Appendix 10: The t-Table (Critical Values for Student's t Distribution)

This appendix provides critical t-values for hypothesis testing (e.g., one-sample or independent t-tests) at common significance levels. Use it to determine if your calculated t-statistic indicates a significant difference (reject null hypothesis when |t| > critical value).

How to Use the t-Table

• Left column: Degrees of freedom (df) — usually n-1 for one-sample or n₁ + n₂ - 2 for two independent samples.
• Top row: Significance level (p, one-tailed or two-tailed depending on test).
• Find the intersection value = critical t.
• If your |calculated t| > critical t → reject null hypothesis (significant at that p level).
• For two-tailed tests, use p/2 values (e.g., for α=0.05 two-tailed, use 0.025 column).

Example 1 (from page content)

Two independent groups, 10 subjects each → df = 18.

Calculated t = 4.51.

Look up df = 18, p = 0.05 → critical t = 1.734.

4.51 > 1.734 → significant difference (p < 0.05). Reject null hypothesis: means differ.

Example 2

One-sample t-test, n = 25 → df = 24.

Calculated t = 2.15.

Look up df = 24, p = 0.05 → critical t = 1.711 (one-tailed) or use 0.025 column = 2.064 (two-tailed).

If one-tailed: 2.15 > 1.711 → significant. If two-tailed: 2.15 > 2.064 → significant.

t Critical Values Table

Tip: For exact p-values or larger df, use software (Excel: T.INV.2T, Google Sheets, R: qt()). See Appendix 5 for technology tips.

Related: Lesson 6 — The t-test • Lesson 7 — Analysis of Variance (ANOVA)