CONFIDENCE.T DAX Function (Statistical)
Returns the confidence interval for a population mean, using a Student’s t distribution.
Syntax
| Parameter | Attributes | Description |
|---|---|---|
| Alpha |
The significance level used to compute the confidence level. The confidence level equals 100*(1 – alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level. |
|
| Standard_dev |
The population standard deviation for the data range and is assumed to be known. |
|
| Size |
The sample size. |
Return values
The half-width of the confidence interval, in the same unit as Standard_dev. The interval goes from the sample mean minus this value to the sample mean plus this value.
Remarks
The confidence interval is a range of values. The sample mean is at the center of this range, and the range is the sample mean ± CONFIDENCE.T.
CONFIDENCE.T uses the Student’s t distribution with Size – 1 degrees of freedom. It multiplies the two-tailed critical value of this distribution for Alpha by Standard_dev / SQRT ( Size ). For example, CONFIDENCE.T ( 0.05, 1, 50 ) returns the same value as T.INV.2T ( 0.05, 49 ) / SQRT ( 50 ), about 0.284. Use CONFIDENCE.T when the standard deviation comes from a small sample. When Size increases, the result gets closer to the result of CONFIDENCE.NORM.
CONFIDENCE.T rounds a decimal Size to the nearest integer. For example, 1.5 gives the same result as 2, and 49.4 gives the same result as 49.
CONFIDENCE.T returns an error in these conditions:
– Alpha is 0 or less, or 1 or more.
– Standard_dev is 0 or less.
– Size is less than 2 after rounding.
– An argument is text that cannot be converted to a number.
A BLANK argument is treated as 0. Therefore, a BLANK argument always returns an error.
Examples
-- CONFIDENCE.NORM returns the confidence interval
-- for a population mean, assuming a normal distribution
-- CONFIDENCE.T uses a Student's T distribution instead
--
-- CONFIDENCE.NORM ( Alpha, StandardDev, SampleSize )
--
-- Confidence level equals 100*(1-alpha)%
-- Alpha 0.05 indicates a 95% confidence level
DEFINE
TABLE SampleData = { 2, 4, 4, 4, 5, 5, 7, 9 }
VAR Mean = AVERAGE ( SampleData[Value] )
VAR StandardDev = STDEV.S ( SampleData[Value] )
VAR SampleSize = COUNTROWS ( SampleData )
VAR Alpha = 0.05 -- 95% confidence level
EVALUATE
{
( "AVERAGE", Mean ),
( "STDEV.S", StandardDev ),
( "CONFIDENCE.NORM", CONFIDENCE.NORM ( Alpha, StandardDev, SampleSize ) ),
( "CONFIDENCE.T", CONFIDENCE.T ( Alpha, StandardDev, SampleSize ) )
}
| Value1 | Value2 |
|---|---|
| AVERAGE | 5.00 |
| STDEV.S | 2.14 |
| CONFIDENCE.NORM | 1.48 |
| CONFIDENCE.T | 1.79 |
Last update: Oct 31, 2026 » Contribute » Show contributors
Contributors: Alberto Ferrari, Marco Russo
Microsoft documentation: https://learn.microsoft.com/en-us/dax/confidence-t-function-dax