# TINV function

Returns the t-value of the Student's t-distribution as a function of the probability and the degrees of freedom.

## Syntax

TINV(probability,degrees_freedom)

Probability     is the probability associated with the two-tailed Student's t-distribution.

Degrees_freedom     is the number of degrees of freedom to characterize the distribution.

## Remarks

• If either argument is nonnumeric, TINV returns the #VALUE! error value.

• If probability < 0 or if probability > 1, TINV returns the #NUM! error value.

• If degrees_freedom is not an integer, it is truncated.

• If degrees_freedom < 1, TINV returns the #NUM! error value.

• TINV is calculated as TINV = p( t<X ), where X is a random variable that follows the t-distribution.

• A one-tailed t-value can be returned by replacing probability with 2*probability. For a probability of 0.05 and degrees of freedom of 10, the two-tailed value is calculated with TINV(0.05,10), which returns 2.28139. The one-tailed value for the same probability and degrees of freedom can be calculated with TINV(2*0.05,10), which returns 1.812462. In some tables, probability is described as (1-p).

TINV uses an iterative technique for calculating the function. Given a probability value, TINV iterates until the result is accurate to within ± 3x10^-7. If TINV does not converge after 100 iterations, the function returns the #N/A error value.

## Example

Probability

Degrees

Formula

Description (Result)

0.054645

60

=TINV([Probability],[Degrees])

t-value of the Student's t-distribution for the specified arguments (1.959997462)

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