方法对比

	多重比较问题	P值与统计显著性
领域	研究统计学	研究统计学
方法族	Process / pipeline	Process / pipeline
起源年份	1935	1925
提出者	Carlo Bonferroni; Benjamini & Hochberg	Ronald Fisher
类型	Concept	Concept
开创性文献	Bonferroni, C. E. (1935). Il calcolo dei coefficienti di correlazione nel caso di variabilità di gruppi. Instituto Italiano di Statistica.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
别名	multiple testing, family-wise error, p-value adjustment, false discovery rate	p-value, significance test, statistical significance, alpha level
相关	4	5
摘要	When conducting multiple statistical tests, the probability of obtaining at least one false positive by chance increases with the number of tests. The multiple comparisons problem (also called the multiplicity problem) occurs because if you conduct 100 hypothesis tests at α = 0.05, you expect ~5 false positives by chance alone, even if all null hypotheses are true. Correction methods—Bonferroni, Benjamini-Hochberg false discovery rate (FDR), and others—adjust the significance threshold or p-values to control error rates. This concept is critical for research integrity and has profound implications for exploratory science.	The p-value is the probability of observing data as extreme as or more extreme than what was actually observed, assuming the null hypothesis is true. Introduced by Ronald Fisher in 1925, it is the foundation of frequentist hypothesis testing. Statistical significance is declared when the p-value falls below a pre-specified threshold (alpha level, typically 0.05).