Frequentistische

Frequentistische Statistik, or frequentist theory, is a school of statistical inference based on the idea that probability expresses the long-run relative frequency of events in repeated samples from a population. In this view, model parameters are fixed constants and randomness arises from the data collection process; conclusions are drawn by considering the expected behavior of procedures across many hypothetical repetitions of the same experiment.

Key concepts include sampling distributions, estimators, and decision rules. Estimation aims to learn population parameters from data; common frequentist methods include maximum likelihood estimation and method of moments. Interval estimation uses confidence intervals, constructed so that, in repeated sampling, a specified proportion of intervals would contain the true parameter (coverage probability). Hypothesis testing employs null hypotheses, test statistics, p-values, and predefined significance levels (alpha); decisions are guided by long-run error rates such as Type I and Type II errors. Goodness-of-fit tests and likelihood ratio tests are also used within a frequentist framework.

Relation to Bayesian statistics is often highlighted: frequentists view probability as a long-run frequency rather than a degree of belief, treat parameters as fixed, and rely on sampling distributions; Bayesian methods incorporate prior information and yield posterior distributions.

Critiques of the frequentist approach focus on the misinterpretation of p-values, the sometimes misunderstood meaning of confidence intervals, and concerns about emphasis on long-run error rates. Nonetheless, frequentist methods remain widespread in science and engineering, informing study design, hypothesis testing, and reporting of results across disciplines.