tinv05

tinv05 is a shorthand notation encountered in statistical literature and software documentation for the critical value of the Student's t-distribution at a 5% significance level, typically in the context of a two-tailed test. The exact meaning of tinv05 can vary by context; in many cases it denotes the inverse t-distribution quantile for a given number of degrees of freedom (df) corresponding to a total alpha of 0.05. In other words, tinv05 usually represents the positive threshold t such that the probability that a t-distributed variable T with df degrees of freedom falls outside the interval (−t, t) is 0.05.

Context and computation: tinv05 is obtained by inverting the cumulative distribution function of the Student's t-distribution. Formally, t = qt(0.975, df) in common statistical computing environments, where qt is the inverse CDF of the t distribution. Several software packages express this value through functions named T.INV, T.INV.2T, qt, or t.ppf depending on the language. The result depends on df; higher df values produce thresholds closer to those of the standard normal distribution.

Example: for df = 20, tinv05 is approximately 2.086, and for df = 30, about 2.042. Note that if a one-tailed 0.05 test is intended, the corresponding tinv value would use a different p-value (0.95 instead of 0.975 in two-tailed contexts).

Notes and variability: tinv05 is not a universal constant. Its exact value depends on the chosen degrees of freedom and on whether the context requires a one-tailed or two-tailed interpretation. Users should consult the specific software documentation to confirm the meaning of tinv05 in that environment.