Poisson designs and minimum detectable effects

andrewpwheeler.com

13 pointsapwheele3 comments

> Counter-intuitive perhaps, you get smaller standard errors when you observe higher counts.

No, the relative error aka. std/mean decreases. For Poisson, var=mean=N => std/mean = sqrt(N)/N = 1/sqrt(N). I'm sure the author knows this but the post is not written very clearly imho. I wonder who the target audience is?

When I was a junior researcher I rather found confusing that variance increases with increased counts. But the perceived "error" is the standard deviation relative to mean, which does decrease as shown above.

The quoted statement is IMO fine -- standard error as a term is only used to refer to the error around an estimate, not the marginal distribution.

Now to the target audience, it was criminologists monitoring counts of things over time. But that monitoring counts of thing over time is applicable to other areas obviously, such as A/B testing for rare events.

That variance increases with counts certainly make more sense for count data. E.g. 5% of buses are late should imply larger variance for larger counts.

It was confusing to me too once upon a time because most distributions are designed to have a homogeneous variance.

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