方法对比

	相关性与因果性	多重比较问题
领域	研究统计学	研究统计学
方法族	Process / pipeline	Process / pipeline
起源年份	1965	1935
提出者	Multiple sources (Bradford Hill, Judea Pearl, Donald Rubin)	Carlo Bonferroni; Benjamini & Hochberg
类型	Concept	Concept
开创性文献	Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd ed.). Cambridge University Press. ISBN: 978-0-521-89560-6	Bonferroni, C. E. (1935). Il calcolo dei coefficienti di correlazione nel caso di variabilità di gruppi. Instituto Italiano di Statistica.
别名	correlation and causation, causal inference, spurious correlation, confounding	multiple testing, family-wise error, p-value adjustment, false discovery rate
相关	4	4
摘要	Correlation measures the strength and direction of association between two variables; causation implies that changes in one variable directly produce changes in another. A strong correlation (e.g., r = 0.9) does not prove causation. Classic examples abound: shoe size and reading ability are correlated in children (confounded by age), but shoe size does not cause reading ability. Understanding when correlation implies causation requires evaluating study design, confounding variables, temporal precedence, and mechanism. Randomized experiments offer the strongest causal evidence; observational studies must carefully control for confounders.	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.