Introduction to Student's t-Tests
The Student's t-test is one of the most widely used statistical tools for hypothesis testing. Introduced by William Sealy Gosset in 1908 under the pseudonym "Student," it determines whether a sample mean differs significantly from a reference value. It's ideal for scenarios with small sample sizes (N < 30) where the population standard deviation is unknown.
T-tests are generally categorized into three variants: one-sample, independent two-sample, and paired (dependent). A one-sample t-test compares a single sample mean to a known or hypothesized population mean. An independent two-sample t-test compares the means of two unrelated groups (e.g., treatment vs. placebo). A paired t-test compares means from the same group at different times (e.g., pre-test vs. post-test).
This calculator computes the one-sample t-statistic, degrees of freedom (df), and a two-tailed p-value, letting you check whether your sample mean differs significantly from a hypothesized value. It does not compute the two-sample or paired variants — see the note below.