This book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testing and how to interpret P-values under a variety of conditions including a single hypothesis test, a collection of hypothesis tests, and tests performed on accumulating data. The author explains how a hypothesis test can be interpreted to draw conclusions, and descriptions of the logic behind frequentist (classical) and Bayesian approaches to interpret the results of a statistical hypothesis test are provided. Both approaches have their own strengths and challenges, and a special challenge presents itself when hypothesis tests are repeatedly performed on accumulating data. Possible pitfalls and methods to interpret hypothesis tests when accumulating data are also analyzed. This book will be of interest to researchers, graduate students, and anyone who has to interpret the results of statistical analyses.
• Presents the classical and Bayesian interpretations of hypothesis tests under various conditions
• Describes how to take samples and the process for planning to take samples
• Explains how to use Excel® to obtain P-values for several common statistical tests and how to interpret them
Author(s): Robert Hirsch
Series: Synthesis Lectures On Mathematics & Statistics
Edition: 1
Publisher: Springer
Year: 2022
Language: English
Commentary: TruePDF
Pages: 94
Tags: Statistics; Statistical Theory And Methods; Bayesian Inference
Preface
Notices
Contents
1 Logic of Hypothesis Testing
1.1 Classical (Frequentist) Approach
1.1.1 Statistical Hypotheses and Conclusions
1.1.2 Errors in Hypothesis Testing
1.1.3 Calculating P-Values
1.1.4 Interpreting P-Values
1.2 Bayesian Approach
1.2.1 Bayes’ Theorem
1.2.2 Multiple Hypotheses
2 Sampling
2.1 Taking Samples
2.2 Model Sampling
2.3 Probability Sampling
2.4 Other Methods of Sampling
3 Basic Statistical Methods
3.1 Selecting a Test
3.2 Student’s t-Tests
3.2.1 Paired t-Test
3.2.2 Independent Sample t-Test
3.3 Regression Analysis
3.4 Correlation Analysis
3.5 Analysis of Variance
3.6 Multiple Regression Analysis
3.7 Z-Tests for Nominal Data
3.7.1 Paired z-Test
3.7.2 Independent Sample z-Test
3.7.3 Test for Trend
4 Interim Analysis
4.1 The Problem
4.2 Sequential Analysis
4.3 Stochastic Curtailment
5 Planning the Sample’s Size
5.1 Studies with No Independent Variable
5.2 Studies with One Independent Variable
5.3 Studies with More Than One Independent Variable
Appendix
Posterior Testing
Index
