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Paper Plane Flight Distance Analysis

A reproducible statistical analysis investigating the effect of paper plane size on flight distance.

Quick Summary

Research Question: Does paper plane size significantly affect flight distance?

Answer: Yes. Paper plane size explains 91.7% of variance in flight distance (F(14,135) = 106.09, p < 0.001, η² = 0.917).

Key Finding: Largest plane (13.18m) flew 18.6× farther than smallest plane (0.71m).

Reproduction Instructions

Follow these steps to reproduce the entire analysis from scratch.

Prerequisites

Required Software:

  • Python 3.8 or higher
  • pip package manager

Required Python Packages:

pandas>=1.5.0
numpy>=1.23.0
scipy>=1.9.0
matplotlib>=3.6.0
seaborn>=0.12.0

Step 1: Install Dependencies

cd "/Users/leo/Desktop/510 Project 2"
pip install pandas numpy scipy matplotlib seaborn

Or create a virtual environment (recommended):

python3 -m venv venv
source venv/bin/activate
pip install pandas numpy scipy matplotlib seaborn

Step 2: Verify Data Files

Ensure the following data files exist in the Data/ directory:

Data/
├── raw_flight_data.csv
└── processed_flights_data.csv

Data file format:

raw_flight_data.csv contains:

  • size_rank: Paper plane size (1-15)
  • width_cm: Paper width in cm
  • height_cm: Paper height in cm
  • area_cm2: Paper area in cm²
  • trial_number: Trial number (1-10)
  • distance_m: Flight distance in meters
  • timestamp: Recording time
  • notes: Trial notes

Step 3: Run Data Processing (Optional)

If you need to regenerate processed data from raw data:

cd Script
python3 data_processing.py

Expected output:

=== Data Processing Script ===
Input: ../Data/raw_flight_data.csv
Output: ../Data/processed_flights_data.csv

Step 1: Reading raw data...
Read 150 raw records

Step 2: Grouping by size...
Grouped into 15 sizes

Step 3: Calculating statistics...
  Size 1: 10 trials, mean = 13.18m
  Size 2: 10 trials, mean = 12.51m
  ...
  Size 15: 10 trials, mean = 0.71m

Processed 15 sizes

Step 4: Exporting processed data...
Data exported to: ../Data/processed_flights_data.csv

=== Processing Complete ===

Step 4: Run Statistical Analysis

Execute the complete statistical analysis:

cd Script
python3 statistical_analysis.py

Expected output:

================================================================================
PAPER PLANE FLIGHT DISTANCE ANALYSIS
================================================================================

1. DATA LOADING
--------------------------------------------------------------------------------
Loaded data from: ../Data/raw_flight_data.csv
Total observations: 150
Number of size groups: 15
Trials per size: 10

2. HYPOTHESES
--------------------------------------------------------------------------------
Null Hypothesis (H0):
  Paper plane size has no effect on flight distance.
  
Alternative Hypothesis (H1):
  Paper plane size affects flight distance.

Significance level: α = 0.05

3. DESCRIPTIVE STATISTICS
--------------------------------------------------------------------------------
[Summary table displayed]

4. ASSUMPTION CHECKING
--------------------------------------------------------------------------------
4.1 Normality Test (Shapiro-Wilk)
Result: 15/15 groups pass normality test (p > 0.05)

4.2 Homogeneity of Variance (Levene's Test)
Result: Unequal variances (p < 0.001)

5. ONE-WAY ANOVA
--------------------------------------------------------------------------------
F-statistic: 106.0873
p-value: 0.000000
Decision: REJECT null hypothesis (p < 0.05)

6. EFFECT SIZE
--------------------------------------------------------------------------------
Eta-squared (η²): 0.9167
Interpretation: large effect size

7. CORRELATION ANALYSIS
--------------------------------------------------------------------------------
Correlation coefficient (r): -0.9240
p-value: 0.000001

8. POST-HOC ANALYSIS
--------------------------------------------------------------------------------
[Pairwise comparison results]

9. CONFIDENCE INTERVALS
--------------------------------------------------------------------------------
[95% CIs for each size]

10. SUMMARY OF FINDINGS
================================================================================
Key Results:
  • ANOVA F-statistic: 106.0873
  • p-value: 0.000000
  • Effect size (η²): 0.9167 (large)
  • Correlation (r): -0.9240

Statistical Conclusion:
  Paper plane size has a SIGNIFICANT effect on flight distance.
  
