One-Sample T-Test Calculator

A T-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, or between a sample mean and a known population mean, when the population standard deviation is unknown and the sample size is relatively small. It’s commonly used in hypothesis testing to assess if a treatment or intervention has a significant effect.

You should use a T-test instead of a Z-test when the population standard deviation is unknown and you are working with a small sample size (typically less than 30). A Z-test is appropriate when the population standard deviation is known and/or the sample size is large (generally n ≥ 30), allowing the Central Limit Theorem to apply.

The main types of T-tests include the one-sample T-test, which compares a sample mean to a known population mean; the independent samples T-test (or two-sample T-test), which compares the means of two independent groups; and the paired samples T-test (or dependent T-test), which compares means from the same group at different times or under different conditions.

To interpret a T-test result, you compare the calculated t-statistic to a critical t-value from a t-distribution table, or more commonly, you look at the p-value. If the p-value is less than your chosen significance level (e.g., 0.05), you reject the null hypothesis, concluding there is a statistically significant difference between the means. If the p-value is greater, you fail to reject the null hypothesis, meaning there isn’t enough evidence for a significant difference.