t model visualization (updates with df)
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The shaded area updates after calculation.
When this method applies
Use this calculator when:
- The two samples are independent.
- The population standard deviations are unknown and not assumed equal.
- At least one condition is met: both samples are large (n₁ ≥ 30 and n₂ ≥ 30) or the populations are (approximately) normal.
Key formulas used
\[
\begin{aligned}
s_{\bar{x}_1-\bar{x}_2} &= \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \\
df &= \frac{\left(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1-1}+\frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}}
\end{aligned}
\]
Degrees of freedom are rounded down to an integer.
Enter values and click Calculate.
Batch mode: paste CSV data (compute many rows at once)
Paste rows as CSV (comma-separated). Header is optional. Supported columns:
x1, x2, s1, s2, n1, n2,
and (optional) conf, alpha, delta0, alt (two/gt/lt), task (ci/ht).