# TINV function

Returns the two-tailed inverse of the Student's t-distribution.

Important: This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

For more information about the new functions, see T.INV.2T function or T.INV function.

## Syntax

TINV(probability,deg_freedom)

The TINV function syntax has the following arguments:

• Probability     Required. The probability associated with the two-tailed Student's t-distribution.

• Deg_freedom     Required. The number of degrees of freedom with which 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 deg_freedom is not an integer, it is truncated.

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

• TINV returns that value t, such that P(|X| > t) = probability where X is a random variable that follows the t-distribution and P(|X| > t) = P(X < -t or X > t).

• 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.

Note:  In some tables, probability is described as (1-p).

Given a value for probability, TINV seeks that value x such that TDIST(x, deg_freedom, 2) = probability. Thus, precision of TINV depends on precision of TDIST. TINV uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error value.

## Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 Data Description 0.05464 Probability associated with the Student's two-tailed t-distribution 60 Degrees of freedom Formula Description Result =TINV(A2,A3) The t-value of the Student's t-distribution based on the arguments in A2 and A3. 1.96
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