Statistics

Statistics is the discipline of collecting, analyzing, interpreting, and communicating data under uncertainty. It uses probability and models to draw conclusions while accounting for variation and limits in evidence.

Probability theory: The mathematical study of random events, their likelihoods, and the rules governing uncertainty. It supplies the formal language for describing sampling variation and uncertain outcomes.
Descriptive statistics: Methods for summarizing and presenting the main features of a dataset. These methods organize observed data before broader conclusions are attempted.
Experimental design: The planning of experiments to estimate effects or test hypotheses while controlling sources of bias and variation. Design determines whether collected data can support causal conclusions.
Causal inference: Methods for estimating the effects of interventions or exposures from data and assumptions. Association alone does not establish causation; causal claims require additional design or assumptions.
P-value: The probability, under a specified null model, of data at least as extreme as those observed. Misreading it as the probability that a hypothesis is true has distorted scientific claims.
Data: Recorded observations or measurements represented in a form that can be analyzed. Statistical methods begin with data whose structure and quality shape every conclusion.
Statistical inference: Methods for using sample data to estimate or test claims about a larger process or population. Inference is the step from observed samples to conclusions under uncertainty.
Survey sampling: Methods for selecting people or units and estimating population characteristics from survey responses. It applies sampling principles to populations that cannot be fully observed.
Bayesian statistics: An approach to inference that combines prior probability distributions with observed data to update beliefs about unknown quantities. It represents uncertainty with posterior distributions and incorporates explicit prior information.
Multiple comparisons problem: The increased chance of false-positive findings when many statistical tests are performed. Large-scale testing requires adjustment or validation to keep apparent discoveries credible.

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