What This Document Is
This document contains detailed academic notes for AMS 315: Data Analysis at Stony Brook University. It focuses on the foundational principles of statistical hypothesis testing, extending core concepts to various analytical scenarios. These notes are designed to supplement coursework and provide a structured approach to understanding statistical inference. The material delves into the theoretical underpinnings of testing procedures, offering a deeper understanding beyond simply applying formulas.
Why This Document Matters
Students enrolled in introductory or intermediate data analysis courses, particularly AMS 315, will find these notes exceptionally valuable. They are ideal for reinforcing lecture material, preparing for exams, and building a strong conceptual foundation in statistical testing. Individuals seeking a more rigorous understanding of hypothesis testing, power analysis, and study design will also benefit. These notes are particularly useful when tackling assignments requiring a detailed understanding of the logic behind statistical decisions.
Topics Covered
* Hypothesis testing fundamentals – null and alternative hypotheses
* One-sample statistical tests
* Two independent sample statistical tests
* Univariate linear regression testing
* Critical value determination
* Rejection rule definition
* Type II error analysis
* Sample size considerations in study design
* Distributions of test statistics under null and alternative hypotheses
What This Document Provides
* A systematic framework for approaching statistical hypothesis testing.
* A detailed exploration of how testing procedures are adapted for different data structures.
* A focus on the relationship between study design and statistical power.
* A structured presentation of key concepts related to statistical inference.
* A foundation for understanding more advanced statistical methods.
