The Excel CONFIDENCE Function

Confidence Interval
In statistics, the confidence interval is the range that a population parameter is likely to fall into, for a given probability.

Eg. For given population and a probability of 95%, the confidence interval is the range, in which a population parameter is 95% likely to fall.

Note that the accuracy of the confidence interval relies on the population having a normal distribution.

The Confidence Interval is discussed further on the Wikipedia Confidence Interval Page
Confidence and Confidence.Norm Functions

In Excel 2010, the CONFIDENCE function has been renamed CONFIDENCE.NORM.

Although the Confidence function has been replaced, Excel 2010 has kept this function, (stored within the list of compatibility functions), for compatibility with earlier versions of Excel.



Basic Description

The Excel CONFIDENCE function uses a Normal Distribution to calculate a confidence value that can be used to construct the confidence interval for a population mean, for a supplied probablity and sample size. It is assumed that the standard deviation of the population is known.

The format of the function is :

CONFIDENCE( alpha, standard_dev, size )

where the arguments are as follows :

alpha - The significance level (=1-confidence level)
- eg. a significance level of 0.05 equates to a confidence level of 95%
standard_dev - The standard deviation of the population
size - The population sample size

To calculate the confidence interval for a population mean, the returned CONFIDENCE value must then be added to, and subtracted from, the sample mean. ie. for the sample mean x :

Confidence Interval = x ± CONFIDENCE


Confidence Function Example

In the spreadsheet below, the Excel Confidence Function is used to calculate the confidence interval, with a significance of 0.05 (ie. a confidence level of 95%), for the mean of a sample of heights of 100 men. The sample mean is 1.8 meters and the standard deviation is 0.07 meters.

  A
1 =CONFIDENCE( 0.05, 0.07, 100 )
2  

The above function returns a confidence value of 0.013719748

Therefore the confidence interval is 1.8 ± 0.013719748, which is equal to :

1.786280252 to 1.813719748


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


Confidence Function Common Errors

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

Common Errors
#NUM! - Occurs if either:
- the supplied alpha is ≤ 0 or ≥ 1
or
- the supplied standard_dev is ≤ 0
or
- the supplied size argument is < 1
#VALUE! - Occurs if any of the supplied arguments are non-numeric
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