Frequentist inference

Frequentist inference draws conclusions from data using procedures evaluated by their behavior across repeated samples, treating unknown parameters as fixed and data as random.

Sampling distribution: The probability distribution of a statistic across repeated samples from the same population. Frequentist procedures are assessed through the distributions their statistics would have under repetition.
Null hypothesis significance testing: A procedure that assesses data against a null hypothesis using a prespecified test statistic and rejection rule. It is the standard frequentist framework for controlling false rejections.
Bayesian inference: A framework that represents uncertainty about parameters with probability distributions and updates them using data. Unlike frequentist inference, it can assign posterior probabilities to parameter values.
Ronald Fisher: A British statistician whose work established foundational methods in experimental design, estimation, and significance testing. Fisher developed significance tests and the p-value as tools for scientific evidence.
Randomized controlled trial: An experiment that assigns participants randomly to interventions or comparison groups. Random assignment supports valid sampling-based comparisons and tests of treatment effects.
Point estimation: The use of sample data to produce a single estimate of an unknown parameter. It is one core way frequentist methods summarize evidence about fixed parameters.
P-value: The probability, under a specified null model, of data at least as extreme as the observed data. It measures how surprising the observation is under the tested null, not the probability that the null is true.
Likelihood principle: The principle that inferences about a parameter should depend on observed data only through its likelihood function. Some frequentist procedures depend on possible outcomes not observed, which the principle rejects.
Jerzy Neyman: A Polish mathematician and statistician who developed confidence intervals and a theory of hypothesis testing. Neyman framed inference through procedures with controlled long-run error rates.
Analysis of variance: A statistical method that partitions variation to test differences among group means. Its F-tests evaluate mean differences using reference distributions under model assumptions.

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