title	Lord Of The Probability and Statistics
emoji	💍
colorFrom	blue
colorTo	red
sdk	docker
pinned	false

Prob Lab 🧙‍♂️📊

“One Distribution to rule them all, One Interval to find them, One Test to bring them all and in the data bind them.”

Prob Lab is an interactive educational platform for exploring probability theory, statistical inference, and hypothesis testing through dynamic simulation. Built with Shiny for Python and Plotly, optimized for both desktop and mobile, and containerized with Docker.

🗺️ The Realms of Analysis (Modules)

Prob Lab consists of three deeply interactive modules designed to correct common statistical misconceptions through real-time sampling and visualization.

🏹 1. CI Explorer (The Quest for the True Parameter)

Visualize the mechanics of confidence intervals and the Central Limit Theorem. Watch how intervals behave under different population distributions and methodologies.

• Key Features:
  • 6 Probability Distributions: Normal, Uniform, Exponential, Log-normal, Poisson, and Binomial.
  • Multiple Formulas: Estimate Mean, Median, Variance, Percentiles, and Proportions.
  • Robust CI Methods: Classical (t, z), rigorous exact methods for proportions (Wald, Wilson, Clopper-Pearson), and Bootstrap (percentile, B=500) for non-parametric statistics.
  • Live Visualizations: Track the proportion of intervals successfully catching the true parameter (like capturing the Ring) dynamically as samples grow.

👁️ 2. p-value Explorer (Piercing the Shadows)

Simulate hypothesis testing repeatedly to watch the accumulation of p-values and understand Type I/Type II errors under the hood.

• Key Features:
  • Interactive Testing: One-sample, Two-sample (Independent), and Paired tests ($t$-test and $z$-test).
  • Outlier Injection: Vulnerability testing! Easily inject outliers via a customized slider to see how parametric tests randomly break and lose power (like the unpredictable influence of a corrupted variable).
  • Complete Control: Dial your True $\mu$, Null $\mu_0$, Sample Size, and $\alpha$ to immediately see the Null vs. Alternative distribution overlaps.

⚔️ 3. Power Explorer (Gathering the Forces)

Master A/B testing design. Calculate and understand the complex relationship between Effect Size (Cohen's $d$), Sample Size ($n$), Significance level ($\alpha$), and Statistical Power ($1-\beta$). Is your sample army large enough to detect the signal?

• Key Features:
  • "Solve For" Architecture: Lock any three parameters and the system dynamically root-finds the fourth (e.g., solve for required $n$ to achieve 80% power).
  • Smart Grouping: Seamlessly groups Sample Sizes ($n_1$ and $n_2$) specifically for independent two-sample tests.
  • Power Curves: A dynamic curve updates in real-time, mapping exactly where your current experimental design sits on the power trajectory.
  • Preset Scenarios: Pre-loaded settings for generic A/B Tests, Clinical Trials, and Psychology Studies.

📜 The Magic Flow (Architecture)

graph TD
    User([User Input]) -->|Shiny Reactive UI| Server[Shiny Python Server]
    
    subgraph Computation Layer
        Server --> Numpy[NumPy Vectorized Sampling]
        Server --> SciPy[SciPy Stats Distributions / Root-finding]
        Server --> Stat[Compute Statistics: Means, CI, p-values]
    end
    
    subgraph Render Engine
        Stat --> Plotly[Plotly Go Charts]
        Plotly --> HTML[Responsive UI Elements]
        HTML --> Shiny[Reactive Shiny Output]
    end
    
    Shiny -->|WebSocket Updates| Dashboard([Interactive Dashboard])
    
    style User fill:#6c5ce7,stroke:#333,stroke-width:2px,color:#fff
    style Dashboard fill:#00b894,stroke:#333,stroke-width:2px,color:#fff
    style Server fill:#f1c40f,stroke:#333,stroke-width:2px,color:#000

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🛠️ Tech Stack

• Framework: Shiny for Python
• Visuals: Plotly (Interactive, HTML-embedded, MathJax integrated)
• Math Engine: NumPy & SciPy
• Deploy: Docker & Hugging Face Spaces

🚀 Run Locally

Ensure you have uv installed to manage the Python environment.

# 1. Sync dependencies
uv sync

# 2. Run the Shiny app
shiny run app.py --host 0.0.0.0 --port 7860

Alternatively, run completely isolated via Docker:

docker build -t prob-lab .
docker run -p 7860:7860 prob-lab