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dmzuckerman / Sampling-Uncertainty

Best Practices article intended for LiveCoMS
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Definition of coverage factor k #31

Closed agrossfield closed 6 years ago

agrossfield commented 6 years ago

Unless I'm missing it, we don't really define what a coverage factor is, and since it's not a common term (I'd never heard of it), we need to be very clear. I think the best solution is an entry in the glossary, plus a line or two in the text where it's first used.

dmzuckerman commented 6 years ago

@dwsideriusNIST would please try to address this? Thank you.

dwsideriusNIST commented 6 years ago

Yes, I'll get to this today or tomorrow.

dwsideriusNIST commented 6 years ago

OK, commit https://github.com/dmzuckerman/Sampling-Uncertainty/commit/be94fcbae895f78801eeee7bd4f5dfc6c51e1380 contains an new definitions section that includes one for the coverage factor. The downside is that taking the coverage factor out of the definition of the confidence interval requires a more generic definition for the CI, resulting in a more theoretical/philosophical definition of both the CI and the coverage factor.

Please give it a read and comment. The problem with taking the coverage factor def out of the CI definition is that I had to switch to the formalized VIM/GUM terminology of "expanded uncertainty." Otherwise, you end up with a circular definitions of the CI and the coverage factor.

dmzuckerman commented 6 years ago

Dan, thanks a lot. I will take a look and see if there is a way to finesse this issue

dwsideriusNIST commented 6 years ago

@dmzuckerman Please do another pull before reading the new definitions - I did a slight rewrite to improve readability.

dmzuckerman commented 6 years ago

thanks for the heads up. i'm in the middle of editing

dmzuckerman commented 6 years ago

Maybe we should switch to x_i or x_j instead of x_k and reserve k for coverage factor??

dwsideriusNIST commented 6 years ago

@dmzuckerman New commit addresses many of your comments, with a few replies added. Regarding the s(x_j) notation: as per my in-text comment, the "x_j" notation is used to stress that the experimental standard deviation is that it is not a property of the random variable, but is computed from the set of of experimental observations. It also follows the pedantic VIM/GUM notation.

For economy of notation, I'm actually in favor of switching to s(x), though with an explanatory footnote to clarify that restriction on the meaning of s(x).