Minoxidil Nanoemulsion Optimization

Factorial design, power simulation, ANOVA, and Tukey HSD

A reproducible R analysis of a 3 × 3 full-factorial experiment optimizing a minoxidil nanoemulsion formulation (Tamanu oil + minoxidil). Two factors are varied — surfactant mixture (Smix, Tween 80 : Span 80) ratio and oil:Smix ratio — and the response is flux (Jss), where higher is better.

⚠️ Note on data: the response data are simulated in silico (02_generate_data.R) to illustrate the full statistical workflow. The same pipeline accepts a real experimental CSV by replacing data/nanoemulsion_data.csv.

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The four analysis steps

Script	What it does
R/01_power_simulation.R	Sample-size "multiverse" simulation: how often does n = 3 detect a true +10-unit flux difference?
R/02_generate_data.R	Builds the 3 × 3 factorial design (27 runs) and simulates flux.
R/03_check_assumptions.R	Fits the ANOVA and validates residual normality (Shapiro-Wilk) + diagnostic plots.
R/04_anova_posthoc.R	Omnibus two-way ANOVA and Tukey HSD post-hoc comparisons + figures.

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Key results

1. Power simulation. With n = 3 replicates and σ = 8 lab noise, the design has >80% power to detect a ≥25-unit flux difference (minimum detectable difference at 80% power ≈ 24.6 units). The observed optimum (F6 vs. baseline) improved flux by ~33 units, corresponding to ~95% power — so n = 3 was adequate for the effect sizes actually seen. A full power curve is in output/power_curve.png.

2. ANOVA (omnibus). All terms are significant:

Source	Df	Sum Sq	F	p
Smix ratio	2	1327.8	264.9	< 0.001
Oil:Smix ratio	2	683.5	136.4	< 0.001
Smix × Oil:Smix	4	271.4	27.1	< 0.001
Residuals	18	45.1

3. Residual diagnostics. Shapiro-Wilk p = 0.66 → residuals are consistent with normality (assumption satisfied).

4. Tukey HSD. The interaction is driven by a synergy: formulation F6 (Smix 2:1 + oil:Smix 1:6) has the highest flux (≈ +33.6 units vs. baseline, p < 0.001), confirming the optimum is the 2:1 × 1:6 combination, not either factor alone.

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Reproduce the analysis

Dependencies (R ≥ 4.1): readr, dplyr, tidyr, ggplot2.

install.packages(c("readr", "dplyr", "tidyr", "ggplot2"))

Run everything (scripts locate the project root automatically):

Rscript R/00_run_all.R

Each script can also be run individually. Outputs are written to output/:

• power_simulation_results.csv
• power_curve.csv, power_curve.png (power vs. effect size)
• shapiro_test.csv
• anova_table.csv
• tukey_interaction.csv
• diagnostic_qq.png, diagnostic_resid_fitted.png
• boxplot_flux.png, interaction_plot.png

The original single-file script is retained for reference at Nanoemulsion_Optimization_Code_original.R.

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Repository structure

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├── R/
│   ├── 00_run_all.R           # master pipeline
│   ├── 01_power_simulation.R
│   ├── 02_generate_data.R
│   ├── 03_check_assumptions.R
│   └── 04_anova_posthoc.R
├── data/
│   └── nanoemulsion_data.csv  # generated 27-run factorial dataset
├── output/                    # generated tables and figures
├── Nanoemulsion_Optimization_Code_original.R
└── README.md

Author

Giang H. Le — pharmaceutical formulation research, minoxidil nanoemulsion optimization. This analysis accompanies a factorial ANOVA and Tukey HSD study of experimental formulation data.