# T.INV.2T function

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

## Syntax

T.INV.2T(probability,deg_freedom)

Argument

Description

Remarks

probability

The probability that is associated with the Student's t-distribution.

• If this argument is equal to or less than zero, this function returns the #NUM! error value.

• If this argument is greater than 1, this function returns the #NUM! error value.

• If this argument is nonnumeric, this function returns the #VALUE! error value.

deg_freedom

The number of degrees of freedom with which to characterize the distribution.

• If this argument is less than 1, this function returns the #NUM! error value.

• If this argument is nonnumeric, this function returns the #VALUE! error value.

• If this argument contains a decimal value, this function ignores the numbers to the right side of the decimal point.

## General remarks

• 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

To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.

 1 2 3
 A B Data Description 0.0546449 Probability that is associated with the two-tailed Student's t-distribution 60 Degrees of freedom Formula Description (Result) =T.INV.2T(A2,A3) The t-value of the Student's t-distribution for the terms in the table (0.117685)
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