T-Distribution Table

Most Common Critical Values at α = 0.05 (Two-Tailed)

Used for 95% confidence intervals and two-tailed hypothesis tests at the 5% significance level:

At n ≥ 30, t critical is within 0.1 of z = 1.960. At n ≥ 100, the difference is negligible — you can use either table.

Complete T-Distribution Table

Values shown are critical t-values for the given α and df. Reject H₀ if |t| > t critical.

Highlighted column (α = 0.05 two-tailed) = most commonly used. Row ∞ = z critical values.

How to Read the T-Table: Step by Step

1. 1
   Calculate degrees of freedom. One-sample: df = n − 1. Two independent samples: df = n₁ + n₂ − 2. Paired: df = n_pairs − 1.
2. 2
   Choose α and tail. Most common: α = 0.05, two-tailed (corresponds to a 95% confidence level). Use one-tailed only when you have a directional hypothesis specified before data collection.
3. 3
   Find the row. Locate df in the left column. If your df falls between table values, use the smaller df (conservative approach).
4. 4
   Find the column. Choose the α column matching your significance level and tail type.
5. 5
   Compare t statistic to t critical. If |t calculated| > t critical → reject H₀. If |t calculated| ≤ t critical → fail to reject H₀.

T-Table vs Z-Table: When to Use Each