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', the test determines whether the means of two groups are significantly different from each other. It is ideal for scenarios with small sample sizes ($N < 30$) where the population standard deviation is unknown.
T-tests are categorized into three standard variants: One-Sample, Independent Two-Sample, and Paired (Dependent) t-tests. A One-Sample t-test compares a single sample mean to a known 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 t-statistics, degrees of freedom ($df$), and p-values for one-tailed and two-tailed tests, allowing researchers and students to verify significance thresholds instantly.