A test for comparing the means of two samples, or the mean of one sample (or even parameter estimates) with a specified value; also known as the "Student t-test" after the pseudonym of its inventor.

A statistical test is a t-test, if it meets the following criteria: (1) It compares a sample statistic to a reference value, (2) divides the difference by a standard error, (3) whose variance is estimated from the same data (i.e., there is some uncertainty about its value), and (4) has a result that is distributed as t. The prototypical example of a t-test is comparing the means of two samples, for example: $$ t=\frac{\bar X_1-\bar X_2}{\sqrt{s^2_\text{pooled}\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} $$ This specific example applies only to cases where the variances are equal, the samples are independent, and the reference value is $0$. However, the t-test is broader; there are versions that address single samples, specified reference values, unequal group variances, and dependent samples. The t-test is also used in other settings, such as to assess parameter estimates (i.e., $\hat\beta$s) in linear models.

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