Here are 100 chapter titles for a book on Hypothesis Testing, progressing from beginner to advanced:
I. Foundations (1-20)
- Introduction to Hypothesis Testing: What and Why?
- The Logic of Hypothesis Testing: A Conceptual Overview
- Null and Alternative Hypotheses: Defining the Claims
- Types of Errors: Type I and Type II Errors
- Significance Level (Alpha): Setting the Threshold
- Power of a Test (1-Beta): Detecting True Effects
- Test Statistics: Measuring the Evidence
- P-values: Quantifying the Evidence
- Critical Regions: Making Decisions
- One-Tailed vs. Two-Tailed Tests: Directionality
- Formulating Hypotheses: Research Questions and Predictions
- Choosing the Right Test: A Guide
- Assumptions of Hypothesis Tests: Validity Checks
- Data Collection and Sampling: The Foundation
- Sample Size Determination: Power and Precision
- Reporting Results: Communicating Findings
- The Role of Hypothesis Testing in Research
- Misinterpretations and Common Pitfalls
- Ethical Considerations in Hypothesis Testing
- Review and Preview: Looking Ahead
II. One-Sample Tests (21-40)
- Z-tests for Means: Known Population Variance
- T-tests for Means: Unknown Population Variance
- One-Sample T-test: Calculations and Examples
- Confidence Intervals and Hypothesis Testing: The Connection
- Non-parametric Tests: Alternatives to T-tests
- Sign Test: A Simple Non-parametric Test
- Wilcoxon Signed-Rank Test: Accounting for Magnitude
- Chi-Square Goodness-of-Fit Test: Testing Distributions
- Kolmogorov-Smirnov Test: Comparing Distributions
- One-Sample Proportion Test: Testing Proportions
- Practice Problems: One-Sample Tests
- Effect Size: Measuring the Magnitude of the Effect
- Cohen's d: A Common Effect Size Measure
- Power Analysis: Determining Sample Size
- Sample Size Calculations for One-Sample Tests
- Dealing with Non-Normal Data: Transformations and Alternatives
- Outlier Detection and Handling: Impact on Tests
- Robustness of Tests: Sensitivity to Assumptions
- Bootstrapping: A Resampling Approach
- Review and Practice: One-Sample Tests
III. Two-Sample Tests (41-60)
- Independent Samples T-test: Comparing Two Means
- Pooled Variance T-test: Equal Variances Assumed
- Unpooled Variance T-test: Unequal Variances
- Paired Samples T-test: Related Samples
- Comparing Two Proportions: Z-test
- Chi-Square Test for Independence: Categorical Data
- Fisher's Exact Test: Small Sample Sizes
- Mann-Whitney U Test: Non-parametric Comparison of Means
- Wilcoxon Rank-Sum Test: Another Non-parametric Option
- Practice Problems: Two-Sample Tests
- Effect Size for Two-Sample Tests: Cohen's d and Hedges' g
- Power Analysis for Two-Sample Tests
- Sample Size Calculations for Two-Sample Tests
- Assumptions of Two-Sample Tests: Checking Validity
- Handling Unequal Variances: Welch's T-test
- Non-parametric Alternatives: When Assumptions are Violated
- Multiple Comparisons Problem: Adjusting P-values
- Bonferroni Correction: A Simple Adjustment
- False Discovery Rate (FDR): Controlling for False Positives
- Review and Practice: Two-Sample Tests
IV. ANOVA and Beyond (61-80)
- Analysis of Variance (ANOVA): Comparing Multiple Means
- One-Way ANOVA: One Factor
- Two-Way ANOVA: Two Factors
- Factorial ANOVA: Multiple Factors
- Interactions: The Combined Effect of Factors
- Post Hoc Tests: Making Pairwise Comparisons
- Tukey's HSD: A Common Post Hoc Test
- Bonferroni Correction for Multiple Comparisons
- Non-parametric ANOVA: Kruskal-Wallis Test
- Repeated Measures ANOVA: Within-Subjects Designs
- Mixed-Design ANOVA: Between- and Within-Subjects Factors
- ANCOVA: Analysis of Covariance
- MANOVA: Multivariate Analysis of Variance
- Hotelling's T-squared Test: Multivariate Two-Sample Test
- Discriminant Analysis: Classifying Observations
- Practice Problems: ANOVA and Related Tests
- Effect Size for ANOVA: Eta-squared and Partial Eta-squared
- Power Analysis for ANOVA
- Assumptions of ANOVA: Checking Validity
- Review and Practice: ANOVA and Beyond
V. Advanced Topics and Applications (81-100)
- Bayesian Hypothesis Testing: An Alternative Approach
- Bayes Factors: Quantifying Evidence for Hypotheses
- Prior and Posterior Distributions: Bayesian Concepts
- Likelihood Ratio Tests: Comparing Models
- Wald Test: Testing Parameters in Models
- Score Test: Another Parameter Test
- Goodness-of-Fit Tests: Beyond Chi-Square
- Anderson-Darling Test: Testing Normality
- Shapiro-Wilk Test: Another Normality Test
- Time Series Analysis: Testing for Trends and Seasonality
- Regression Analysis: Hypothesis Testing for Relationships
- Linear Regression: Testing Slopes and Intercepts
- Multiple Regression: Testing Multiple Predictors
- Logistic Regression: Hypothesis Testing for Categorical Outcomes
- Survival Analysis: Testing for Differences in Survival Times
- Meta-Analysis: Combining Results from Multiple Studies
- Clinical Trials: Hypothesis Testing in Medical Research
- Statistical Process Control: Monitoring Quality
- History of Hypothesis Testing: A Detailed Account
- Open Problems and Future Directions in Hypothesis Testing