Use unbiased std for uncertainty estimates

[jthorton]

Updates the uncertainty functions on protocol results to return the unbiased estimate of the standard deviation from the sample population.

Questions

• Would it be better to return the SE = std / sqrt(n) which is the uncertainty in the estimate of the average rather than the spread of the data? Where std is the unbiased estimate?
• What do we do when n=1 the uncertainty will now return Nan?

Checklist

• All new code is appropriately documented (user-facing code must have complete docstrings).
• Added a news entry, or the changes are not user-facing.
• Ran pre-commit: you can run pre-commit locally or comment on this PR with pre-commit.ci autofix.

Manual Tests: these are slow so don't need to be run every commit, only before merging and when relevant changes are made (generally at reviewer-discretion).

• GPU integration tests
• example notebook testing
• packaging tests: run this for any large feature PRs or PRs that add test data.

Developers certificate of origin

• I certify that this contribution is covered by the MIT License here and the Developer Certificate of Origin at https://developercertificate.org/.

[github-actions]

No API break detected ✅

[IAlibay]

Just needs a news item, otherwise looks good.

[hannahbaumann]

Would it be better to return the SE = std / sqrt(n) which is the uncertainty in the estimate of the average rather than the spread of the data? Where std is the unbiased estimate?

I'm also not so sure, I think both options make sense, but of course answer a different question. Is there something in the best practices paper about this?

[IAlibay]

I would prefer the standard deviation rather than the standard error as the main measure of uncertainty.

We can discuss this more offline.