Definition
A t-test is a statistical test used to compare the means of two groups and determine whether the difference between them is statistically significant. It is one of the most commonly used hypothesis tests for numerical data.
Types of T-Tests
There are three main types, each suited to a different situation.
A company wants to know if a new training program improves employee performance.
Before training: average score = 72 (n = 30)
After training: average score = 78 (n = 30)
A paired t-test (same employees measured twice) gives p = 0.01. The improvement is statistically significant.
If instead the company compared trained employees to a separate untrained group, they would use an independent t-test.
Why It Matters
The t-test is the workhorse of statistical comparison. Researchers use it to test whether a drug lowers blood pressure, whether a teaching method improves test scores, or whether a website change affects conversion rates.
The t-test was developed by William Sealy Gosset in 1908 for quality control at the Guinness brewery. It is designed specifically for small samples where the population standard deviation is unknown, making it practical for real-world situations where you rarely have perfect information.
The t-test compares two group means. Choose paired t-tests for before/after comparisons and independent t-tests for separate groups.