方法对比

	稳健卡方检验	稳健 Fisher 精确检验
领域	统计学	统计学
方法族	Hypothesis test	Hypothesis test
起源年份	1984 (power divergence); 1900 (Pearson baseline)	1935 (base); mid-p robustification 1961+
提出者	Cressie & Read (power divergence framework); Pearson chi-square extended by multiple authors	Fisher (1935); mid-p extension by Lancaster (1961) and others
类型	Robust categorical association / goodness-of-fit test	Robust exact conditional test
开创性文献	Cressie, N., & Read, T. R. C. (1984). Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society: Series B, 46(3), 440–464.	Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley-Interscience. ISBN: 978-0471360933
别名	robust chi-squared test, Cressie-Read power divergence test, adjusted chi-square test, robust contingency test	mid-p Fisher's exact test, robust exact test for contingency tables, conditional robust Fisher test, Fisher mid-p test
相关	3	3
摘要	The robust chi-square test extends the classic Pearson chi-square framework to remain reliable when standard assumptions — especially the minimum expected-cell-count rule — are violated. Using power divergence statistics (Cressie & Read, 1984) or resampling-based corrections, it produces valid inferences for sparse contingency tables, small samples, and unbalanced categorical data where the ordinary chi-square approximation breaks down.	The robust Fisher's exact test extends Fisher's classic exact test for contingency tables by applying conservative-correcting adjustments — most commonly the mid-p correction — to reduce the extreme conservatism of the standard exact test. This produces better-calibrated Type I error rates while maintaining validity in small and sparse samples.