# Documentation/Calc Functions/T.DIST

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T.DIST

## Category:

Statistical Analysis

## Summary:

Calculates values for either the probability density function or the cumulative distribution function of the Student's t-distribution (often known more simply as just the t-distribution). The Student's t-distribution is often used to test a hypothesis about a population’s mean when the population’s standard deviation is not known. The Student’s t-distribution can be used with any statistic whose distribution is approximately normal.

## Syntax:

T.DIST(Number; DegreesFreedom; Cumulative)

## Returns:

Returns a real number which is a value from the probability density function (range 0 to 0.4 exclusive) or the cumulative distribution function (range 0 to 1 exclusive) of the specified Student's t-distribution.

## Arguments:

Number is a real number or a reference to a cell containing that number which is the value for which the Student’s t-distribution is to be calculated.

DegreesFreedom is a positive integer value or a reference to a cell containing that value which is the number of degrees of freedom of the sample for the Student’s t-distribution. This is typically assumed to be the number of samples minus 1.

Cumulative can be 0 or False to calculate the probability density function. It can be any other value or True to calculate the cumulative distribution function.

• If DegreesFreedom is less than 1 then the function returns an error value.
• If DegreesFreedom is a non-integer value then the function uses its floor value, i.e. it is truncated to an integer.

## Additional details:

• For more details on probability density and cumulative distribution function of Student's t-distribution, visit Wikipedia.

## Examples:

Formula Description Returns
=T.DIST(5.8;1;TRUE()) The function calculates the cumulative distribution function for the Student's t-distribution. 0.945653294267737
=T.DIST(5.8;1;0) The function calculates the probability distribution function for the Student's t-distribution. 0.009189084474128
=T.DIST(5.8;1.5;0) The function calculates the probability distribution function for the Student's t-distribution. Here DegreesFreedom is non-integer value 1.5 so the function truncates it to integer 1. 0.009189084474128
=T.DIST(5.8;0.9;0) The function returns an error value since DegreesFreedom is less than 1. Err:502

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T.DIST