This tool performs Student’s t-tests for comparing means. Choose from one-sample, paired, or independent two-sample tests with automatic p-value computation.
How to Use
- Select test type: One-Sample, Paired, or Two-Sample (Independent).
- Enter your data in the text area(s) — numbers separated by commas, spaces, or new lines.
- For a one-sample test, set the hypothesized mean (defaults to 0).
- Click Calculate to see the t-statistic, degrees of freedom, p-value, confidence interval, and Cohen’s d.
Test Types
- One-Sample: Tests whether the mean of a single sample differs from a hypothesized value (μ₀).
- Paired: Tests whether the mean difference between paired observations is zero. Both samples must have the same length.
- Two-Sample (Independent): Tests whether the means of two independent groups differ. Uses Welch’s correction when variances are unequal (F-ratio > 3); otherwise assumes equal variances with pooled standard error.
Output Values
- t-statistic: The test statistic — larger absolute values indicate stronger evidence against the null hypothesis.
- Degrees of Freedom (df): Determines the t-distribution used for the p-value. Welch’s df may be fractional.
- p-value (two-tailed): Probability of observing a test statistic at least as extreme as yours, assuming the null hypothesis is true. Lower values indicate stronger evidence against the null.
- 95% CI for the difference: The range of plausible values for the true mean difference at 95% confidence.
- Cohen’s d: Standardised effect size — 0.2 = small, 0.5 = medium, 0.8 = large.
