tinv2

Tinv2 is a statistical function used to obtain the critical value of the Student's t distribution for a two-tailed test. It returns the positive t-value such that the probability of observing an absolute value larger than that t, under a t distribution with a specified number of degrees of freedom, equals the given significance level p.

Formally, if T follows a t distribution with df degrees of freedom, tinv2(p, df) yields t such that P(|T| > t) = p. Equivalently, t = F_T^{-1}(1 − p/2), where F_T is the cumulative distribution function of the t distribution with df degrees of freedom. The function is used to determine critical values for two-tailed hypothesis tests or to construct confidence intervals.

In practice, tinv2 appears in various software implementations under names like the two-tailed inverse t function. For example, Excel provides T.INV.2T(p, df); SciPy and other statistical libraries expose equivalent functionality via t.ppf(1 − p/2, df). Typical inputs require 0 < p < 1 and df > 0. As df grows large, tinv2 approaches the corresponding z-value from the standard normal distribution. An example: tinv2(0.05, 30) yields approximately 2.04, the two-tailed critical value for a 5% significance level with 30 degrees of freedom.