The Excel TDIST Function

Related Function:
TINV Function

TDIST, T.DIST.RT & T.DIST.2T

In Excel 2010, the TDIST function has been replaced by two functions, the T.DIST.RT function (which calculates the right-tailed Student's T-Distribution), and the T.DIST.2T function (calculates the two-tailed Student's T-Distribution).

The Excel 2010 T.DIST.RT has an advantage over the TDIST function, in that it can accept negative values of x. Therefore, although the TDIST function has been kept in Excel 2010 (for compatibility with earlier versions of Excel), if you have Excel 2010, the T.DIST.RT or the T.DIST.2T should be used rather than the TDIST function.



Basic Description

The Excel TDIST function calculates the Student's T Distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

The format of the function is :

TDIST( x, degrees_freedom, tails )

where the function arguments are:

x - The value at which you want to evaluate the Student's T Distribution
degrees_freedom - The number of degrees of freedom (must be ≥ 1)
tails - The number of tails for the distribution. This must be either :
1 - returns the one-tailed distribution
2 - returns the two-tailed distribution

Note that the Excel Tdist Function doesn't allow the argument x to be < 0. Therefore, if you want to calculate the Student's T Distribution for values of x that are < 0, you should use the relationships :

TDIST( -x, df, 1 ) = 1 - TDIST( x, df, 1 )

and

TDIST( -x, df, 2 ) = TDIST( x, df, 2 )

Tdist Function Examples

Example 1

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

The chart on the right shows the 1-tailed 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 Tdist function, as follows:

=TDIST( 1, 10, 1 )

This gives the result 0.170446566, or 17.04%


If you want to calculate the value of the function, at x = -1, this must be done using the relationship TDIST( -x, df, 1 ) = 1-TDIST( x, df, 1 ). Therefore, the formula to calculate the function at x = -1 is :

=1-TDIST( 1, 10, 1 )

This gives the result 0.829553434, or 82.96%.


Example 2

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

The chart on the right shows the two-tailed 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 Tdist function, as follows:

=TDIST( 1, 10, 2 )

This gives the result 0.340893132, or 34.09%.


If you want to calculate the value of the function, at x = -1, this must be done using the relationship TDIST( -x, df, 2 ) = TDIST( x, df, 2 ). Therefore, the formula to calculate the function at x = -1 is simply :

=TDIST( 1, 10, 2 )

which, as shown above, gives the result 0.340893132, or 34.09%.


Further information and examples of the Excel Tdist function can be found on the Microsoft Office website.


Tdist Function Errors

If you get an error from your Excel Tdist function this is likely to be one of the following:

Common Errors
#NUM! - Occurs if either:
- the supplied x argument is < 0
or
- the supplied degrees_freedom argument is < 1
or
- the supplied tails argument is not equal to 1 or 2
#VALUE! - Occurs if any of the supplied arguments are non-numeric
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