🎯 Statistical Tests Overview

🔬 One-Sample T-Test

t = (x̄ - μ₀) / (s/√n)

Compare sample mean against known value

📊 Two-Sample T-Test

t = (x̄₁-x̄₂)/√(s₁²/n₁+s₂²/n₂)

Compare means between independent groups

🔗 Paired T-Test

t = d̄ / (s_d/√n)

Analyze before/after or matched pair data

🎲 Chi-Square Test

χ² = Σ(O-E)²/E

Test goodness of fit and independence

🔬 Interactive Hypothesis Testing Simulator

Design Your Hypothesis Test

⚙️ Test Configuration

📝 Hypothesis Statements

📊 Sample Data

Group 1
Group 2

📊 Test Results

🔍 Three Ways to Test Hypotheses

All Methods Give the Same Conclusion!

💡 Key Insight:

Whether you use critical values, p-values, or R's t.test() function, you'll reach the same statistical conclusion. Choose the method that makes most sense for your analysis!

🌾 Agricultural Data Simulator

Before/After Treatment Analysis

⚙️ Treatment Parameters

📊 Paired T-Test Results

📈 Before/After Comparison

🎲 Chi-Square Test Interactive Demo

🎲 Dice Fairness Test

Observed Frequencies

📊 Contingency Table Test

Gender vs Fruit Preference

🍎 Apple 🍌 Banana 🍊 Orange
Male
Female

🎯 Practice Quiz

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🎓 Key Takeaways

🔬

Hypothesis Testing Benefits

  • • Rigorous statistical inference
  • • Evidence-based decisions
  • • Quantified uncertainty
  • • Reproducible results
📊

Test Selection Guide

  • • Paired for before/after
  • • Independent for group comparisons
  • • Chi-square for categorical data
  • • One-sample for known standards
🌿

Environmental Applications

  • • Biodiversity studies
  • • Treatment effectiveness
  • • Climate change impacts
  • • Conservation decisions