================================================================================
ANALYSIS COMPLETE
================================================================================

Time to complete: ~5 seconds

Step 5: Generate Visualizations

Create all 10 figures for presentation and report:

cd Script
python3 create_visualizations.py

Expected output:

================================================================================
GENERATING VISUALIZATIONS FOR PRESENTATION
================================================================================
Loading data...
Loaded 150 observations

1. Creating bar chart: Mean distance by size...
   Saved: 01_mean_distance_by_size.png

2. Creating line plot: Distance trend with regression...
   Saved: 02_distance_trend.png

3. Creating scatter plot: Correlation analysis...
   Saved: 03_scatter_correlation.png

4. Creating box plot: Distribution by size...
   Saved: 04_boxplot_distribution.png

5. Creating error bar plot: Confidence intervals...
   Saved: 05_confidence_intervals.png

6. Creating variance comparison plot...
   Saved: 06_variance_comparison.png

7. Creating individual trials plot...
   Saved: 07_individual_trials.png

8. Creating effect size visualization...
   Saved: 08_effect_size.png

9. Creating pairwise comparison plot...
   Saved: 09_pairwise_comparisons.png

10. Creating size dimensions visualization...
   Saved: 10_size_dimensions.png

================================================================================
ALL VISUALIZATIONS SAVED TO: ../Figures/
================================================================================

Time to complete: ~10 seconds

Output location: All figures saved to Figures/ directory as high-resolution PNG files (300 DPI).

Step 6: Run Power Analysis (Optional)

To see the power analysis that justified sample size:

cd Script
python3 power_analysis_planner.py

Expected output:

=== Settings ===
alpha=0.050 (two-tailed), target power=0.80, CV=0.25
Number of sizes=15, planned n per group: n=10

=== Key Comparisons (Required n per group & Power at n=10) ===
Size 5 vs 6: means=(6.73,4.56), Δ=2.17m, n_req≈7, power@n=10≈0.93
Size 1 vs 6: means=(13.18,4.56), Δ=8.62m, n_req≈2, power@n=10≈1.00
Size 14 vs 15: means=(1.74,0.71), Δ=1.03m, n_req≈2, power@n=10≈1.00
Size 3 vs 4: means=(7.44,7.48), Δ=0.04m, n_req≈34126, power@n=10≈0.05

Project Structure

510 Project 2/
│
├── README.md
├── REPORT.md
│
├── Data/
│   ├── raw_flight_data.csv
│   └── processed_flights_data.csv
│
├── Script/
│   ├── data_collection.py
│   ├── data_processing.py
│   ├── statistical_analysis.py
│   ├── create_visualizations.py
│   └── power_analysis_planner.py
│
└── Figures/
    ├── 01_mean_distance_by_size.png
    ├── 02_distance_trend.png
    ├── 03_scatter_correlation.png
    ├── 04_boxplot_distribution.png
    ├── 05_confidence_intervals.png
    ├── 06_variance_comparison.png
    ├── 07_individual_trials.png
    ├── 08_effect_size.png
    ├── 09_pairwise_comparisons.png
    └── 10_size_dimensions.png

Experimental Design Summary

Variables

Independent Variable: Paper plane size

  • 15 levels (Size 1 = largest, Size 15 = smallest)
  • Size 1: US Letter (27.94 × 21.59 cm, area = 603.22 cm²)
  • Each size: width and height reduced by 1 cm
  • Size 15: 13.94 × 7.59 cm, area = 105.80 cm²

Dependent Variable: Flight distance (meters)

Sample Size

  • n = 10 trials per size
  • N = 150 total observations (15 sizes × 10 trials)
  • Justified by a priori power analysis (target power = 0.80, α = 0.05)

Controls

  • Same folding technique (standard dart fold)
  • Same throwing method
  • Indoor environment (minimal wind)
  • Consistent measurement procedure

Key Results

Statistical Test Results

Test Result Interpretation
One-way ANOVA F(14, 135) = 106.09, p < 0.001 Highly significant
Effect size η² = 0.917 Large effect (91.7% variance explained)
Correlation r = -0.924, p < 0.001 Strong negative correlation
R² 0.854 85.4% variance explained by linear trend

Descriptive Statistics

Size Mean (m) SD (m) 95% CI
1 (largest) 13.18 2.56 [11.35, 15.01]
5 6.73 1.31 [5.79, 7.67]
10 2.53 0.49 [2.18, 2.88]
15 (smallest) 0.71 0.14 [0.61, 0.81]

