Use this t-Statistic Calculator to calculate the t value, standard error, and degrees of freedom for one-sample, independent two-sample, Welch, pooled, or paired data.

Calculation Methods

One-sample:

t = (x̄ − μ₀) ÷ (s ÷ √n)

Welch two-sample:

t = (x̄₁ − x̄₂) ÷ √(s₁²/n₁ + s₂²/n₂)

Pooled two-sample:

t = (x̄₁ − x̄₂) ÷ [sₚ × √(1/n₁ + 1/n₂)]

For paired data, calculate the difference within each pair and run a one-sample t calculation on those differences.

Example

Suppose a sample has a mean of 12, hypothesized mean of 10, standard deviation of 4, and sample size of 16.

SE = 4 ÷ √16 = 1

t = (12 − 10) ÷ 1 = 2.00

df = 16 − 1 = 15

Important Note

The t statistic alone does not determine statistical significance. A full hypothesis test also requires degrees of freedom, test direction, a p-value or critical value, and appropriate assumptions.

Use paired mode only for matched observations. For independent groups, Welch’s method is generally preferable when equal population variances cannot be justified.

Sources

• NIST/SEMATECH — t-Test
• NIST/SEMATECH — Two-Sample t-Test for Equal Means