Welcome to Week 8! This week, we dive deep into hypothesis testing methods - essential skills for making statistical inferences in agricultural and biological research. Learn one-sample tests, paired t-tests, and chi-square analysis!

🎯 What You'll Learn This Week

🔬 One-Sample T-Tests - Compare sample means against known values

📊 Two-Sample T-Tests - Compare means between independent groups

🔗 Paired T-Tests - Analyze before/after or matched pair data

🎲 Chi-Square Tests - Test goodness of fit and independence

⚖️ Critical Value Method - Manual hypothesis testing approach

📈 P-Value Method - Modern statistical inference approach

🚀 Getting Started: Step-by-Step Guide

Step 1: Launch Week 8 Binder Environment 🌐

Click the "Launch Week 8" button above to start your R environment. This will take 2-5 minutes to load with all necessary packages for hypothesis testing.

Step 2: Navigate to Class Activity 📚

Once Binder loads, you'll see the Jupyter Notebook interface. In the left panel, you'll see:

assignment/ - Assignment 8 on biodiversity wildfire analysis
class_activity/ - Week 8 comprehensive tutorial
Various files (README.md, runtime.txt, etc.)

Click on the class_activity folder to access this week's content.

Step 3: Open the Week 8 Lab Notebook 📖

Inside the class_activity folder, double-click on Week8_Correlation_Analysis.ipynb to open the interactive lab notebook.

Step 4: Explore Hypothesis Testing Methods 📊

This week we'll work with multiple datasets including iris and agricultural yield data! The notebook will guide you through:

One-sample t-tests using critical value and p-value methods
Two-sample independent t-tests for group comparisons
Paired t-tests for before/after agricultural treatment analysis
Chi-square tests for categorical data analysis
Comprehensive interpretation of statistical results

🎯 Interactive Learning Tools

Practice with Hypothesis Testing Concepts

Use these interactive tools to understand hypothesis testing concepts before working with R code:

💡 Tip: Use these tools to practice hypothesis formation and visualize statistical concepts before applying them in your R notebook!

🧮 Key R Functions This Week

One-Sample T-Tests

            t.test(data, mu = 4, alternative = "two.sided")  # Two-tailed test

            t.test(data, mu = 4, alternative = "greater")   # One-tailed (greater)

            t.test(data, mu = 4, alternative = "less")      # One-tailed (less)

            qt(1 - alpha/2, df = n-1)                      # Critical t-value

Two-Sample and Paired T-Tests

            t.test(group1, group2, paired = FALSE)          # Independent samples

            t.test(before, after, paired = TRUE)            # Paired samples

            t.test(group1, group2, var.equal = FALSE)       # Welch's t-test

            subset(data, Species == "setosa")               # Data filtering

Chi-Square Tests

            chisq.test(observed, p = expected/sum(expected)) # Goodness of fit

            chisq.test(contingency_table)                   # Test of independence

            matrix(c(data), nrow = 2, byrow = TRUE)         # Create contingency table

            pt(t_stat, df = n-1)                            # P-value calculation

📝 Assignment 8: Biodiversity Wildfire Analysis

Step 1: Access Assignment Folder 📋

From the main directory, click on the assignment folder to access Assignment 8.

Step 2: Open Assignment 8 Notebook 📄

Double-click on Assignment8.ipynb to open your assignment on biodiversity analysis.

Assignment Overview (15 points total)

📊

Part 1: Data Import & Visualization (3 points)

Load biodiversity data and check distributions

🔬

Part 2A: General Effect Test (3 points)

Test if wildfire significantly affected biodiversity

📈

Part 2B: Increase Test (3 points)

Test if wildfire significantly increased biodiversity

📉

Part 2C: Decrease Test (3 points)

Test if wildfire significantly reduced biodiversity

🤔

Part 3: Analysis Limitations (3 points)

Discuss limitations of the statistical analysis

Step 3: Analyze Wildfire Impact Data 🔥

The assignment focuses on environmental research applications:

Biodiversity Analysis - Compare pre- and post-wildfire biodiversity indices
Paired T-Tests - Use appropriate statistical methods for before/after data
Directional Hypotheses - Test specific predictions about wildfire effects
Critical Thinking - Evaluate limitations of statistical approaches

Learn to make evidence-based environmental decisions using rigorous statistical testing!

🌿 Why This Matters in Environmental Science

🔥 Wildfire Impact - Assess ecological effects of natural disturbances

🌱 Treatment Effects - Test agricultural intervention effectiveness

🦋 Biodiversity Studies - Compare species richness across conditions

🌡️ Climate Research - Analyze environmental change impacts

🧪 Experimental Design - Choose appropriate statistical tests

Hypothesis Testing Skills Help You:

Make rigorous statistical inferences about environmental changes
Choose appropriate tests for different data types and research questions
Interpret p-values and confidence intervals correctly
Understand limitations of statistical analyses
Communicate scientific findings with statistical support

💾 Saving Your Work

⚠️ Important: Binder environments are temporary! Always save your work locally.

Download Your Notebook 📥

When you're done working, save your progress:

Save your notebook: File → Save
Download .ipynb file: File → Download
Export HTML/PDF: File → Save and Export Notebook As → HTML

Continue Your Progress Later 🔄

To resume your work:

Launch Binder again
Click Upload button
Upload your saved .ipynb file
Continue where you left off!

📤 Submission Requirements

For Assignment 8, submit TWO files to UC Davis Canvas:

📄

HTML/PDF Report

Your completed assignment with all outputs and analysis

💾

.ipynb File

Your notebook code as backup

Due Date: Check Canvas for assignment deadline

🎯 Learning Objectives

By the end of this week, you will be able to:

✅ Form appropriate null and alternative hypotheses

✅ Perform one-sample t-tests using multiple methods

✅ Conduct two-sample and paired t-tests appropriately

✅ Apply chi-square tests for categorical data

✅ Interpret statistical results and draw valid conclusions

✅ Understand limitations of statistical analyses

❓ Need Help?

📧 Contact Information

Mohammadreza Narimani
📧 mnarimani@ucdavis.edu
🏫 Department of Biological and Agricultural Engineering, UC Davis

🔧 Common Issues

Hypothesis confusion? Remember: H₀ = no effect, H₁ = there is an effect
Paired vs independent? Use paired for before/after or matched data
P-value interpretation? p < 0.05 suggests rejecting null hypothesis
Alternative direction? "less" tests if first < second, "greater" tests first > second

📚 Additional Resources

T-Test Assumptions: Check normality and independence of data
Chi-Square Requirements: Expected frequencies should be ≥ 5
Effect Size: Consider practical significance beyond statistical significance

🌟 Tips for Success

💡 Best Practices

Check assumptions - Verify data meets test requirements
Visualize first - Use histograms and boxplots to understand data
Choose correct test - Match test type to research question
Interpret carefully - Statistical significance ≠ practical importance
Consider limitations - Think about what your analysis cannot tell you

⚡ Keyboard Shortcuts

Shift + Enter Run current cell and move to next

Ctrl + Enter Run current cell and stay in place

Tab Auto-complete function names

?function Get help for any R function

🎉 Ready to Start?

Click the Binder badge below to launch Week 8!

Launch Week 8 Interactive Environment

Happy hypothesis testing! 🔬📊

Last updated: November 2024 | PLS 120 - Applied Statistics in Agriculture | UC Davis
Week 8: Hypothesis Testing and Statistical Analysis

📊 Week 8: Hypothesis Testing and Statistical Analysis