Properties of t-values

Question

Does anyone know what the properties of t-values are?

As I know it's just the ration $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$$ which follows a t-distribution.

Used in mean-comparison tests and as a consequence also to check the significance of single independent variables in regression analysis. To generalize, t-values are used for hypothesis testing. Am I right with these properties? Thanks!

Answer 1

I think of properties as intrinsic to something, not as a function of how it is used. To rattle off a few properties:

1. It approaches cauchy distribution as df $\rightarrow0$
2. Is approaches a normal (0,1) distrbution as df $\rightarrow \infty$
3. It is symmetric and relatively light tailed compared to a normal RV with equivalent mean and variance (not to be confused with the fact that it produces wider confidence intervals)