Latin rectangle

In combinatorial mathematics, a Latin rectangle is an r × n matrix that has the numbers 1, 2, 3, ..., n as its entries with no number occurring more than once in any row or column where r ≤ n. An n × n Latin rectangle is called a Latin square. If r < n, then it is possible to append n − r rows to an r × n Latin rectangle to form a Latin square, using Hall's marriage theorem.

In statistics, Latin rectangles have applications in the design of experiments.

References

Mirsky, L. Transversal Theory, New York, Academic Press, 1971.

Design of experiments

Scientific method	Scientific experiment Statistical design Control Internal and external validity Experimental unit Blinding Optimal design: Bayesian Random assignment Randomization Restricted randomization Replication versus subsampling Sample size

Treatment and blocking	Treatment Effect size Contrast Interaction Confounding Orthogonality Blocking Covariate Nuisance variable

Models and inference	Linear regression Ordinary least squares Bayesian Random effect Mixed model Hierarchical model: Bayesian Analysis of variance (Anova) Cochran's theorem Manova (multivariate) Ancova (covariance) Compare means Multiple comparison

Designs Completely randomized	Factorial Fractional factorial Plackett-Burman Taguchi Response surface methodology Polynomial and rational modeling Box-Behnken Central composite Block Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized controlled trial Sequential analysis Sequential probability ratio test

Glossary Category Statistics portal Statistical outline Statistical topics

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Latin rectangle

See also

References