Statistical Tables — z, t, Chi-Square and F
The four distribution tables from the back of a statistics textbook, on the web. Each comes with instructions and a worked example.
Standard Normal Table (z Table) — Cumulative Probability Φ(z)
Standard normal cumulative probabilities Φ(z) = P(Z ≤ z) from z = −3.49 to 3.49, with how to read rows and columns, negative z and right-tail probabilities.
T2t Distribution Table — Critical Values by Degrees of Freedom
Critical values of Student's t distribution for df 1–1000 and ∞, one-tailed α 0.25 to 0.0005 with matching two-tailed levels, plus examples for t-tests and confidence intervals.
T3Chi-Square Distribution Table — Critical Values χ²(α, df)
Right-tail critical values of the chi-square distribution for df 1–100 (α 0.995 to 0.001), with examples for choosing df in goodness-of-fit and independence tests.
T4F Distribution Table — Critical Values for α = 0.05 and 0.01
Critical values of the F distribution by numerator df₁ and denominator df₂ at α = 0.05 and 0.01, with examples for ANOVA and equal-variance tests.
Table or calculator?
Tables are handy for looking up critical values at standard significance levels. If you only need α = 0.05 or 0.01, as in exam problems, a table is enough.
If you need an exact p-value, or degrees of freedom that are not in the table (such as the fractional df of a Welch t-test), use a calculator instead. The t-test, chi-square and normal calculators on this site use the same algorithms as these tables and work for any value.
Accuracy
The table values are computed with numerical algorithms based on the incomplete beta and gamma functions and then rounded. They may differ from a printed textbook table by one unit in the last digit because of rounding.
Which table?
- z table: cumulative probabilities of normally distributed values; tests and intervals when the population SD is known
- t table: tests and confidence intervals for a mean with small samples and unknown population SD
- Chi-square table: goodness-of-fit and independence tests for categorical data; confidence intervals for a variance
- F table: ANOVA, comparing two variances, testing a regression model