# 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 (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• 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

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

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

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses