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.

Syntax: 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.

1 =CONFIDENCE( 0.05, 0.07, 100 )

The above function returns a confidence value of 0.013719748
Therefore the confidence interval is 1.8 ± 0.013719748, which is equal to the range 1.786280252 to 1.813719748


Confidence Function Common Errors

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

#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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