Statistical inference

Statistical inference uses sample data to draw conclusions about a population, model, or underlying process while accounting for uncertainty.

Probability theory: The mathematical study of random events and uncertainty. It supplies the language for quantifying uncertainty in conclusions drawn from samples.
Point estimation: The use of sample data to produce a single estimate of an unknown quantity. It gives one central value for a population quantity or model parameter.
Frequentist statistics: An approach that interprets probability through long-run frequencies and evaluates procedures by repeated-sampling behavior. It contrasts with Bayesian inference in how probability and uncertainty are interpreted.
Statistical significance: A designation indicating that data would be sufficiently unusual under a specified null hypothesis and threshold. It is a common but limited way to summarize evidence from a test.
Random sampling: A sampling method in which selection is governed by chance. Random selection helps connect observed data to the population being studied.
Confidence interval: An interval procedure designed to cover a fixed parameter at a stated rate across repeated samples. It expresses estimation uncertainty through a range with a long-run coverage guarantee.
Bayesian inference: Inference that updates prior probability distributions with observed data using Bayes' theorem. Its posterior probabilities answer questions that frequentist procedures frame differently.
P-value: The probability, assuming a null hypothesis and model, of results at least as extreme as those observed. Misreading p-values can turn a calibrated test result into an unsupported claim.
Sampling distribution: The probability distribution of a statistic across repeated samples from the same process. It describes how much an estimate would vary across repeated samples.
Hypothesis testing: A procedure that evaluates data against a specified null hypothesis using a test statistic and decision rule. It assesses whether observed data conflict with a precise statistical claim.

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