Abstract

There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that all approaches make reference to the evidence in the data concerning questions of interest as a justification for the methodology employed. It is fair to say, however, that none of the most commonly used methodologies is absolutely explicit about how statistical evidence is to be characterized and measured. We will discuss the general problem of statistical reasoning and the development of a theory for this that is based on being precise about statistical evidence. This will be shown to lead to the resolution of a number of problems.

Highlights

  • There are a variety of approaches to conducting statistical analyses and most seem well-motivated from an intuitive point-of-view

  • Likelihood ratios are considered as measuring the evidence in the data supporting the truth of one value versus another and the Bayes factor is considered as a measure of statistical evidence

  • There are treatments that recognize the concept of statistical evidence as a central aspect of statistical reasoning as in [1,2,3,4,5,6,7]

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Summary

Introduction

There are a variety of approaches to conducting statistical analyses and most seem well-motivated from an intuitive point-of-view. With the increasing importance of, what we will call here, statistical reasoning in almost all areas of science, this ambiguity can be seen as an important problem to resolve. There is a tradition of the consideration of the meaning of evidence in the philosophy of science, sometimes called confirmation theory, with [8] being an accessible summary. While much of this literature has many relevant things to say about statistical evidence, it is fair to say that there is no treatment that gives an unambiguous definition of what it is together with developing a satisfactory theory of statistical reasoning based on this.

Purpose of a Theory of Statistical Reasoning
The Ingredients
Checking the Ingredients
The Rules of Statistical Inference
Problem E
Problem H
Measuring Bias
Conclusions
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