One-Sample T-Test Calculator
One-Sample T-Test Calculator
Enter your sample's mean, standard deviation, and size, along with the value you're testing it against (e.g. a claimed population average, a target, or a previous benchmark). Choose whether you're testing for any difference (two-tailed) or specifically a higher or lower value (one-tailed). This calculates the t-statistic and its p-value.
- Formula: t = (sample mean − hypothesized mean) ÷ (standard deviation ÷ √n), with degrees of freedom = n − 1.
- Small p-value = strong evidence against the hypothesis: a p-value below your chosen significance threshold (commonly 0.05) suggests the observed difference is unlikely to be due to chance alone.
- Two-tailed vs. one-tailed: choose two-tailed when you just want to know if the means differ at all; choose one-tailed only when you have a specific directional claim decided in advance (e.g. "the new process takes less time," not just "different").
What does the p-value from this test actually tell me?
It's the probability of observing a difference at least this large, purely by random chance, if the hypothesized mean were actually true — it does not tell you the probability that your hypothesis is correct.
Should I always use a two-tailed test?
Two-tailed is the safer, more common default since it tests for any difference in either direction — only switch to one-tailed if you had a specific direction in mind before collecting your data, since choosing it afterward to get a smaller p-value is a form of bias.
One-Sample T-Test Calculator
Enter your sample's mean, standard deviation, and size, along with the value you're testing it against (e.g. a claimed population average, a target, or a previous benchmark). Choose whether you're testing for any difference (two-tailed) or specifically a higher or lower value (one-tailed). This calculates the t-statistic and its p-value.
- Formula: t = (sample mean − hypothesized mean) ÷ (standard deviation ÷ √n), with degrees of freedom = n − 1.
- Small p-value = strong evidence against the hypothesis: a p-value below your chosen significance threshold (commonly 0.05) suggests the observed difference is unlikely to be due to chance alone.
- Two-tailed vs. one-tailed: choose two-tailed when you just want to know if the means differ at all; choose one-tailed only when you have a specific directional claim decided in advance (e.g. "the new process takes less time," not just "different").
What does the p-value from this test actually tell me?
It's the probability of observing a difference at least this large, purely by random chance, if the hypothesized mean were actually true — it does not tell you the probability that your hypothesis is correct.
Should I always use a two-tailed test?
Two-tailed is the safer, more common default since it tests for any difference in either direction — only switch to one-tailed if you had a specific direction in mind before collecting your data, since choosing it afterward to get a smaller p-value is a form of bias.