方法对比

	Crossover Multi-Arm Experiment	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	Mid-20th century; multi-arm extensions formalized by 1970s–1980s	1935
提出者	Developed from early crossover trial methodology (Williams 1949; Cochran & Cox 1957)	Ronald A. Fisher
类型	Within-subject experimental design with multiple treatment arms	Parametric blocked ANOVA
开创性文献	Jones, B., & Kenward, M. G. (2003). Design and Analysis of Cross-Over Trials (2nd ed.). Chapman and Hall/CRC. ISBN: 978-1584883869	Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119492443
别名	multi-arm crossover trial, multi-period multi-treatment crossover, CMAT, multi-treatment crossover experiment	Latin Square, Greco-Latin Square, Latin Kare ve Greco-Latin Kare Deseni
相关	5	5
摘要	A crossover multi-arm experiment is a within-subject experimental design in which each participant receives three or more treatments (arms) across successive periods, with random assignment to sequence. Because every participant experiences all arms, the design eliminates between-subject variability from treatment comparisons, dramatically increasing statistical power for a given sample size. It is widely used in clinical pharmacology, psychology, agriculture, and behavioral research.	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.