The interactive t table provides critical values for the Student's t-distribution, which is used in statistical inference when sample sizes are small and population standard deviation is unknown. Hover over any value in the table to see the corresponding area highlighted in the distribution chart above. The table shows critical values for right-tailed tests. For df > 100, you can approximate using the normal distribution (Z table).
How to Use the t Table
- Find your degrees of freedom (df) in the leftmost column
- Select the desired significance level (α for one-tailed or α/2 for two-tailed tests) from the top row
- The intersection gives you the critical t-value for your test
- Hover over any value to see the corresponding area in the distribution chart
Examples of Finding Critical Values
Example 1: One-Tailed Test
Suppose you are conducting a one-tailed t-test with 12 observations (df = 11) and a significance level of α = 0.05.
- Find df = 11 in the leftmost column
- Look for the column with α = 0.05
- The critical value is 1.796
- Reject H₀ if your calculated t-statistic is greater than 1.796
R
qt(1 - 0.05, 11)
# [1] 1.795885Example 2: Two-Tailed Test
For a two-tailed test with 20 observations (df = 19) and a significance level of α = 0.05 (0.025 in each tail):
- Find df = 19 in the leftmost column
- For a two-tailed test with α = 0.05, look for the column with α/2 = 0.025
- The critical value is 2.093
- Reject H₀ if your calculated t-statistic is less than -2.093 or greater than 2.093
R
qt(1 - 0.025, 19)
# [1] 2.093024