Business Calculators · free & public domain

Statistical Tables

Thirteen tables, 19,230 values, every one computed from its own distribution rather than transcribed. Free to use, no signup, dedicated to the public domain.

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Z-Score Table (Standard Normal Distribution)Cumulative area under the standard normal curve to the left of z, from −3.99 to 3.99.800 valuest-Distribution Table (Critical Values)Critical values of Student’s t by degrees of freedom, for one- and two-tailed tests.343 valuesChi-Square Distribution TableCritical values of χ² by degrees of freedom, right-tail areas from 0.999 to 0.001.468 valuesF-Distribution Table (Critical Values)Critical values of F for five α levels, by numerator and denominator degrees of freedom.4,255 valuesBinomial Distribution TableExact binomial probabilities P(X = x) for n = 2 to 25 on a regular grid of p.7,308 valuesPoisson Distribution TableExact Poisson probabilities P(X = x) for means λ from 0.1 to 30.970 valuesPearson Correlation Critical Values (PPMC)Critical values of Pearson’s r by sample size, for testing H₀: ρ = 0.210 valuesTukey Studentized Range (q) TableCritical values of the studentized range q for Tukey’s HSD post-hoc comparisons.2,432 valuesSign Test Critical ValuesCritical values for the sign test, built on the conservative rule so the true error rate never exceeds α.224 valuesWilcoxon Signed-Rank Critical ValuesCritical values for the Wilcoxon signed-rank test, conservative construction, n to 60.224 valuesSpearman Rank Correlation Critical ValuesCritical values of Spearman’s rₛ, exact permutation enumeration to n = 14.144 valuesRuns Test Critical ValuesLower and upper critical run counts at α = 0.05 for testing a sequence for randomness.1,152 valuesRandom Number TableReproducible uniform random digits for drawing simple random samples.700 values

Why these are free

A critical value is a mathematical fact. Φ(1.96) = 0.9750 comes out the same for anyone who computes it correctly, and facts carry no copyright — the Supreme Court settled that in Feist v. Rural Telephone. So rather than reproduce anyone's printed table, we generated every value from the distribution itself, chose our own row and column ranges, and put the result in the public domain under CC0 1.0.

One place we differ on purpose. The sign, Wilcoxon and runs tables use the conservative construction, so the true error rate never exceeds the α you asked for. Many printed versions instead pick whichever value lands nearest α — at n = 5, α = 0.05, a Wilcoxon test built that way actually runs at 0.0625.

Every table names the method that produced it and links the primary literature. If you want the test performed rather than a value looked up, the Proof Workbench runs t, r, χ² and ANOVA in your browser.