Glossary

Research, statistics and methods terms — concise, sourced definitions that complement the full method and topic pages.

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Admissible decision ruleIn statistical decision theory, a decision rule is admissible if no other rule dominates it, meaning no alternative rule has uniformly smaller or equal risk for all parameter values with strictly smaller risk for at least one. Inadmissible rules are suboptimal and can always be replaced by a superior rule.
Algebra of random variablesThe mathematical framework defining arithmetic operations—addition, subtraction, multiplication, and division—on random variables, where results are themselves random variables. It encompasses rules for computing expectations, variances, and distributions of derived variables, forming the basis for probability theory and statistical modeling.
Alternative hypothesisIn hypothesis testing, the hypothesis accepted when the null hypothesis is rejected; it represents the claim the researcher seeks to support. Denoted H₁ or Hₐ, it may be one-sided (e.g., μ > μ₀) or two-sided (μ ≠ μ₀), and is never directly tested but supported by evidence against the null.
Analysis of varianceA statistical method that partitions total variability in a response variable into components attributable to different sources—between-group and within-group variation—to test whether group means differ significantly. It uses the F-statistic and was developed by R.A. Fisher. Commonly abbreviated as ANOVA.
Atomic eventA single-element subset of a sample space that cannot be decomposed further; also called an elementary or simple event. For example, rolling a '3' on a die is an atomic event. All atomic events are mutually exclusive and collectively exhaustive, forming the finest-grained partition of the sample space.

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HistogramA graphical display of the distribution of continuous data using adjacent rectangular bars, where each bar's width represents a class interval and its height (or area) represents the frequency or probability density of observations falling within that interval.

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VarianceThe expected squared deviation of a random variable from its mean; the fundamental measure of spread in a distribution or dataset. Population variance is denoted σ² and sample variance s² (dividing by n−1 for unbiasedness). As the square of the standard deviation, variance is the preferred dispersion measure in statistical theory because of its convenient mathematical properties.

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Yates's correction for continuityA continuity correction proposed by Frank Yates that reduces the absolute difference between observed and expected frequencies by 0.5 in each cell of a 2×2 contingency table before computing the chi-square statistic. Applied to better approximate the continuous chi-square distribution with small samples, though it is criticized for being overly conservative.

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Z-testA hypothesis test based on the standard normal distribution, applicable when the population variance is known or the sample size is large enough to invoke the central limit theorem. Used for one-sample and two-sample comparisons of means and proportions. The test statistic z = (x̄ − μ₀) / (σ / √n) is compared against critical values from the standard normal table.