方法对比

	交叉分数析因子实验	全因子实验
领域	实验设计	实验设计
方法族	Process / pipeline	Process / pipeline
起源年份	1950s–1970s (fractional factorial from 1940s; crossover integration from 1960s–1970s)	1926 (Fisher's foundational paper); codified by the 1950s–1960s
提出者	Box, Hunter & Hunter (fractional factorial); Senn & Williams (crossover integration)	Ronald A. Fisher
类型	Within-subject multi-factor experimental design	Experimental design
开创性文献	Senn, S. (2002). Cross-over Trials in Clinical Research (2nd ed.). Wiley. ISBN: 978-0471496533	Box, G. E. P., Hunter, J. S., & Hunter, W. G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery (2nd ed.). Wiley-Interscience. ISBN: 978-0471718130
别名	crossover FF design, within-subject fractional factorial, repeated-measures fractional factorial, crossover FFE	full factorial design, complete factorial design, 2^k factorial design, FFD
相关	5	6
摘要	A crossover fractional factorial experiment is a within-subject design in which each participant receives a strategically chosen subset of all possible factor-level combinations in a defined sequence, with washout periods between treatment periods. By combining the run-economy of fractional factorial designs with the within-subject efficiency of crossover designs, it allows estimation of main effects and selected interactions while controlling for between-subject variability using far fewer participants and experimental runs than a full factorial crossover.	A full factorial experiment runs every possible combination of all chosen factor levels, making it the gold standard for simultaneously estimating main effects, two-way interactions, and higher-order interactions among multiple independent variables. Introduced through Ronald Fisher's foundational work on factorial designs in the 1920s and systematised by Box, Hunter, and Montgomery, it provides complete information about how factors act individually and in combination on an outcome.