Frequentistik

Frequentistik, or frequentist statistics, is a school of statistical inference that defines probability as the long-run relative frequency of an event in repeated, identical trials. In this view, model parameters are fixed but unknown quantities, and randomness arises from the data-generating process. Inference is based on the sampling distribution of estimators and test statistics rather than on degrees of belief about parameters.

Core tools include hypothesis testing under a pre-specified error rate (Neyman–Pearson framework), p-values to measure compatibility of data with a null hypothesis, and confidence intervals whose nominal coverage statements are interpreted as long-run frequencies over repeated sampling. Parameter estimation is typically carried out via estimators derived from sampling distributions, with maximum likelihood methods commonly used within this framework.

Historically, frequentist ideas emerged in the early 20th century through the contributions of Ronald Fisher, Jerzy Neyman and Egon Pearson. The approach contrasts with Bayesian statistics, which treat parameters as random variables and update beliefs with prior distributions using Bayes' theorem.

Criticisms include the reliance on long-run error rates that may be difficult to verify in a single study, common misinterpretations of confidence intervals, and the exclusion of prior information. Critics also point out that some real-world decisions require probabilistic statements about parameters themselves, which frequentism does not directly provide.

Frequentist methods are widely used across sciences, medicine, psychology, and industry, particularly in fixed-sample experiments, clinical trials, and quality control. They form the standard reference framework for many statistical tests and estimation procedures.