This book provides a coherent description of foundational matters concerning statistical inference and shows how statistics can help us make inductive inferences about a broader context, based only on a limited dataset such as a random sample drawn from a larger population. By relating those basics to the methodological debate about inferential errors associated with p-values and statistical significance testing, readers are provided with a clear grasp of what statistical inference presupposes, and what it can and cannot do. To facilitate intuition, the representations throughout the book are as non-technical as possible.
The central inspiration behind the text comes from the scientific debate about good statistical practices and the replication crisis. Calls for statistical reform include an unprecedented methodological warning from the American Statistical Association in 2016, a special issue “Statistical Inference in the 21st Century: A World Beyond p < 0.05” of The American Statistician in 2019, and a widely supported call to “Retire statistical significance” in Nature in 2019.
The book elucidates the probabilistic foundations and the potential of sample-based inferences, including random data generation, effect size estimation, and the assessment of estimation uncertainty caused by random error. Based on a thorough understanding of those basics, it then describes the p-value concept and the null-hypothesis-significance-testing ritual, and finally points out the ensuing inferential errors. This provides readers with the competence to avoid ill-guided statistical routines and misinterpretations of statistical quantities in the future.Intended for readers with an interest in understanding the role of statistical inference, the book provides a prudent assessment of the knowledge gain that can be obtained from a particular set of data under consideration of the uncertainty caused by random error. More particularly, it offers an accessible resource for graduate students as well as statistical practitioners who have a basic knowledge of statistics. Last but not least, it is aimed at scientists with a genuine methodological interest in the above-mentioned reform debate.
Author(s): Norbert Hirschauer, Sven Grüner, Oliver Mußhoff
Series: SpringerBriefs in Applied Statistics and Econometrics
Edition: 1st ed. 2022
Publisher: Springer
Year: 2022
Language: English
Pages: 140
City: Cham
Preface
Contents
Abbreviations
Chapter 1: Introduction
Chapter 2: The Meaning of Scientific and Statistical Inference
2.1 The Starting Point: Errors and the Assessment of Validity
2.2 External Validity
2.3 Internal Validity
2.4 Chapter Summary: Scientific Inference Is More Than Statistical Inference
2.5 Recommended Reading
Chapter 3: The Basics of Statistical Inference: Simple Random Sampling
3.1 The Starting Point: Descriptive Statistics of a Given Dataset
3.2 Random Sampling, Sampling Error, and Sampling Distribution
3.3 Estimation and Estimation Uncertainty in Simple Random Sampling
3.3.1 Sample-Based Estimation of Effect Sizes and Standard Errors
3.3.2 An Illustrative Application: Gender Pay Gap
3.3.3 Sample-to-Sample Variability of Point and Standard Error Estimates
3.4 Chapter Summary: Statistical Assumptions Are Empirical Commitments
3.5 Recommended Reading
Chapter 4: Estimation Uncertainty in Complex Sampling Designs
4.1 Overview of Different Sampling Designs
4.2 Stratified Sampling
4.3 Cluster Sampling
4.4 Convenience Samples Contaminated by Selection Bias
4.4.1 Non-randomness: The Big Challenge in the Social Sciences
4.4.2 Approaches to Correct for Selection Bias in Convenience Samples
4.5 Full Populations and Finite Population Correction
4.6 Chapter Summary: Inference Requires Considering the Sampling Design
4.7 Recommended Reading
Chapter 5: Knowledge Accumulation Through Meta-analysis and Replications
5.1 The Basics of Meta-analysis
5.1.1 Dealing with Different Measurements and Model Specifications
5.1.2 Synthesizing Effect Sizes and Standard Errors Across Several Studies
5.2 Evaluation of the Quality of Research Through Replications
5.3 Chapter Summary: Our Best Estimators Estimate Correctly on Average
5.4 Recommended Reading
Chapter 6: The p-Value and Statistical Significance Testing
6.1 The p-Value Concept
6.2 Null-Hypothesis-Significance-Testing
6.2.1 Dichotomization of the p-Value and Significance Declarations
6.2.2 The Statistical Ritual ``NHST´´ and Misinterpretations of Single Studies
6.2.3 Perpetuation of the Statistical Ritual ``NHST´´ in Replication Studies
6.2.4 Malpractices and Publication Bias Associated with NHST
6.2.5 Approaches Aimed at Mitigating Publication Bias
6.3 The Historical Origins of the NHST-Framework
6.3.1 NHST: An Ill-bred Hybrid of Two Irreconcilable Statistical Approaches
6.3.2 Inductive Behavior (Hypothesis Testing) and Type I Error Rates α
6.3.3 Inductive Belief (Significance Testing) and p-Value Thresholds
6.4 Chapter Summary: Significance Declarations Should Be Avoided
6.5 Recommended Reading
Chapter 7: Statistical Inference in Experiments
7.1 Inferential Cases in Group Mean Comparisons
7.2 Causal Inference
7.2.1 Overview of Experimental Designs Aimed at Establishing Causality
7.2.2 The Uncertainty of Causal Effect Estimates Caused by Randomization
7.2.3 Inference in Random Assignment of Randomly Recruited Subjects
7.3 Inferences Without Randomization or Random Sampling
7.3.1 Fictitious Random Sampling
7.3.2 Fictitious Randomization
7.4 Chapter Summary: Causal Inference Is Different from Generalization
7.5 Recommended Reading
Chapter 8: Better Inference in the 21st Century: A World Beyond p < 0.05
References
Index
