方法对比

	交叉析因实验	拉丁方设计与拉丁方-希腊方设计
领域	实验设计	实验设计
方法族	Process / pipeline	Hypothesis test
起源年份	1920s–1960s (synthesis of factorial and crossover traditions)	1935
提出者	R. A. Fisher (factorial principles, 1920s); crossover integration developed in biostatistics through mid-20th century	Ronald A. Fisher
类型	Experimental design	Parametric blocked ANOVA
开创性文献	Jones, B., & Kenward, M. G. (2014). Design and Analysis of Cross-Over Trials (3rd ed.). Chapman and Hall/CRC. ISBN: 978-1439861424	Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119492443
别名	within-subject factorial design, repeated-measures factorial experiment, factorial crossover trial, crossover factorial trial	Latin Square, Greco-Latin Square, Latin Kare ve Greco-Latin Kare Deseni
相关	5	5
摘要	A crossover factorial experiment combines two powerful design principles: factorial structure, which studies multiple factors and their interactions simultaneously, and crossover structure, in which each participant receives more than one treatment combination across sequential periods. By serving as their own control, participants reduce between-subject variability, improving statistical power while also revealing how different factor levels interact within the same individual.	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×n arrangement. Formalised by Ronald A. Fisher in his 1935 monograph The Design of Experiments, the design dramatically reduces experimental error by absorbing variation from two extraneous sources before the treatment effects are estimated.