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.
