Statistical Tables

The reference tables from the back of your textbook.

Critical values and probabilities for the distributions used in every introductory statistics course, computed exactly rather than rounded from a printed page, with an interactive lookup on each one.

Standard Normal (Z) Table

Cumulative area to the left of z

The classic standard normal table: cumulative probability P(Z < z) for z from -3.49 to 3.49, plus a quick two-way lookup.

Student t-Table

Critical values for every common confidence level

Critical t-values for one- and two-tailed tests, for degrees of freedom from 1 to 120 and beyond, at the significance levels used in coursework.

Chi-Square Table

Critical values by degrees of freedom

Critical chi-square values for goodness-of-fit and independence tests, for degrees of freedom from 1 to 100 at the standard significance levels.

F-Table

Critical values for ANOVA and regression F-tests

Critical F-values by numerator and denominator degrees of freedom, at a significance level you choose, for ANOVA and regression F-tests.

Binomial Probability Table

P(X=k) and P(X≤k) by n and p

Exact binomial probabilities for common numbers of trials and success probabilities, laid out like a textbook table.

Mann-Whitney U Critical Values

Exact critical U by sample size

Exact critical values for the Mann-Whitney (rank-sum) test, computed by enumerating every possible rank arrangement for sample sizes 4 to 20.

Wilcoxon Signed-Rank Critical Values

Exact critical W by sample size

Exact critical values for the Wilcoxon signed-rank test, computed by enumerating every possible sign assignment, for sample sizes 5 to 30.

Studentized Range (Tukey q) Table

Critical q for Tukey's HSD test

Critical values of the studentized range statistic for 2 to 20 groups and any error degrees of freedom, at α = 0.10, 0.05 and 0.01.

Pearson Correlation Critical Values

The smallest significant |r| by sample size

Critical values of the Pearson correlation coefficient for degrees of freedom from 1 to 1,000 at the usual one- and two-tailed significance levels.

Poisson Probability Table

P(X=k) and P(X≤k) by mean rate λ

Exact Poisson probabilities for mean rates from 0.1 to 20, in both individual and cumulative form.

Spearman's Rank Correlation Critical Values

Exact critical rho for small samples

Critical values of Spearman's rho, exact for 4 to 16 pairs by counting every possible ranking, with accurate approximations up to n = 100.

Kolmogorov-Smirnov Critical Values

Exact D by sample size

Exact critical D values for the one-sample, two-sided Kolmogorov-Smirnov test, for sample sizes 5 to 100, computed by exact finite-sample matrix methods.

Grubbs' Test Critical Values

Exact critical G for one outlier

Exact critical values for Grubbs' single-outlier test, sample sizes 3 to 100, derived directly from the Student t distribution.

Runs Test Critical Values

Exact lower–upper run counts

Exact critical run counts for the Wald-Wolfowitz runs test, for n1 and n2 from 3 to 20, from the closed-form null distribution.

Kruskal-Wallis Exact Critical Values

Exact H for 3 small groups

Exact critical values of the Kruskal-Wallis H statistic for 3 groups with sizes 2 to 5, from exhaustive enumeration of the exact null distribution.

Friedman Test Exact Critical Values

Exact Fr for small repeated-measures designs

Exact critical values of the Friedman Fr statistic for 3 conditions (2-9 subjects) and 4 conditions (2-4 subjects), from exhaustive enumeration.

Durbin-Watson Table

Exact dL / dU autocorrelation bounds

Exact Durbin-Watson dL and dU bounds for 15 to 100 observations and 1 to 5 predictors, computed via Imhof's method and checked against the published Savin-White tables.

Shapiro-Wilk Critical Values

Monte Carlo estimated, clearly labeled

Critical W values for the Shapiro-Wilk normality test, n = 5 to 100, estimated by large-scale Monte Carlo simulation and checked against published references.

Need to compute a test rather than look up a critical value directly? Try the statistics calculators, or the interactive tools for a visual version of the same distributions.