hi,
the simple practical solution would be to use a bootstrap. The theory of the ratio of two poisson variables is quite involved.
regards
In digital media, we have a metric called "conversion rate", which is simply conversions / impressions.
Impressions represent the total number of times that an ad was viewed. Conversions can be defined as any action, but for the sake of example, let's say that it's the number of times that someone watched a video after clicking an ad.
So, for example, if there were 10 views of an ad, and 25 video views, the conversion rate would be 2.5. The data generally looks like this:
Ad | Month | Impressions | Conversions | Conversion Rate
Ad 1 | Sep 2016 | 7000 | 600 | 0.086
Ad 2 | Sep 2016 | 2000 | 5000 | 2.50
Ad 3 | Sep 2016 | 5000 | 100 | 0.02
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I'm familiar with finding CIs for proportions, but--as far as I can tell--conversion rate isn't a proportion, since the numerator and denominator can change independently. i.e. you could theoretically have unlimited conversions, and an increase in impressions wouldn't necessarily cause any change in conversions.
Could someone clarify what exactly this type of metric represents and what CI approach I should take? In laymen's terms, I would just define it as a "rate", but every reference text about finding CIs for rates just describes how to find CIs for proportions. I was thinking this might be a case for using Poisson CIs, but I'm not quite sure. The explanations of Poisson rates describe them as events per a period of time, whereas this is count of event A per the count of event B.
Any help would be greatly appreciated! Thanks!
hi,
the simple practical solution would be to use a bootstrap. The theory of the ratio of two poisson variables is quite involved.
regards
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