10: Acceleration comparison plots
• Block 11: Heart rate visualization
• Block 12: Correlation analysis
• Expected Output: Multiple visualizations and statistics tables

6. Hypothesis Testing (Blocks 13-20)

• Block 13: Setup test data
• Blocks 14-16: T-tests (High vs Low intensity)
• Blocks 17-18: ANOVA (Multiple activities)
• Block 19: Post-hoc pairwise comparisons
• Block 20: ANOVA visualizations
• Expected Output: Statistical test results with p-values

7. Additional Analysis (Block 21)

• Inter-subject variation analysis
• Subject-activity heatmaps
• Expected Output: Variation metrics and heatmaps

8. Final Summary (Block 22)

• Comprehensive results summary
• Data export options
• Expected Output: Summary statistics and saved files

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🔬 Analysis Pipeline

1. Data Loading

Load 10 subject files → Combine into single DataFrame → Validate data integrity

2. Data Cleaning

Check missing values → Imputation (forward/backward fill) → Remove null class → Outlier detection (IQR method) → Remove outliers → Validate cleaned data

Outlier Detection Method:

• Uses Interquartile Range (IQR)
• Threshold: 3 × IQR
• Formula: [Q1 - 3×IQR, Q3 + 3×IQR]

3. Feature Engineering

Raw sensor data → Calculate magnitude:

• Chest acceleration magnitude = √(x² + y² + z²)
• Ankle acceleration magnitude = √(x² + y² + z²)
• Arm acceleration magnitude = √(x² + y² + z²)

ECG signals → Heart rate estimation:

• Group by subject and activity
• Calculate standard deviation
• Apply scaling factor: HR = 70 + (ECG_std × 30)

4. Statistical Analysis

A. Descriptive Statistics

• Mean, standard deviation, min, max for each activity
• Sample sizes and distributions
• Coefficient of variation across subjects

B. Inferential Statistics

• Independent T-tests for binary comparisons
• One-way ANOVA for multiple group comparisons
• Post-hoc pairwise tests with Bonferroni correction

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📈 Statistical Tests Explained

T-Test (Independent Samples)

Purpose: Compare means between two independent groups

Hypotheses:

• H₀ (Null): μ₁ = μ₂ (no difference in means)
• H₁ (Alternative): μ₁ ≠ μ₂ (means are different)

Test Statistic:

t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Interpretation:

• p < 0.05: Reject null hypothesis (significant difference)
• p ≥ 0.05: Fail to reject null hypothesis (no significant difference)

Effect Size (Cohen's d):

d = (μ₁ - μ₂) / σ_pooled

• |d| < 0.2: Small effect
• 0.2 ≤ |d| < 0.5: Medium effect
• |d| ≥ 0.5: Large effect

Our Application:

• Compare high-intensity (Jogging, Running) vs low-intensity (Sitting, Standing)
• Variables: chest acceleration magnitude, heart rate estimate

One-Way ANOVA

Purpose: Compare means across three or more groups

Hypotheses:

• H₀: μ₁ = μ₂ = μ₃ = ... = μₖ (all group means equal)
• H₁: At least one group mean differs

Test Statistic:

F = MS_between / MS_within

Interpretation:

• p < 0.05: At least one group differs significantly
• p ≥ 0.05: No significant differences between groups

Post-Hoc Tests:

• When ANOVA is significant, conduct pairwise comparisons
• Bonferroni Correction: α_adjusted = α / number_of_comparisons
• Controls for Type I error inflation in multiple comparisons

Our Application:

• Compare 5 activities: Walking, Jogging, Running, Sitting, Cycling
• Variables: chest acceleration magnitude, heart rate estimate

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Results Interpretation

Expected Findings

1. Acceleration Magnitude

High-Intensity Activities (Jogging, Running):

• Expected Mean: 12-20 m/s²
• Higher variability due to dynamic movements
• Significant difference from low-intensity activities

Low-Intensity Activities (Sitting, Standing):

• Expected Mean: 9-11 m/s² (close to gravity)
• Lower variability due to minimal movement
• Primarily captures gravitational acceleration

Statistical Significance:

• T-test p-value: Expected < 0.001 (highly significant)
• Cohen's d: Expected > 0.8 (large effect size)

2. Heart Rate Estimate

High-Intensity Activities:

• Expected Range: 100-140 bpm
• Reflects increased cardiovascular demand

Low-Intensity Activities:

• Expected Range: 65-80 bpm
• Near resting heart rate

Statistical Significance:

• T-test p-value: Expected < 0.01 (significant)
• Moderate to large effect size

3. ANOVA Results

Expected Pattern (Acceleration Magnitude):

Running > Jogging > Walking > Cycling > Sitting

F-statistic: Expected > 100 (very large) P-value: Expected < 0.0001 (extremely significant)

Post-Hoc Comparisons:

• Running vs Sitting: Highly significant (p < 0.001)
• Jogging vs Walking: Moderately significant (p < 0.05)
• Walking vs Sitting: Significant (p < 0.01)

Interpretation Guidelines

P-Value Interpretation

• *p < 0.001: Very strong evidence against H₀ ()
• p < 0.01: Strong evidence against H₀ ()
• *p < 0.05: Moderate evidence against H₀ ()
• p ≥ 0.05: Insufficient evidence to reject H₀ (ns)

Practical Significance

• Consider both statistical and practical significance
• Large sample sizes can yield significant p-values for trivial differences
• Always examine effect sizes and mean differences

Visualizations

• Box plots: Show distribution, median, quartiles, outliers
• Violin plots: Show full distribution shape
• Heatmaps: Reveal patterns across subjects and activities

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