# TINV Function

#### Basic Description

The Excel TINV function calculates the inverse of the two-tailed Student’s T Distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

**Syntax:** TINV( probability, degrees_freedom )

Where the function arguments are listed in the table below:

probability | – | The probability (between 0 and 1) for which you want to evaluate the inverse of the Student’s T Distribution. |

degrees_freedom | – | The number of degrees of freedom (must be ≥ 1) |

Excel uses an iterative method to calculate the Tinv function and seeks to find a result, x, such that TDIST( x, degrees_freedom, 2 ) = probability.

Note that the Excel Tinv Function calculates the inverse of the two-tailed Student’s T Distribution. – if you want to calculate the inverse of the one-tailed t-distribution you can simply double the probability. ie. The one-tailed inverse Student’s T Distribution = TINV( 2*probability, degrees_freedom ).

#### Tinv Function Examples

The chart on the right shows the 2-tailed Inverse Student’s T Distribution with 10 degrees of freedom.

If you want to calculate the value of this function for a probability of 0.25, this can be done using the Excel Tinv function, as follows:

=TINV( 0.25, 10 )

This gives the result *1.221255395*.

If you want to calculate the value of the one-tailed inverse Student’s T-Distribution for a Probability of 0.25, this can be done by doubling the probability, as follows :

=TINV( 0.5, 10 )

This gives the result *0.699812061*.

#### Tinv Function Errors

If you get an error from your Excel Tinv function this is likely to be one of the following :

#NUM! | – | Occurs if either The supplied probability argument is < 0 or > 1 or the supplied degrees_freedom argument is < 1 |

#VALUE! | – | Occurs if either of the supplied arguments are non-numeric |