# T.INV.2T function

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

## Syntax

T.INV.2T(probability,deg_freedom)

The T.INV.2T function syntax has the following arguments:

• Probability     Required. The probability associated with the 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, T.INV.2T returns the #VALUE! error value.

• If probability <= 0 or if probability > 1, T.INV.2T returns the #NUM! error value.

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

• If deg_freedom < 1, T.INV.2T returns the #NUM! error value.

• T.INV.2T 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 T.INV.2T(0.05,10), which returns 2.28139. The one-tailed value for the same probability and degrees of freedom can be calculated with T.INV.2T(2*0.05,10), which returns 1.812462.

Given a value for probability, T.INV.2T seeks that value x such that T.DIST.2T(x, deg_freedom, 2) = probability. Thus, precision of T.INV.2T depends on precision of T.DIST.2T.

## 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 0.546449 Probability associated with the two-tailed Student's t-distribution 60 Degrees of freedom Formula Description (Result) Result =T.INV.2T(A2,A3) T-value of the Student's t-distribution for the terms above (0.606533076) 0.606533

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