Documentation/Calc Functions/T.DIST.RT
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Function name:
T.DIST.RT
Category:
Statistical Analysis
Summary:
Calculates right tail 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.RT(Number; Degrees freedom)
Returns:
Returns a real number in the range [0, 1], which is the right tail probability value for the given arguments. This represents the total area under the right tail 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 above Number.
Arguments:
Number is a real number, or a reference to a cell containing that number, which is the value at which the right tail 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.RT reports a #VALUE! error.
- If Degrees freedom is less than 1, then T.DIST.RT reports an invalid argument error (Err:502).
- If Degrees freedom is a non-integer value, then T.DIST.RT truncates it to an integer value.
Additional details:
- T.DIST.RT 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 right tail probability for the t-distribution is:
- [math]\displaystyle{ \text{T.DIST.RT}(x;\:\nu)~=~\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 right tail probability plots for four sample t-distributions.
- For valid arguments, the following relationships exist with other Calc functions:
T.DIST.RT(x; y) = 0.5 * T.DIST.2T(x; y)
T.DIST.RT(x; y) = TDIST(x; y; 1)
T.DIST.RT(x; y) = 1 - T.DIST(x; y; TRUE)
- Also note that for valid arguments:
T.DIST.RT(x; y) + T.DIST.RT(-x; y) = 1
- The name space for T.DIST.RT is
COM.MICROSOFT.T.DIST.RT
. - For more information on the t-distribution, visit Wikipedia's Student's t-distribution page.
Examples:
Formula | Description | Returns |
---|---|---|
=T.DIST.RT(A1; A2) where cells A1 and A2 contain the values 0.5 and 2 respectively. | Here the function calculates the right tail probability for the given values. Note that the formula =T.DIST.RT(0.5; 2.9) returns the same value because the Degrees freedom argument is truncated to an integer value. |
0.333333333333333 |
=T.DIST.RT(-1.5; 5) | Here the function calculates the right tail probability for a negative value of the Number argument. | 0.903048159878763 |
=T.DIST.RT(0; 25) | Here the function calculates the value of the right tail probability when the Number argument is set to 0. Note that with Number equal to 0, a call to T.DIST.RT returns the same result for any valid value of the Degrees freedom argument. | 0.5 |
=T.DIST.RT(1.5; 5) | Here the function calculates the right tail probability for a positive value of the Number argument. Note from a previous example that the formula =T.DIST.RT(-1.5; 5) + T.DIST.RT(1.5; 5) returns 1. |
0.0969518401212368 |
Related LibreOffice functions:
ODF standard:
None
Related (or similar) Excel functions:
T.DIST.RT