Statistical Optimization of Multi-Factor Adsorption Processes Using Factorial ANOVA

📄 Overview

This repository contains the complete supplementary materials for the methodology paper "Statistical Optimization of Multi-Factor Adsorption Processes Using Factorial ANOVA: A JASP-Based Methodology Demonstration" (Rababah, 2025).

The study demonstrates a comprehensive statistical framework for optimizing multi-factor adsorption processes using factorial analysis of variance (ANOVA), with emphasis on detecting and interpreting interaction effects that are unattainable through traditional one-factor-at-a-time (OFAT) approaches.

🎯 Key Contributions

Complete factorial ANOVA workflow using accessible open-source software (JASP)
Interaction effects analysis revealing that optimal dosage depends on adsorbent type
Simple effects decomposition showing differential dosage sensitivity across materials
Reproducible methodology with all data, code, and analysis files provided
Educational resource for researchers learning factorial experimental design

📊 Study Summary

Aspect	Details
Dataset	2,304 synthetic experiments (768 conditions × 3 replicates)
Adsorbents	Activated Carbon, Biochar, MOF, Zeolite
Factors	Adsorbent type, Dosage (4 levels), Contact time (4 levels), Initial concentration (4 levels), pH (3 levels)
Models	Langmuir isotherm, Pseudo-second-order kinetics
Variability	CV = 6.6–8.7% (realistic laboratory precision)
Analysis Software	JASP v0.18.3 (open-source)
Data Generation	Python 3.8+ with NumPy, Pandas, SciPy

🔬 Key Findings

Main Results

Analysis	F-statistic	p-value	Effect Size (η²)	Interpretation
One-way ANOVA (Adsorbent Type)	F(3,2300) = 34.8	p < .001	η² = .043	Significant differences among adsorbents
Two-way ANOVA (Adsorbent × Dosage)	F(9,2288) = 17.74	p < .001	η² = .042	Critical interaction effect
Three-way ANOVA (+ Contact Time)	F(27,2208) = 0.06	p = 1.000	η² < .001	No higher-order interaction

Descriptive Statistics by Adsorbent Type

Adsorbent	Mean qₑ (mg/g)	SD	Min	Max
MOF	47.26	59.16	0.199	300.0
Activated Carbon	41.87	50.63	0.153	239.0
Biochar	29.96	34.68	0.099	158.4
Zeolite	23.48	23.27	0.124	102.8

Simple Effects Analysis (Dosage Sensitivity)

Adsorbent	F-statistic	η²	95% CI	Interpretation
MOF	F(3,572) = 17.0	.380	[.321, .433]	Highest sensitivity
Activated Carbon	F(3,572) = 10.2	.366	[.306, .420]	High sensitivity
Biochar	F(3,572) = 6.46	.366	[.275, .391]	Moderate sensitivity
Zeolite	F(3,572) = 85.59	.310	[.249, .365]	Lower sensitivity

📈 Visualizations

Figure 1: Adsorbent Type × Dosage Interaction (Key Finding)

The non-parallel lines indicate a significant interaction effect: optimal dosage strategy depends on adsorbent type. MOF shows the steepest decline, indicating highest dosage sensitivity.

Figure 2: Distribution of Adsorption Capacity

Figure 3: Mean Adsorption Capacity (±SE)

Figure 4: Heatmap - Adsorbent × Dosage

Figure 5: Simple Effects - Dosage Sensitivity (η²)

All adsorbents show large effect sizes (η² > 0.14), but MOF and Activated Carbon demonstrate the highest dosage sensitivity.

📁 Repository Structure

Adsorption-Factorial-ANOVA/
│
├── 📄 README.md                          # This file
├── 📄 LICENSE                            # CC BY 4.0 License
├── 📄 CITATION.cff                       # Citation metadata
├── 📄 .gitignore                         # Git ignore rules
│
├── 📂 data/
│   ├── adsorption_dataset_full.csv       # Complete dataset (2,304 experiments)
│   └── DATA_DICTIONARY.md                # Variable descriptions and metadata
│
├── 📂 code/
│   ├── generate_adsorption_dataset.py    # Python script for data generation
│   ├── create_figures.py                 # Python script for figure generation
│   └── requirements.txt                  # Python dependencies
│
├── 📂 analysis/
│   ├── adsorption_JASP_analysis.jasp     # JASP analysis file (reproducible)
│   └── JASP_QUICKSTART_GUIDE.md          # Step-by-step JASP instructions
│
├── 📂 results/
│   └── figures/
│       ├── Figure1_interaction_plot.png  # Adsorbent × Dosage interaction
│       ├── Figure2_boxplots_by_adsorbent.png
│       ├── Figure3_bar_chart_means.png
│       ├── Figure4_heatmap_adsorbent_dosage.png
│       ├── Figure5_simple_effects_eta_squared.png
│       ├── Figure6_removal_efficiency_pH.png
│       ├── Figure7_kinetics_by_adsorbent.png
│       └── Figure8_violin_plot.png
│
└── 📂 docs/
    ├── DETAILED_QA_DATASET_GENERATION.md # Q&A about methodology
    └── GITHUB_SETTINGS.md                # Repository setup guide

🚀 Quick Start

Option 1: Reproduce the Analysis in JASP

Download JASP (free): https://jasp-stats.org/download/
Download the dataset: data/adsorption_dataset_full.csv
Follow the guide: analysis/JASP_QUICKSTART_GUIDE.md
Or open: analysis/adsorption_JASP_analysis.jasp directly

