During the 20th century, population ecology and science in general
relied on two very different statistical paradigms to solve its
inferential problems: error statistics (also referred to as classical
statistics and frequentist statistics) and Bayesian statistics. A great
deal of good science was done using these tools, but both schools suffer
from technical and philosophical difficulties. At the turning of the
21st century (Royall in Statistical evidence: a likelihood paradigm.
Chapman & Hall, London, 1997
Lele in The nature of scientific evidence: statistical, philosophical
and empirical considerations. The University of Chicago Press, Chicago,
pp 191–216, 2004a
evidential statistics emerged as a seriously contending paradigm.
Drawing on and refining elements from error statistics, likelihoodism,
Bayesian statistics, information criteria, and robust methods,
evidential statistics is a statistical modern synthesis that smoothly
incorporates model identification, model uncertainty, model comparison,
parameter estimation, parameter uncertainty, pre-data control of error,
and post-data strength of evidence into a single coherent framework. We
argue that evidential statistics is currently the most effective
statistical paradigm to support 21st century science. Despite the power
of the evidential paradigm, we think that there is no substitute for
learning how to clarify scientific arguments with statistical arguments.
In this paper we sketch and relate the conceptual bases of error
statistics, Bayesian statistics and evidential statistics. We also
discuss a number of misconceptions about the paradigms that have
hindered practitioners, as well as some real problems with the error and
Bayesian statistical paradigms solved by evidential statistics.