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Command Summary

Calculates the inverse of the cumulative [*https://en.wikipedia.org/wiki/Student%27s_t-distribution Student's t-distribution] function with degrees of freedom ν.

Command Syntax

invT(probability, ν)

Menu Location


  1. 2ND DISTR to access the distribution menu
  2. 4 to select invT(, or use arrows.

Calculator Compatibility

TI-84+/SE (OS 2.30 or greater)

Token Size

2 bytes

invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom ν, it will return the number x such that tcdf(-E99,x,ν) is equal to p



invT( is meant for use with so-called "one-tailed' tests; for two-tailed tests, the proper expression to use (corresponding to the inverse of tcdf(-x,x,ν)) is invT(.5(1+p),ν)


Unlike the Tpdf( and Tcdf( commands, the invT( command does not have a closed-form formula. However, it can be expressed in terms of the inverse incomplete beta function.

For one degree of freedom, invT( is expressible in terms of simpler functions:

<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right) </math>

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