Option 2: Generate New Dataset

# Clone the repository
git clone https://github.com/Anfal-AR/Adsorption-Factorial-ANOVA.git
cd Adsorption-Factorial-ANOVA

# Install dependencies
pip install numpy pandas scipy matplotlib seaborn

# Generate dataset
python code/generate_adsorption_dataset.py

# Generate figures
python code/create_figures.py

Option 3: Adapt for Your Research

Modify adsorbent parameters in code/generate_adsorption_dataset.py
Adjust experimental conditions (dosages, times, concentrations)
Generate custom dataset for your specific system
Follow the same JASP workflow for analysis

📐 Methodology

Data Generation Framework

┌─────────────────────────────────────────────────────────┐
│  STEP 1: Define Parameters (Literature-Based)          │
│  • Adsorbent properties (qmax, KL, k2)                 │
│  • Experimental conditions (dosage, time, conc, pH)    │
└─────────────────────────────────────────────────────────┘
                        ↓
┌─────────────────────────────────────────────────────────┐
│  STEP 2: Solve Langmuir + Mass Balance                 │
│  • Iterative numerical root-finding (scipy.fsolve)     │
│  • Ensures physical consistency                        │
└─────────────────────────────────────────────────────────┘
                        ↓
┌─────────────────────────────────────────────────────────┐
│  STEP 3: Apply Modifying Factors                       │
│  • pH effects (0.75–1.0 multiplier)                    │
│  • Kinetic limitations (PSO model)                     │
│  • Dosage effects (aggregation at high dosages)        │
└─────────────────────────────────────────────────────────┘
                        ↓
┌─────────────────────────────────────────────────────────┐
│  STEP 4: Add Experimental Noise                        │
│  • Normal distribution with CV = 7–10%                 │
│  • Ensures realistic laboratory variability            │
└─────────────────────────────────────────────────────────┘

Statistical Analysis Workflow

Descriptive Statistics → Assumption Checking → One-way ANOVA
                                                    ↓
                                            Two-way ANOVA
                                                    ↓
                                    Significant Interaction?
                                          /           \
                                        Yes            No
                                         ↓              ↓
                              Simple Effects      Report Main
                                Analysis          Effects Only
                                         ↓
                              Three-way ANOVA
                              (if needed)

📖 Adsorption Models Used

Langmuir Isotherm

$$q_e = \frac{q_{max} \times K_L \times C_e}{1 + K_L \times C_e}$$

Where:

qₑ = equilibrium adsorption capacity (mg/g)
qₘₐₓ = maximum adsorption capacity (mg/g)
Kₗ = Langmuir constant (L/mg)
Cₑ = equilibrium concentration (mg/L)

Pseudo-Second-Order Kinetics

$$q_t = \frac{k_2 \times q_e^2 \times t}{1 + k_2 \times q_e \times t}$$

Where:

qₜ = adsorption capacity at time t (mg/g)
k₂ = rate constant (g/(mg·min))
t = contact time (min)

Adsorbent Parameters (Literature-Based)

Adsorbent	qₘₐₓ (mg/g)	Kₗ (L/mg)	k₂ (g/(mg·min))	Noise (CV)
Activated Carbon	250	0.15	0.0003	8%
Biochar	180	0.10	0.0002	10%
MOF	300	0.20	0.00035	7%
Zeolite	120	0.08	0.00025	9%

🔧 Dependencies

For Data Generation & Visualization (Python)

numpy>=1.20.0
pandas>=1.3.0
scipy>=1.7.0
matplotlib>=3.5.0
seaborn>=0.11.0

For Statistical Analysis

JASP v0.17+ (free, open-source): https://jasp-stats.org/

📚 Citation

If you use this dataset, methodology, or code in your research, please cite:

@article{rababah2025factorial,
  title={Statistical Optimization of Multi-Factor Adsorption Processes 
         Using Factorial ANOVA: A JASP-Based Methodology Demonstration},
  author={Rababah, Anfal},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.17563321},
  url={https://doi.org/10.5281/zenodo.17563321}
}

APA Format:

Rababah, A. (2025). Statistical optimization of multi-factor adsorption processes using factorial ANOVA: A JASP-based methodology demonstration. Zenodo. https://doi.org/10.5281/zenodo.17563321

🤝 Contributing

Contributions are welcome! Please feel free to:

🐛 Report bugs or issues
💡 Suggest improvements to the methodology
📝 Improve documentation
🔧 Add new features to the data generation script
🌍 Translate guides to other languages

📜 License

This work is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

You are free to:

Share — copy and redistribute the material
Adapt — remix, transform, and build upon the material

Under the following terms:

Attribution — You must give appropriate credit and indicate if changes were made

👤 Author

Anfal Rababah

📧 Email: Anfal0Rababah@gmail.com
🔬 ORCID: 0009-0003-7450-8907
🌐 Platform: SparkSkyTech Educational Platform

🙏 Acknowledgments

JASP Team for developing and maintaining the open-source JASP software
Scientific Community for establishing the theoretical foundations of adsorption models
Claude (Anthropic) for assistance with literature organization, technical writing refinement, and Python code development

Open Science • Reproducible Research • Accessible Statistics

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script		script
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README.md		README.md

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