Frequentist statistics

Frequentist statistics interprets probability as long-run relative frequency across repeated trials and evaluates procedures by their repeated-sampling behavior.

Sampling distribution: The probability distribution of a statistic across repeated samples drawn under the same conditions. Frequentist guarantees describe how statistics vary across hypothetical repetitions of the sampling process.
Probability theory: The mathematical study of random events, distributions, and uncertainty. Frequentist inference uses probability models to describe outcomes across repetitions.
Bayesian statistics: An approach to statistics that represents uncertainty about parameters with probability distributions and updates them using data. Bayesian methods can assign probabilities to hypotheses, unlike standard frequentist inference.
Ronald Fisher: A British statistician who developed influential methods in experimental design, estimation, and significance testing. Fisher established a major approach to inference based on likelihood and significance tests.
Experimental design: The planning of experiments to obtain informative, interpretable data while controlling sources of variation. Randomization and replication support the repeated-sampling assumptions behind frequentist analyses.
Maximum likelihood estimation: A method that estimates model parameters by maximizing the likelihood of the observed data. Its sampling properties let frequentists assess estimator bias, consistency, and precision.
Random variable: A variable whose possible values and probabilities are specified by a probability model. Sample statistics are treated as random variables before the data are observed.
Likelihood principle: The principle that statistical evidence about parameters is contained in the likelihood of the observed data. Some frequentist procedures depend on possible outcomes not observed, in tension with this principle.
Jerzy Neyman: A Polish mathematician and statistician who helped develop confidence intervals and statistical decision procedures. His work made long-run coverage and controlled error rates central to inference.
Analysis of variance: A statistical method for comparing means by partitioning observed variation into components. Its tests assess mean differences using sampling distributions under specified assumptions.

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