Drawing conclusions from samples, and knowing how much to trust them.
10 topics · 11 curated works
No prior grounding assumed.
OpenIntro Statistics
David Diez, Christopher Barr & Mine Çetinkaya-Rundel · 2012
A free, open-licensed introductory statistics textbook that builds estimation and hypothesis testing from first principles for readers with no…
Assumes you know the vocabulary.
Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing
Yoav Benjamini & Yosef Hochberg · 1995
Replaces control of the chance of any single false rejection with control of the expected proportion of false rejections among all rejections, giving…
Primary sources and full treatments.
On the Mathematical Foundations of Theoretical Statistics
Ronald A. Fisher · 1922
Coins 'likelihood' as distinct from probability and argues that the estimator maximising it extracts all the information a sample contains about a…
+8 more at this level
11 works
David Diez, Christopher Barr & Mine Çetinkaya-Rundel
A free, open-licensed introductory statistics textbook that builds estimation and hypothesis testing from first principles for readers with no calculus background.
link checked 17 Sept 2026Yoav Benjamini & Yosef Hochberg
Replaces control of the chance of any single false rejection with control of the expected proportion of false rejections among all rejections, giving multiple testing a procedure that stays powerful as the number of tests grows.
link checked 17 Sept 2026Ronald A. Fisher
Coins 'likelihood' as distinct from probability and argues that the estimator maximising it extracts all the information a sample contains about a parameter.
link checked 17 Sept 2026Jerzy Neyman & Egon S. Pearson
Formalises hypothesis testing as a choice between two kinds of error and proves which test region minimises one for a fixed bound on the other, the Neyman-Pearson lemma.
link checked 17 Sept 2026Jerzy Neyman
Defines the confidence interval as a procedure that covers the true parameter a fixed proportion of the time under repeated sampling, deliberately stopping short of any probability claim about a single realised interval.
link checked 17 Sept 2026C. R. Rao
Derives what became the Cramer-Rao lower bound, showing that the Fisher information in a sample sets a hard floor on how precise any unbiased estimator can be.
link checked 17 Sept 2026Wassily Hoeffding
Introduces U-statistics and proves their asymptotic normality, giving rank-based nonparametric methods the same large-sample machinery parametric estimators already had.
link checked 17 Sept 2026Abraham Wald
Proves that the maximum likelihood estimator converges to the true parameter value as sample size grows, under conditions general enough to extend well beyond the cases Fisher had checked by hand.
link checked 17 Sept 2026Charles Stein
Shows that the sample mean, the obvious and universally used estimator, is inadmissible in three or more dimensions because a shrinkage estimator does uniformly better everywhere in the parameter space.
link checked 17 Sept 2026Bradley Efron
Shows that resampling the observed data itself, rather than relying on a formula, can estimate an estimator's standard error and bias for almost any statistic.
link checked 17 Sept 2026Philippe Rigollet (MIT OpenCourseWare)
Builds the mathematical statistics under the methods — why maximum likelihood works, what a confidence interval actually asserts — rather than teaching tests as recipes.
link checked 17 Sept 2026