Frequentism

Frequentism is a school of statistical inference in which probability expresses the long-run frequency of an event under repeated sampling from a population. In this view, parameters are fixed but unknown, and randomness arises only through the data and the sampling process. Inference is evaluated by long-run operating characteristics rather than degrees of belief about parameters.

Key tools and concepts include confidence intervals, p-values, and pre-specified error control. Confidence intervals are constructed so that, in repeated sampling, a specified proportion of such intervals would contain the true parameter. Hypothesis testing focuses on controlling error rates: the Type I error (false positive) rate and, depending on the framework, Type II error. The Neyman-Pearson approach formalizes decision rules and rejection regions for simple hypotheses, while Fisher emphasized test statistics and p-values as measures of evidence against the null hypothesis. Modern practice often blends these traditions.

Estimators are typically based on sampling distributions, with maximum likelihood estimation being a central method. The bootstrap and other resampling techniques are frequently used to approximate sampling distributions and to construct confidence intervals.

Criticism of frequentism centers on its interpretation of probability as limiting frequency, which omits subjective belief and prior information, and on interpretive pitfalls of p-values. It may understate uncertainty in small samples or complex models. The philosophy contrasts with Bayesian inference, which treats parameters as random and combines prior information with data to form a posterior distribution. Despite differences, frequentist methods remain foundational in many scientific disciplines and are widely taught and applied.