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Inferential Statistics in Practice: From Probability to ANOVA


🔍 Project Overview 

This project demonstrates the application of inferential statistics to solve multiple real-world problems across sports analytics, manufacturing quality control, marketing operations and healthcare.

The objective was to move beyond descriptive statistics and apply probability theory, hypothesis testing, and ANOVA techniques to draw meaningful conclusions and support data-driven decision-making.

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🎯 Key Objectives

  • Apply probability concepts to real datasets

  • Use normal distribution and Z-tests for quality analysis

  • Perform hypothesis testing (Z-test, T-test)

  • Analyze multi-factor effects using One-Way & Two-Way ANOVA

  • Translate statistical results into business insights and recommendations

🧠 Problem 1: Sports Injury Probability Analysis

Business Question

Can player position help explain the likelihood of foot injuries in a football team?

Approach

  • Used conditional probability and joint probability

  • Analyzed injury distribution across playing positions

Key Insight

  • Overall injury probability: 61%

  • Strikers had the highest injury likelihood among injured players

  • Player position plays a significant role in injury risk

Impact

Helps coaching and medical staff focus preventive care strategies on high-risk positions.

🏭 Problem 2: Manufacturing Quality Control (Normal Distribution)

Business Question

What proportion of cement gunny bags fail strength requirements?

Approach

  • Assumed normal distribution

  • Used Z-score-based probability estimation

  • Visualized probability regions for decision clarity

Key Insights

  • ~11% of bags fall below minimum strength threshold

  • Over 82% meet acceptable strength criteria

  • Identified risk zones contributing to material loss

Impact

Supports supply chain quality checks and reduces wastage risk.

🧪 Problem 3: Stone Hardness Testing (Hypothesis Testing)

Business Question

Are unpolished stones suitable for high-quality printing?

Statistical Techniques Used

  • Z-test (large sample, known population mean)

  • Independent two-sample T-test

  • Outlier treatment and distribution analysis

Key Findings

  • Mean hardness of unpolished stones is significantly below required threshold

  • Polished stones show higher and more consistent hardness

Recommendation

Zingaro is justified in rejecting unpolished stones for printing applications.

🦷 Problem 4: Dental Implant Hardness Analysis (ANOVA)

Business Question

How do dentist, method, and alloy influence implant hardness?

Techniques Used

  • One-Way ANOVA

  • Two-Way ANOVA with interaction effects

  • Shapiro-Wilk Test (normality)

  • Levene Test (variance equality)

  • Tukey post-hoc analysis

Key Insights

  • Dentist alone does not significantly impact hardness

  • Implant method significantly affects hardness

  • Strong interaction exists between dentist and method

  • Optimal methods vary by alloy type

Business Impact

  • Standardizes implant procedures

  • Improves treatment outcomes

  • Reduces variability in medical results

🛠 Skills Demonstrated

Statistical & Analytical Skills

  • Probability theory

  • Hypothesis testing

  • Z-test, T-test

  • One-Way & Two-Way ANOVA

  • Post-hoc analysis

Tools & Techniques

  • Python

  • Pandas, NumPy

  • SciPy, StatsModels

  • Data visualization

  • Statistical interpretation

📈 Overall Impact

This project showcases the ability to:

  • Choose the right statistical test for each problem

  • Validate assumptions before modeling

  • Interpret statistical output in business terms

  • Support decisions with data-backed evidence

🏁 Conclusion

Inferential statistics is a critical foundation for data science and analytics.
This project demonstrates how statistical methods can directly support sports strategy, manufacturing quality, marketing optimization, and healthcare decision-making.













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