T.DIST Function

Basic Description

The Excel T.DIST function calculates the one-tailed Student’s T Distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets. The T.DIST function is new to Excel 2010 and so is not available in earlier versions of Excel.

Syntax: T.DIST( x, degrees_freedom, cumulative )

where the function arguments are:

x The value at which you want to evaluate the distribution
degrees_freedom The number of degrees of freedom (must be ≥ 1)
cumulative A logical argument which denotes the type of distribution to be used:

TRUE = Cumulative Distribution Function
FALSE = Probability Density Function

 

Plot of 1-Tailed Cumulative Student's T Distribution with 10 Degrees of Freedom

Cumulative Student’s T-Distribution with 10 Degrees of Freedom

T.Dist Function Examples

Example 1

The chart on the right shows the one-tailed cumulative Student’s T Distribution with 10 degrees of freedom.

If you want to calculate the value of this function at x = 1, this can be done using the Excel T.Dist function, as follows:

=T.DIST( 1, 10, TRUE )

This gives the result 0.829553434, or 82.96%.

Plot of 2-Tailed Student's T Distribution with 10 Degrees of Freedom

Probability Density Function with 10 Degrees of Freedom

Example 2

The chart on the right shows the one-tailed probability density function for the Student’s T Distribution, with 10 degrees of freedom.

If you want to calculate the value of this function at x = -1, this can be done using the Excel T.Dist function, as follows:

=T.DIST( -1, 10, FALSE )

This gives the result 0.230361989, or 23.04%.


Common Errors

If you get an error from the Excel T.Dist function this is likely to be one of the following:

#NUM! Occurs if cumulative is TRUE and the supplied degrees_freedom argument is < 1
#DIV/0! Occurs if cumulative is FALSE and the supplied degrees_freedom argument is < 1
#VALUE! Occurs if any of the supplied arguments are non-numeric

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