t is the distribution of the t-statistic that results from a t-test. Use this tag only for questions about the distribution; use [t-test] for questions about the test.
$t$ is the name of a continuous probability distribution that describes the sampling distribution of an asymptotically normally-distributed inferential statistic when the variance must be estimated from the data and the sample size is sufficiently small that the variance estimate contains a large amount of uncertainty. As the sample size increases, such estimates of the variance become less uncertain and the $t$-distribution converges to the normal. A common rule of thumb is that when the sample size $\ge30$, $t$ is approximately normal.
The pdf of the $t$ distribution is: $$ t=\frac{\Gamma\left(\frac{\nu+1}{2}\right)}{\sqrt{\nu\pi}(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu}\right)^{-\frac{\nu+1}{2}} $$ The $t$-distribution has only one parameter, $\nu$, which is the degrees of freedom.
Use this tag for questions about the $t$-distribution; use t-test for questions about the test.