Conclusion

Paper plane size significantly affects flight distance

  • Null hypothesis rejected (p < 0.001)
  • Large effect size (η² = 0.917)
  • Strong linear relationship (r = -0.924)
  • Smaller planes fly significantly shorter distances

Troubleshooting

Common Issues and Solutions

Issue 1: ModuleNotFoundError

ModuleNotFoundError: No module named 'pandas'

Solution: Install missing packages

pip install pandas numpy scipy matplotlib seaborn

Issue 2: File not found error

FileNotFoundError: [Errno 2] No such file or directory: '../Data/raw_flight_data.csv'

Solution: Ensure you're running scripts from the Script/ directory

cd Script
python3 statistical_analysis.py

Issue 3: Permission denied when saving figures

PermissionError: [Errno 1] Operation not permitted

Solution: Check write permissions for Figures/ directory

chmod -R 755 ../Figures/

Issue 4: Matplotlib backend issues

ImportError: Cannot load backend 'TkAgg'

Solution: Set matplotlib to use a different backend

export MPLBACKEND=Agg
python3 create_visualizations.py

Verification Checklist

After running all scripts, verify the following outputs exist:

Data Files

  • Data/raw_flight_data.csv (150 rows)
  • Data/processed_flights_data.csv (15 rows)

Figures (all in Figures/ directory)

  • 01_mean_distance_by_size.png
  • 02_distance_trend.png
  • 03_scatter_correlation.png
  • 04_boxplot_distribution.png
  • 05_confidence_intervals.png
  • 06_variance_comparison.png
  • 07_individual_trials.png
  • 08_effect_size.png
  • 09_pairwise_comparisons.png
  • 10_size_dimensions.png

Expected Results

  • ANOVA F-statistic ≈ 106.09
  • p-value < 0.001
  • Effect size (η²) ≈ 0.917
  • Correlation (r) ≈ -0.924

Quick Start (One Command)

To run the complete analysis pipeline:

cd Script && \
python3 data_processing.py && \
python3 statistical_analysis.py && \
python3 create_visualizations.py && \
echo "Analysis complete! Check Figures/ for visualizations."

Total time: ~20 seconds

Documentation

Complete Report

See REPORT.md for the full written report including:

  • Background and motivation
  • Detailed methodology
  • Complete statistical results
  • Interpretation and discussion
  • Limitations
  • Conclusions and recommendations
  • References

Script Documentation

Each Python script includes:

  • Clear function definitions
  • Step-by-step output messages
  • Error handling
  • Structured output format

Data Description

Raw Data Format (raw_flight_data.csv)

Column Type Description Example
size_rank int Size identifier (1-15) 1
width_cm float Paper width (cm) 27.94
height_cm float Paper height (cm) 21.59
area_cm2 float Paper area (cm²) 603.22
trial_number int Trial number (1-10) 1
distance_m float Flight distance (m) 13.84
timestamp string Recording time 2025-11-01 22:57:44
notes string Trial notes Size 1 Trial 1

Processed Data Format (processed_flights_data.csv)

Column Type Description
size_rank int Size identifier (1-15)
width_cm float Paper width (cm)
height_cm float Paper height (cm)
area_cm2 float Paper area (cm²)
mean_m float Mean flight distance (m)
trial_1 to trial_10 float Individual trial distances (m)

System Requirements

Minimum Requirements

  • OS: Windows 10, macOS 10.14+, or Linux
  • Python: 3.8 or higher
  • RAM: 2 GB
  • Storage: 100 MB

Recommended Requirements

  • OS: macOS 11+, Windows 11, or Ubuntu 20.04+
  • Python: 3.10 or higher
  • RAM: 4 GB
  • Storage: 500 MB

Tested Environments

  • macOS 14.0 (Sonoma) with Python 3.11
  • Windows 11 with Python 3.10
  • Ubuntu 22.04 with Python 3.10

Citation

If you use this analysis or methodology, please cite:

[Your Name]. (2025). Effect of Paper Plane Size on Flight Distance: 
A Statistical Analysis. [Course Number], [University].

Contact

Author: [Your Name]
Email: [your.email@example.com]
Course: [Course Number]
Date: November 2, 2025

For questions about reproduction or methodology, please contact the author.

License

This project is provided for educational purposes. All code and documentation are available for academic use with proper attribution.

Last Updated: November 2, 2025

Reproducibility Status: Fully reproducible

Estimated Time to Reproduce: 20-30 minutes (including installation)

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