Statistical tables
Interactive lookups and printable tables, with explanations that help you use the answer. Start with the distribution your method needs.
Common distributions
Z-Table (Standard Normal Distribution Table)
Normal probabilities, percentiles, and known-σ mean intervals
Area to the left: P(Z ≤ z)t-Table (Student's t Distribution Table)
Mean tests and intervals when population σ is estimated
Choose df and one or two tailsChi-Square Table (χ² Distribution)
Categorical tests and inference about a normal population’s variance
Choose df and right-tail αF-Table (F-Distribution Critical Values)
ANOVA, overall regression tests, and variance ratios
Choose numerator and denominator dfChoosing a statistical test
Choose by outcome type, study design, and what you want to compare.
Additional tables
Binomial Distribution Table ↗
Cumulative binomial probabilities for n = 5, 10, 15 and 20, with explicit tail conventions, model assumptions and a worked example.
Degrees of Freedom Table & Reference ↗
Degrees of freedom for common tests and models, with paired counts, Welch approximations, fitted-parameter adjustments and rank conditions.
Geometric Distribution Table ↗
Exact and cumulative probabilities for trials until first success, with the failures-versus-trials convention stated explicitly.
Hypergeometric Distribution Table ↗
Exact probabilities for uniform sampling without replacement, with finite-population parameters, full supports and a worked comparison.
Multinomial Distribution Reference ↗
Calculate probabilities of labeled category counts. Distinguish a count vector from an unordered pattern or a single outcome sequence.
Negative Binomial Distribution Table ↗
Negative binomial probabilities using failures before r successes. Translate to total trials and avoid conflicting parameter conventions.
Poisson Distribution Table ↗
Poisson cumulative probabilities for lambda 0.5–20, with exposure units, exact and upper-tail examples, and model limitations.
A few things to check first
- Which distribution? A large sample alone doesn’t mean you should use z instead of t. For mean inference with estimated population standard deviation, use the t-distribution.
- Which tail? A central 95% interval puts 2.5% in each tail. A two-tailed test at α = 0.05 also splits α across the two tails.
- Which degrees of freedom? The formula depends on the method. Welch’s t-test can have fractional df; a pooled two-sample t-test uses n₁ + n₂ − 2.
A critical value is a cutoff under a model, not proof of a meaningful effect. Check assumptions and consider effect size and uncertainty alongside significance.
Statistics formula sheet
Essential formulas and critical values. Available to read, print, or download.