Tdist function

This article describes the formula syntax and usage of the TDIST function in Microsoft Excel.

Description

Returns the Percentage Points (probability) for the Student t-distribution where a numeric value (x) is a calculated value of t for which the Percentage Points are to be computed. The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the 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.DIST.2T function and T.DIST.RT function.

Syntax

TDIST(x,deg_freedom,tails)

The TDIST function syntax has the following arguments:

• X     Required. The numeric value at which to evaluate the distribution.

• Deg_freedom     Required. An integer indicating the number of degrees of freedom.

• Tails     Required. Specifies the number of distribution tails to return. If Tails = 1, TDIST returns the one-tailed distribution. If Tails = 2, TDIST returns the two-tailed distribution.

Remarks

• If any argument is non-numeric, TDIST returns the #VALUE! error value.

• If Deg_freedom < 1, TDIST returns the #NUM! error value.

• The Deg_freedom and Tails arguments are truncated to integers.

• If Tails is any value other than 1 or 2, TDIST returns the #NUM! error value.

• If x < 0, then TDIST returns the #NUM! error value.

• If Tails = 1, TDIST is calculated as TDIST = P( X>x ), where X is a random variable that follows the t-distribution. If Tails = 2, TDIST is calculated as TDIST = P(|X| > x) = P(X > x or X < -x).

• Since x < 0 is not allowed, to use TDIST when x < 0, note that TDIST(-x,df,1) = 1 – TDIST(x,df,1) = P(X > -x) and TDIST(-x,df,2) = TDIST(x,df,2) = P(|X| > x).

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
1.959999998	Value at which to evaluate the distribution
60	Degrees of freedom
Formula	Description (Result)	Result
=TDIST(A2,A3,2)	Two-tailed distribution (0.054644930, or 5.46 percent)	5.46%
=TDIST(A2,A3,1)	One-tailed distribution (0.027322465 or 2.73 percent)	2.73%

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