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T Table (Student's t-Distribution)

Critical values for one-tailed and two-tailed t-tests at common significance levels (α = 0.10, 0.05, 0.025, 0.01, 0.005).

Student's t-Distribution Critical Values
Two-tailed α levels shown
df α = 0.20 (two-tail) α = 0.10 (two-tail) α = 0.05 (two-tail) α = 0.02 (two-tail) α = 0.01 (two-tail) α = 0.002 (two-tail) α = 0.001 (two-tail)

How to Use the T Table

The t-distribution table gives critical values for the t-distribution. When conducting a t-test, you compare your calculated t-statistic to the critical value to decide whether to reject the null hypothesis.

Steps

  1. Determine your degrees of freedom (df). For a one-sample t-test: df = n − 1
  2. Choose your significance level (α). Common values: 0.05 or 0.01
  3. Find the row for your df
  4. Find the column for your α level (one-tailed or two-tailed)
  5. If |t-statistic| > critical value → reject the null hypothesis
Example

You run a one-sample t-test with n = 15 (df = 14) and α = 0.05 (two-tailed).

From the table: Critical value = 2.145

If your t-statistic is 2.8 (|2.8| > 2.145), you reject the null hypothesis at α = 0.05.

Note: As degrees of freedom increase toward infinity, the t-distribution approaches the standard normal distribution. At df = ∞, the critical value for α = 0.05 (two-tailed) is exactly 1.960 — the same as the Z-table.

FAQ

When do I use the t-distribution instead of the z-distribution?
Use the t-distribution when: (1) your sample size is small (n < 30), (2) the population standard deviation is unknown (which is almost always in practice), or (3) both conditions apply. The t-distribution has heavier tails than the normal distribution, which accounts for the extra uncertainty from estimating the population standard deviation.
What are degrees of freedom?
Degrees of freedom (df) represent the number of independent pieces of information used to estimate a parameter. For a one-sample t-test, df = n − 1. For an independent samples t-test, df = n₁ + n₂ − 2. The concept captures how many values in a dataset are "free to vary" after constraints are imposed.
What's the difference between one-tailed and two-tailed tests?
A two-tailed test checks for differences in either direction (is X different from Y?). A one-tailed test checks for differences in only one direction (is X greater than Y?). For a two-tailed test at α = 0.05, use the α = 0.05 column. For a one-tailed test at α = 0.05, use the α = 0.10 column (since one-tailed α = 0.05 corresponds to two-tailed α = 0.10).