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Comment by mock-possum | Hacker News Reader

To give a little preview of the content of the (very short) paper:

> In statistics, the standard error has a clear technical definition: it is the estimated standard devi- ation of a parameter estimate. In practice, though, challenges arise when we go beyond the simple balls-in-urn model to consider generalizations beyond the population from which the data were sampled. This is important because generalization is nearly always the goal of quantitative studies. In this brief paper we consider three examples:

> What is the standard error when the bias is unknown and changing (my bathroom scale)?

>How do you interpret standard errors from a regression fit to the entire population (all 50 states)?

> How should we account for nonsampling error when reporting uncertainties (election polls)?

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This and "standard deviation" are a couple of those terms for which I'd be interested in a definition that didn't assume quite so much domain knowledge (maybe one step above a totally naive layman's metaphor). I hear the terms all the time, but I only have intuitive statistics knowledge (averages, curves, controls, etc). I recall doing a brief Wikipedia dive once and coming up dissatisfied.

Maybe this (and the answers therein) can help: https://stats.stackexchange.com/q/550619/18417

(Note that the second number in that share URL can be linked to you as a user - this is a stackoverflow/stackexchange tracking feature that I think leaks personal information. I see that your SE user name seems to line up with the HN user name.)

That's actually quite illuminating!

My statistics textbook at home covers this in pretty clear detail. I bought mine from abebooks for like 10 bucks, seems money well spent. Stats Wikipedia is written by and for stats PhDs. My recollection on standard deviation:

1. It's a descriptive statistic; we want to summarize how closely data clusters around its central ("mean") value.

2. We could just calculate the average distance, but we kind of want to penalize large outliers. We want the sequence [50,50,50,50,47,53] to have a higher deviation than [51,49,51,49,51,49], even though they both have a total distance from 50 of 6.

3. To achieve this, we use "root mean squared" -- square each sample's distance from average, then average those values, and finally take the square root of that average. In this manner, samples with large distances have a greater effect on the outcome.

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