Power Pivot Principles: The A to Z of DAX Functions – CONFIDENCE.NORM

In our long-established Power Pivot Principles articles, we continue our series on the A to Z of Data Analysis eXpression (DAX) functions. This week, we look at CONFIDENCE.NORM.

The CONFIDENCE.NORM function

Is CONFIDENCE your NORM? This DAX 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.NORM. For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE.NORM is a range of population means.

For any population mean, μ₀, in this range, the probability of obtaining a sample mean further from μ₀ than x is greater than the significance level required, alpha; for any population mean, μ₀, not in this range, the probability of obtaining a sample mean further from μ₀ than 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 μ₀. Then we will not reject that hypothesis if μ₀ is in the confidence interval and will reject that hypothesis if μ₀ is not in the confidence interval. The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.

The CONFIDENCE.NORM function employs the following syntax to operate:

• 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.NORM returns the #VALUE! error value
• if alpha is ≤ 0 or ≥ 1, CONFIDENCE.NORM returns the #NUM! error value
• if standard_dev ≤ 0, CONFIDENCE.NORM returns the #NUM! error value
• if size is not an integer, it is truncated
• if size < 1, CONFIDENCE.NORM 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:

• this function is not supported for use in DirectQuery mode when used in calculated columns or row-level security (RLS) rules.

Please see my example below:

i.e. for an alpha of 5% (or a confidence interval of 95%), with a standard deviation of the population of 3.0 and a sample size of 100 (for a Normal distribution), the confidence interval around the sample mean will be 0.5880.

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