Statistical Reasoning Based on Characterizing Evidence

The goal of a theory of statistical reasoning is to provide scientists with a logically sound
approach to answering questions concerning an object of interest after collecting data which
is presumed to contain evidence concerning the correct answers. There are several aspects
of this which go beyond simply recording estimates or hypothesis assessment. These include
a methodology for choosing the ingredients beyond the data that form part of the analysis,
providing clear recommendations on the data collection so that reliable inferences can be drawn,
checking the subjectively chosen ingredients against the data to ensure implicit assumptions
are not contradicted as well as delineating how these ingredients need to be modified when
necessary and finally, sepcifying the inferences. An outline of such a theory is discussed
where the primary ingredient is a clear characterization of statistical evidence. Applications
are made to two well-known problems, the avoidance of absurd regions when characterizing
the error in an estimate and the combination of evidence from different studies.