Project 9: Statistical Inference Workbench

Build an inference workbench for estimation, intervals, tests, and power-aware decision making.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 2 weeks
Main Programming Language Python
Alternative Programming Languages R, Julia
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 2. The “Micro-SaaS / Pro Tool”
Prerequisites Projects 6-8
Key Topics Estimation, CI, hypothesis tests, power analysis

1. Learning Objectives

  1. Implement point estimators and uncertainty intervals.
  2. Compare CLT and bootstrap confidence intervals.
  3. Select and run z/t/chi-square/ANOVA tests appropriately.
  4. Integrate power analysis into pre-analysis planning.

2. All Theory Needed (Per-Concept Breakdown)

2.1 Estimation and Interval Logic

  • Fundamentals: Estimators map samples to parameter guesses; intervals communicate precision.
  • Deep Dive into the concept: Bias/variance tradeoffs, asymptotic approximations, and bootstrap alternatives shape confidence in estimates.

2.2 Testing and Decision Errors

  • Fundamentals: Hypothesis tests evaluate compatibility of data with null assumptions.
  • Deep Dive into the concept: Type I/II tradeoffs and power planning determine practical decision reliability.

3. Project Specification

3.1 What You Will Build

A CLI workbench that produces estimates, intervals, test results, and power-based decision notes.

3.2 Functional Requirements

  1. Point estimation module for means/proportions.
  2. CI module (normal approx + bootstrap).
  3. Test module (z, t, chi-square, ANOVA).
  4. Power planning and minimum sample size recommendations.

3.3 Non-Functional Requirements

  • Reproducible test runs and report manifests.
  • Explicit assumptions logged per method.

3.4 Example Usage / Output

$ python inference_workbench.py --config configs/uplift.yaml
Point estimate: 0.0132
95% CI (CLT): [0.0041, 0.0223]
95% CI (bootstrap): [0.0038, 0.0227]
p-value: 0.0047
Power: 0.91
Decision: effect likely above practical threshold

3.5 Real World Outcome

You produce inference reports that are explicit about uncertainty and error costs, not only significance labels.

4. Solution Architecture

Input config -> estimator/CI/test modules -> power module -> decision report

5. Implementation Guide

5.1 Development Environment Setup

pip install numpy scipy statsmodels

5.2 Project Structure

P09/
  inference_workbench.py
  configs/
  outputs/

5.3 The Core Question You Are Answering

“What conclusion is justified given uncertainty, assumptions, and error costs?”

5.4 Concepts You Must Understand First

  1. Bias and variance
  2. Confidence intervals
  3. Hypothesis testing framework
  4. Power and effect size

5.5 Questions to Guide Your Design

  1. Which test is valid for each data type/assumption set?
  2. How will you encode practical significance thresholds?
  3. How do you prevent p-hacking workflows?

5.6 Thinking Exercise

Explain how two analyses with the same p-value can lead to opposite business decisions.

5.7 The Interview Questions They’ll Ask

  1. What does a confidence interval mean?
  2. Why can significant results be practically trivial?
  3. When use bootstrap CI over CLT CI?
  4. What is the difference between Type I and Type II errors?
  5. Why is power analysis pre-study critical?

5.8 Hints in Layers

  • Hint 1: Implement one test path first.
  • Hint 2: Add interval alternatives.
  • Hint 3: Add power logic and planning mode.
  • Hint 4: Add assumptions audit in final report.

5.9 Books That Will Help

Topic Book Chapter
Inference foundations Casella & Berger Ch. 7-10
Practical testing OpenIntro Statistics inference chapters
Power planning applied biostatistics references selected

6. Testing Strategy

  • Validate against known textbook examples.
  • Compare CI methods on skewed synthetic data.
  • Verify power outputs against external calculators.

7. Common Pitfalls & Debugging

Pitfall Symptom Solution
Wrong test selection conflicting conclusions assumption-driven routing
Missing practical threshold overreaction to tiny effects effect-size gate
No power planning underpowered studies pre-analysis sample-size module

8. Extensions & Challenges

  • Add sequential testing controls.
  • Add equivalence testing path.

9. Real-World Connections

  • Product A/B decision systems.
  • Clinical and quality-control decision pipelines.

10. Resources

  • Casella & Berger
  • OpenIntro Statistics

11. Self-Assessment Checklist

  • I can pick tests from assumptions.
  • I can explain CI and p-value limitations.
  • I can plan study power before data collection.

12. Submission / Completion Criteria

Minimum: one complete estimator+CI+test+power pipeline.

Full: supports multiple metric types with assumptions audit trails.