A one-sample t-test: how far your sample's average sits, in standard errors, from a number you're testing it against.
Recalculated live from the four fields to the left; only your browser sees them.
The one-sample t-test determines whether a sample mean is significantly different from a known or hypothesized population mean. It is appropriate when the population standard deviation is unknown and you are estimating it from the sample instead.
For the defaults (x-bar = 52, mu = 50, s = 5, n = 30): SE = 5 / sqrt(30) = 0.9129; t = (52 - 50) / 0.9129 = 2.191; df = 29. With 29 degrees of freedom, a t of 2.191 exceeds the critical value of 2.045 at alpha = 0.05 two-tailed, so the result would be statistically significant at that threshold.
These are the standard published Student's t critical values, not something this calculator looks up on its own; use them to judge your own t-statistic by eye before running it through the p-value calculator for an exact figure:
Notice the critical value creeps down toward 1.96 as degrees of freedom grow: with enough data the t-distribution converges on the normal curve, which is why the z-score calculator's 1.96 threshold and this table's tail end line up. Source: standard Student's t-distribution tables, consistent with NIST's Engineering Statistics Handbook.
One-sample only. It compares the mean of a single sample against a hypothesized or known population mean. It does not implement a two-sample or Welch's t-test, which compares two independent samples against each other and needs both groups' means, standard deviations, and sizes.
Degrees of freedom for a one-sample t-test is n minus 1. The example uses a sample size of 30, so 30 minus 1 leaves 29 degrees of freedom, which is what the t-distribution's shape depends on.
That field is the value you're testing against, not something you look up. It might be a manufacturer's claimed spec, a historical average, or a target from a previous study. The test asks whether your sample's mean is different enough from that specific number to matter.
Compare the absolute value of your t-statistic to a critical value from a t-table at your degrees of freedom and chosen significance level; the reference table above has common ones. This calculator reports the t-statistic itself but does not flag significance automatically. For an exact p-value from your t-statistic and degrees of freedom, use the p-value calculator.