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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 &lt 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.
Preface
Abbreviations
Introduction
The Meaning of Scientific and Statistical Inference
The Starting Point Errors and the Assessment of Validity
External Validity
Internal Validity
Summary Scientific Inference Is More Than Statistical Inference
Recommended Reading
The Basics of Statistical Inference Simple Random Sampling
The Starting Point Descriptive Statistics of a Given Dataset
Random Sampling, Sampling Error, and Sampling Distribution
Estimation and Estimation Uncertainty in Simple Random Sampling
Sample-Based Estimation of Effect Sizes and Standard Errors
An Illustrative Application Gender Pay Gap
Sample-to-Sample Variability of Point and Standard Error Estimates
Summary Statistical Assumptions Are Empirical Commitments
Recommended Reading
Estimation Uncertainty in Complex Sampling Designs
Overview of Different Sampling Designs
Stratified Sampling
Cluster Sampling
Convenience Samples Contaminated by Selection Bias
Non-randomness The Big Challenge in the Social Sciences
Approaches to Correct for Selection Bias in Convenience Samples
Full Populations and Finite Population Correction
Summary Inference Requires Considering the Sampling Design
Recommended Reading
Knowledge Accumulation Through Meta-analysis and Replications
The Basics of Meta-analysis
Dealing with Different Measurements and Model Specifications
Synthesizing Effect Sizes and Standard Errors Across Several Studies
Evaluation of the Quality of Research Through Replications
Summary Our Best Estimators Estimate Correctly on Average
Recommended Reading
The p-Value and Statistical Significance Testing
The p-Value Concept
Null-Hypothesis-Significance-Testing
Dichotomization of the p-Value and Significance Declarations
The Statistical Ritual ``NHST´´ and Misinterpretations of Single Studies
Perpetuation of the Statistical Ritual ``NHST´´ in Replication Studies
Malpractices and Publication Bias Associated with NHST
Approaches Aimed at Mitigating Publication Bias
The Historical Origins of the NHST-Framework
NHST An Ill-bred Hybrid of Two Irreconcilable Statistical Approaches
Inductive Behavior (Hypothesis Testing) and Type I Error Rates α
Inductive Belief (Significance Testing) and p-Value Thresholds
Summary Significance Declarations Should Be Avoided
Recommended Reading
Statistical Inference in Experiments
Inferential Cases in Group Mean Comparisons
Causal Inference
Overview of Experimental Designs Aimed at Establishing Causality
The Uncertainty of Causal Effect Estimates Caused by Randomization
Inference in Random Assignment of Randomly Recruited Subjects
Inferences Without Randomization or Random Sampling
Fictitious Random Sampling
Fictitious Randomization
Summary Causal Inference Is Different from Generalization
Recommended Reading
Better Inference in the st Century A World Beyond p &lt
References
Index