Documentation/Calc Functions/T.DIST.2T

TDF LibreOffice Document Liberation Project Community Blogs Weblate Nextcloud Redmine Ask LibreOffice Donate

Calc Functions Home | List of functions | Abbreviations

Function name:

T.DIST.2T

Category:

Statistical Analysis

Summary:

Calculates two-tailed probability values for the t-distribution. The t-distribution is often known as the Student's t-distribution.

T-distributions are a family of continuous probability distributions and each has a curve with the same general bell shape that is symmetric about 0. Each t-distribution is characterized by a parameter known as the number of degrees of freedom, often denoted by the lowercase Greek letter nu ([math]\displaystyle{ \nu }[/math]). The t-distribution approaches the normal distribution as the number of degrees of freedom increases. T-distributions are often used to model small sample sizes.

Syntax:

T.DIST.2T(Number; Degrees freedom)

Returns:

Returns a real number in the range [0, 1], which is the two-tailed probability value for the given arguments. This represents the total area under the two tails of the probability density function of the specified t-distribution and is equal to the total probability that the value of a random variable lies below -Number or above +Number.

Arguments:

Number is a non-negative real number, or a reference to a cell containing that number, which is the value at which the two-tailed probability is to be evaluated.

Degrees freedom is a positive integer, or a reference to a cell containing that number, which is the number of degrees of freedom of the t-distribution. This is typically assumed to be the number of samples minus 1.

If either Number or Degrees freedom is non-numeric, then T.DIST.2T reports a #VALUE! error.
If Number is less than 0, then T.DIST.2T reports an invalid argument error (Err:502).
If Degrees freedom is less than 1, then T.DIST.2T reports an invalid argument error (Err:502).
If Degrees freedom is a non-integer value, then T.DIST.2T truncates it to an integer value.

Additional details:

T.DIST.2T is provided for interoperability with Microsoft Excel.
Calc provides four related functions that return values from the t-distribution and these are:

T.DIST. Calculates t-distribution values from either the probability density function or the cumulative distribution function of the specified t-distribution. These are sometimes referred to as "left tailed" values.
T.DIST.2T. Calculates the total area under the two tails of the probability density function of the specified t-distribution. This represents the total probability that the value of a random variable lies below [math]\displaystyle{ -\text{ABS}(Number) }[/math] or above [math]\displaystyle{ +\text{ABS}(Number) }[/math].
T.DIST.RT. Calculates the total area under the right tail of the probability density function of the specified t-distribution. This represents the total probability that the value of a random variable lies above Number.
TDIST. A dual purpose function that can calculate either of the two types of value calculated by T.DIST.2T or T.DIST.RT.

The formula for calculating a two-tailed probability for the t-distribution is:

[math]\displaystyle{ \text{T.DIST.2T}(x;\:\nu)~=~2 \times \int_{x}^{\infty}\frac{ \Gamma\!\left(\frac{\nu +1}{2}\right)}{\sqrt{\pi\:\nu}~~\Gamma\!\left(\frac{\nu}{2}\right)}\left (1+\frac{t^2}{\nu}\right)^{ -\frac{(\nu+1)}{2}} dt }[/math]

where

[math]\displaystyle{ \Gamma }[/math] is the gamma function.
[math]\displaystyle{ \nu }[/math] is the (positive) number of degrees of freedom of the t-distribution.

Note that the random variable x in the above formula often appears as t in other sources.

The following figure shows two-tailed probability plots for four sample t-distributions.

For valid arguments, the following relationships exist with other Calc functions:

T.DIST.2T(x; y) = 2 * T.DIST(-x; y; TRUE)

T.DIST.2T(x; y) = 2 * T.DIST.RT(x; y)

T.DIST.2T(x; y) = TDIST(x; y; 2)

The name space for T.DIST.2T is COM.MICROSOFT.T.DIST.2T.
For more information on the t-distribution, visit Wikipedia's Student's t-distribution page.

Examples:

Formula	Description	Returns
=T.DIST.2T(A1; A2) where cells A1 and A2 contain the values 0.5 and 2 respectively.	Here the function calculates the two-tailed probability for the given values. Note that the formula `=T.DIST.2T(0.5; 2.9)` returns the same value because the Degrees freedom argument is truncated to an integer value.	0.666666666666667
=T.DIST.2T(0; 25)	Here the function calculates the peak value of the two-tailed probability for the t-distribution with 25 degrees of freedom. Note that if the Number argument is set to 0, a call to T.DIST.2T returns the same result for any valid value of the Degrees freedom argument.	1

Related LibreOffice functions:

ODF standard:

None

Related (or similar) Excel functions:

T.DIST.2T