Standard Error of Non-Percentage-Based Metrics (such as cost per conversion rather than conversion rate)

I'm using the following post and have been able to figure out the Standard Error range for conversion rate calculated metrics:

https://www.periscopedata.com/blog/how-to-calculate-confidence-intervals-in-sql

However, when I do the same for calculated metrics such as cost per event, it doesn't work.  The reason being that the mean could be greater than 1 so the formula results in the square root of a negative value.  Ideas on how to get around that?  Thanks!  Using SQL.

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  • Hi Brien Jones ! Great question, the formula for standard error in this blog post is for variables with a Bernoulli distribution (in other words, there is either a "success" (1) or a "failure" (0)). p describes the proportion of successes, so this is always a value between 0 and 1.

    In your case here, you describe a variable with a mean greater than 1. Note that this is not a Bernoulli variable. Thus, you want to calculate the standard error by taking the standard deviation of the sample divided by the square root of n (the size of the population). 

    The attached screenshot shows the formula I've described above. You can read more about it from the source here.

    This is an example of how you can run this calculation in Python, so you can see how the math plays out, of course you can repurpose this for SQL as well. Hope this helps!

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  • Thanks Neha Kumar you rock!!!

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