What This Document Is
This document contains lecture notes from AMS 572: Data Analysis I, offered at Stony Brook University. Specifically, these notes cover foundational concepts and methods within categorical data analysis – a crucial branch of statistics focused on understanding relationships between variables when the data represent qualities or categories rather than numerical measurements. It builds upon core statistical principles to explore techniques for analyzing this type of data.
Why This Document Matters
These notes are exceptionally valuable for students enrolled in a first-level data analysis course, particularly those needing a detailed record of lecture material. They are most helpful when used in conjunction with textbook readings and homework assignments, serving as a focused resource for review before exams or when tackling complex analytical problems. Individuals preparing to apply statistical methods in fields like social sciences, public health, or market research will find the concepts presented here particularly relevant.
Topics Covered
* Fundamentals of binomial distributions and probability calculations.
* Hypothesis testing for single proportions.
* Comparative inference for two population proportions.
* Confidence interval construction for differences in proportions.
* Chi-square tests for assessing relationships between categorical variables.
* Multinomial experiments and their application in data analysis.
* Statistical significance testing and p-value interpretation.
What This Document Provides
* A structured presentation of key definitions and statistical notation.
* Explanations of the theoretical underpinnings of various statistical tests.
* Formulas and equations related to proportion estimation and hypothesis testing.
* Illustrative examples demonstrating the application of statistical concepts (detailed solutions are included within the full document).
* Guidance on utilizing statistical software (SAS) for data analysis.
* A comprehensive overview of the principles behind inference on several proportions.
