مقایسهٔ روش‌ها

	مقدار پی و اهمیت آماری	مشکل مقایسه‌های چندگانه
حوزه	آمار پژوهش	آمار پژوهش
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1925	1935
پدیدآور	Ronald Fisher	Carlo Bonferroni; Benjamini & Hochberg
نوع	Concept	Concept
منبع بنیادین	Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.	Bonferroni, C. E. (1935). Il calcolo dei coefficienti di correlazione nel caso di variabilità di gruppi. Instituto Italiano di Statistica.
نام‌های دیگر	p-value, significance test, statistical significance, alpha level	multiple testing, family-wise error, p-value adjustment, false discovery rate
مرتبط	5	4
خلاصه	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).	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.