Overview

Returns the probability for the T distribution (student's distribution).

Applying the Formula

All statistical formulas are calculated using the Statistics class, and the following table describes how to use its TDistribution method.

 

	Value/Description	Example
Formula Name:	T Distribution	Statistics.TDistribution (1.96, 30, true)
Parameters:	tValue: The T value for which you want the distribution. degreeOfFreedom: an integer value that represents the degree of freedom. oneTail: If true one-tailed distribution is used, otherwise two-tailed distribution is used.	Statistics.TDistribution(1.96, 30, true)
Return:	A double that represents the T cumulative distribution function probability.	-

 

Statistical Interpretation

Another important distribution that is related to the normal distribution is the t distribution. Suppose that Z and Y are independent random variables. Let Z be a standard normal random variable (mean of 0, variance of 1). And Y a chi-square variable with m degrees of freedom.

Let us make the definition:

Then it is said that the variable T has the t distribution with m degrees of freedom (The t distribution is sometimes called Students distribution).

Looking at the form of the density function provides some clues about the nature of the t distribution. Since g(x) = g(-x), it follows that the density function is symmetric about x = 0. The maximum value of g(x) occurs when x = 0:

 

Figure 1: T distribution.

 

The density function has a bell shape that is roughly similar to the standard normal distribution. A t random variable has a higher chance of being far from 0 than does a standard normal random variable. However, as the number of degrees of freedom increases the t distribution approaches very close to the standard normal distribution.

Example

The following sample calculates the T distribution probability.

See Also

 

 

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