Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Adaptive Clinical Trial Design
Adaptive clinical trial design is a flexible experimental framework, formalised by Bauer and Köhne in 1994, in which pre-specified rules allow the trial to be modified mid-course — adjusting sample size, treatment arms, or randomisation rat...
Completely Randomized Design
The completely randomized design is the most fundamental experimental design, in which experimental units are assigned to treatments entirely at random with no restrictions. Analysed by one-way ANOVA, it was formalised by R. A. Fisher in th...
Conjoint Analysis
Conjoint analysis is a preference-measurement technique that decomposes overall product evaluations into the separate utility values — called part-worths — that respondents assign to each attribute level. Formalised by Green and Srinivasan...
Crossover Design
A crossover design is an experimental design in which each participant receives all treatments under investigation, but in a different sequence and across separate time periods. Each subject thus acts as their own control, which substantial...
Destination Choice Experiment
A destination choice experiment is a stated-preference technique that asks travellers to choose among experimentally designed hypothetical destinations, each described by a bundle of attributes such as price, travel distance, climate, the t...
Discrete Choice Experiment
A discrete choice experiment (DCE) is a stated-preference method in which respondents repeatedly choose their preferred option from sets of alternatives described by systematically varied attributes, allowing the analyst to estimate how eac...
Dose-Response Design
Dose-response design is a framework for planning and analysing experiments that characterise the relationship between the amount of a stimulus — such as a drug dose or a chemical concentration — and the magnitude of a biological or physiolo...
Equivalence / Non-Inferiority Trial
An equivalence or non-inferiority trial is a clinical study design that tests whether a new intervention is clinically equivalent to, or no worse than, an established standard by a pre-specified margin. Codified in Schuirmann's 1987 Two One...
Fractional Factorial Design
The fractional factorial design is an economical experimental strategy that investigates k factors by running only a carefully chosen 1/2^p fraction of the full 2^k factorial experiment. Formalized by George E. P. Box and J. Stuart Hunter i...
Full Factorial Design
A full factorial design is a parametric experimental method in which every combination of factor levels is tested simultaneously, enabling the estimation of all main effects and all interaction effects in a single study. Rooted in R. A. Fis...
Latin Square Design
The Latin square design is a blocked experimental design that simultaneously controls two independent nuisance factors — the row block and the column block — so that each treatment appears exactly once in every row and every column of an n×...
Learning Curve
The learning curve models how performance improves predictably as cumulative experience accumulates. Formalized by Theodore Wright in 1936 using aircraft manufacturing data, it expresses the relationship between the number of practice trial...
Mixture Design
Mixture experiment design is a class of constrained experimental design in which the factors are the proportions of components in a blend, subject to the constraint that all proportions sum to one. The framework was formalised by Henry Sche...
Multi-Armed Bandit
The multi-armed bandit (MAB) is an adaptive experimental framework that allocates trials sequentially across competing arms to minimise cumulative regret while simultaneously learning which arm performs best. Formalised by Robbins in 1952 a...
Optimal Experimental Design
Optimal experimental design is a computer-aided approach to constructing experiments that maximises statistical efficiency for a given model and run budget. Formalised by V. V. Fedorov in 1972, it selects experimental points from a candidat...
Plackett-Burman Design
The Plackett-Burman design is a two-level orthogonal screening design introduced by R.L. Plackett and J.P. Burman in 1946 that allows researchers to estimate the main effect of each factor independently using the smallest possible number of...
Randomized Complete Block Design
The Randomized Complete Block Design (RCBD) is a parametric experimental design and hypothesis-testing framework that isolates and removes a known source of heterogeneity — called a block — before comparing treatment means. Introduced by Ro...
Randomized Controlled Trial
A randomized controlled trial (RCT) is the gold standard experimental design in clinical and health research, in which participants are randomly allocated to a treatment group or a control group so that the effect of an intervention can be...
Response Surface Methodology
Response Surface Methodology is a collection of statistical and mathematical techniques for building an empirical second-order polynomial model that relates a continuous response variable to two or more controllable input factors, and then...
Sequential Design
Sequential and group sequential trial designs allow a study to be stopped early — or continued — based on interim analyses conducted as data accumulate. The core framework was formalised by O'Brien and Fleming in 1979 and extended by Lan an...
Sibling Fixed-Effects Design
The sibling fixed-effects, or sibling-comparison, design controls for everything that siblings share by construction. Genes (on average half), parents, household income, neighborhood, schooling, and family culture are differenced out when y...
Standardized Mean Difference for Single-Case Designs
The between-case standardized mean difference is an effect-size measure that puts the result of a single-case experiment on the same numerical scale as Cohen's d from a conventional between-groups study, so that single-case and group findin...
Taguchi Method
The Taguchi Method is a robust design methodology developed by Genichi Taguchi, first systematized in his 1987 work, that uses orthogonal arrays to study many control factors in a minimum number of experimental runs while quantifying produc...