The philosophy of statistics is the study of the mathematical, conceptual, and philosophical foundations and analyses of statistics and statistical inference. For example, Dennis Lindely argues for the more general analysis of statistics as the study of
uncertainty.[1] The subject involves the
meaning,
justification,
utility, use and abuse of
statistics and its
methodology, and
ethical and
epistemological issues involved in the consideration of choice and interpretation of data and methods of
statistics.[2]
Topics of interest
Foundations of statistics involves issues in
theoretical statistics, its goals and
optimization methods to meet these goals,
parametric assumptions or lack thereof considered in
nonparametric statistics,
model selection for the underlying
probability distribution, and interpretation of the meaning of inferences made using statistics, related to the
philosophy of probability and the
philosophy of science. Discussion of the selection of the goals and the meaning of optimization, in foundations of statistics, are the subject of the philosophy of statistics. Selection of distribution models, and of the means of selection, is the subject of the philosophy of statistics, whereas the mathematics of optimization is the subject of nonparametric statistics.
Issues arise involving
sample size, such as cost and efficiency, are common, such as in polling and pharmaceutical research.
Extra-mathematical considerations in the design of experiments and accommodating these issues arise in most actual experiments.[further explanation needed]
Leo Breiman exposed the diversity of thinking in his article on 'The Two Cultures', making the point that statistics has several kinds of inference to make, modelling and prediction amongst them.[4]
Objectivity in statistics is often confused with truth whereas it is better understood as replicability, which then needs to be defined in the particular case.
Theodore Porter develops this as being the path pursued when trust has evaporated, being replaced with criteria.[5]
Ethics associated with
epistemology and
medical applications arise from potential abuse of statistics, such as selection of method or
transformations of the data to arrive at different probability conclusions for the same data set. For example, the meaning of applications of a
statistical inference to a single person, such as one single cancer patient, when there is no frequentist interpretation for that patient to adopt.
Campaigns for
statistical literacy must wrestle with the problem that most interesting questions around individual risk are very difficult to determine or interpret, even with the computer power currently available.
Hacking, Ian (1964). "On the Foundations of Statistics". The British Journal for the Philosophy of Science. 15 (57): 1–26.
doi:
10.1093/bjps/xv.57.1.
JSTOR685624.