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.

Syntax: 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%.

 

Tdist Function Errors

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

#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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