Statistical Evidence

Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

This book provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It attempts to establish a gold standard for how a statistical analysis should proceed. The book illustrates relative belief theory using many examples and describes the strengths and weaknesses of the theory. The author also addresses fundamental statistical issues, including the meaning of probability, the role of subjectivity, the meaning of objectivity, and the role of infinity and continuity.

The purpose of this book is to discuss whether statistical methods make sense. The present volume begins the task of providing interpretations and explanations of several theories of statistical evidence. It should be relevant to anyone interested in the logic of experimental science. Have we achieved a true Foundation of Statistics? We have made the link with one widely accepted view of science and we have explained the senses in which Bayesian statistics and p-values allow us to draw conclusions. This book has substantial implications for all users of Statistical methods.

Aimed at students and researchers in statistics and in the medical and health care sector as well as those who use and assess medical data, this work addresses common pitfalls in experimental design, focusing on the errors and misleading data that stem from flawed experiments and analytical methods in medical research.

Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

Many scientists now widely agree that the current paradigm of statistical significance should be abandoned or largely modified. In response to these calls for change, a Special Issue of Econometrics (MDPI) has been proposed. This book is a collection of the articles that have been published in this Special Issue. These seven articles add new insights to the problem and propose new methods that lay a solid foundation for the new paradigm for statistical significance.

The subject of this book is the reasoning under uncertainty based on sta tistical evidence, where the word reasoning is taken to mean searching for arguments in favor or against particular hypotheses of interest. The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain spe cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of sta tistical models called functional models. The second aspect deals with the uncertainty under which the formal reasoning takes place. For this aspect, the theory of hints [27] is the appropriate tool. Basically, we assume that some uncertain perturbation takes a specific value and then logically eval uate the consequences of this assumption. The original uncertainty about the perturbation is then transferred to the consequences of the assumption. This kind of reasoning is called assumption-based reasoning. Before going into more details about the content of this book, it might be interesting to look briefly at the roots and origins of assumption-based reasoning in the statistical context. In 1930, R. A. Fisher [17] defined the notion of fiducial distribution as the result of a new form of argument, as opposed to the result of the older Bayesian argument.

Statistical Evidence in Medical Trials is a lucid, well-written and entertaining text that addresses common pitfalls in evaluating medical research. Including extensive use of publications from the medical literature and a non-technical account of how to appraise the quality of evidence presented in these publications, this book is ideal for health care professionals, students in medical or nursing schools, researchers and students in statistics, and anyone needing to assess the evidence published in medical journals. Stephen D. Simon earned a Ph.D. in statistics from the University of Iowa in 1982. He currently works as a research biostatistician at Children's Mercy Hospitals and Clinics in Kansas City, MO. He has authored or co-authored over 60 publications in a variety of medical and statistical journals, four of which have won awards. He has given a wide range of lectures and classes on statistics, evidence based medicine, research ethics, and quality control.