Hypothesis Testing

This part is the inferential core of the handbook. Its purpose is to turn exploratory findings into formal decisions under uncertainty using null/alternative hypotheses, test statistics, and p-values.

Use this section after descriptive exploration, not before. In practice, you should first inspect data quality and distributional behavior, then choose tests that match the data structure and assumptions.

How This Part Is Structured

Block	Purpose	Main chapters
Core framework	Build testing logic and notation	Normal Distribution Review, Population, Sample, One-sided vs Two-sided, Sigma Unknown, CLT
Single-parameter tests	Test means, variances, proportions, and standard deviations	Statistical Tests with Unknown Variance, Testing Population Mean, Testing Variance, Testing Population Proportion, Testing Standard Deviation
Group-comparison tests	Compare independent/paired groups and equivalence	Difference Between Means, Difference Mean Paired, Testing Difference in Variances, One-sample t-test, Paired/Unpaired/Welch tests, TOST
Distribution and count tests	Test distributional or categorical assumptions	Median Test, Chi-squared Tests, Kolmogorov-Smirnov Test
Multi-group and dependency tests	Handle ANOVA-type designs and association/correlation testing	One-way ANOVA, Kruskal-Wallis, Two-way ANOVA, Repeated Measures ANOVA, Friedman Test, Testing Correlations, Causality
Integrated practice	Apply end-to-end test workflows	Problems

How To Use It

Start from your analysis purpose in 4  The Big Picture: Why We Analyze Data and then choose the formal test path with Appendix A — Method Selection Guide (Appendix A).
When a chapter mentions assumptions, verify those assumptions with the corresponding descriptive diagnostics before interpreting p-values.