The philosophy of statistics involves the meaning, justification,

utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...

, use and abuse of statistics and its

methodology In its most common sense, methodology is the study of research methods. However, the term can also refer to the methods themselves or to the philosophical discussion of associated background assumptions. A method is a structured procedure for br ...

, and

ethical Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns ma ...

and epistemological issues involved in the consideration of choice and interpretation of data and methods of statistics.

Topics of interest

Foundations of statistics The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist ...

involves issues in

theoretical statistics The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...

, its goals and

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

methods to meet these goals, parametric assumptions or lack thereof considered in

nonparametric statistics Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being dist ...

model selection Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the ...

for the underlying probability distribution, and interpretation of the meaning of inferences made using statistics, related to the

philosophy of probability The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one b ...

and the

philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ult ...

. 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. * David Cox makes the point that any kind of interpretation of evidence is in fact a statistical model, although it is known through Ian Hacking's work that many are ignorant of this subtlety. * Issues arise involving

sample size Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a populatio ...

, 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. * The motivation and justification of data analysis and

experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

, as part of the

scientific method The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific ...

are considered. * Distinctions between

induction Induction, Inducible or Inductive may refer to: Biology and medicine * Labor induction (birth/pregnancy) * Induction chemotherapy, in medicine * Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell t ...

and

logical deduction Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false ...

relevant to inferences from

data In the pursuit of knowledge, data (; ) is a collection of discrete Value_(semiotics), values that convey information, describing quantity, qualitative property, quality, fact, statistics, other basic units of meaning, or simply sequences of sy ...

and evidence arise, such as when

frequentist Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or pro ...

interpretations are compared with degrees of certainty derived from Bayesian inference. However, the difference between induction and ordinary reasoning is not generally appreciated. * 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. * Issues in the philosophy of statistics arise throughout the

history of statistics Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. In early times, the meaning was restricted to information about states, particularly demographics ...

. Causality considerations arise with interpretations of, and definitions of, correlation, and in the theory of measurement. * 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. *

Ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concer ...

associated with

epistemology Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epis ...

and

medical Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care practic ...

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.

Topics of interest

Notes

Further reading