# A to Z of Excel Functions: the CONFIDENCE Function

25 September 2017

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the CONFIDENCE function. *

**The CONFIDENCE function**

Do you need more **CONFIDENCE** in your Excel files? This function returns the confidence interval for a population mean, using the theory associated with the normal distribution.

To explain: the confidence interval is a range of values around a sample mean, **x**, which sits at the centre of this range, *i.e. *the range is **x** ± **CONFIDENCE**. For example, if **x** is the sample mean of delivery times for products ordered through the mail, **x ± CONFIDENCE** is a range of population means.

For any population mean, **μ _{0}**, in this range, the probability of obtaining a sample mean further from

**μ**than

_{0}**x**is greater than the significance level required,

**alpha**; for any population mean,

**μ**, not in this range, the probability of obtaining a sample mean further from

_{0}**μ**than

_{0}**x**is less than this level,

**alpha**. In other words, assume that we use

**x**, a standard deviation

**standard_dev**, and

**size**to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is

**μ**. Then we will not reject that hypothesis if

_{0}**μ**is in the confidence interval and will reject that hypothesis if

_{0}**μ**is not in the confidence interval. The confidence interval does not allow us to infer that there is probability

_{0}**1 – alpha**that our next package will take a delivery time that is in the confidence interval.

The **CONFIDENCE **function employs the following syntax to operate:

**CONFIDENCE**(**alpha**, **standard_dev**,** size**)

**alpha:**this is required. This represents 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:**this is also required. This is the population standard deviation for the data range and is assumed to be known**size:**also required. This is the sample size.

It should be further noted that:

- if any argument is non-numeric,
**CONFIDENCE**returns the*#VALUE!*error value - if
**alpha**is ≤ 0 or ≥ 1,**CONFIDENCE**returns the*#NUM!*error value - if
**standard_dev**≤ 0,**CONFIDENCE**returns the*#NUM!*error value - if
**size**is not an integer, it is truncated - if
**size**< 1,**CONFIDENCE**returns the*#NUM!*error value - if we assume
**alpha**equals 0.05, we need to calculate the area under the standard normal curve that equals**1 - alpha**, or 95%. This value is ± 1.96. The confidence interval is therefore:

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every other business day.*