error propagation

[ajschumacher]

OpenStax text on Significant Figures https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-figures

We then determine the average weight of the 5-lb bag of apples is 5.1 ± 0.3 lb from using half of the range.

If the measurements going into the calculation have small uncertainties (a few percent or less), then the method of adding percents can be used for multiplication or division. This method states the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation.

1. For multiplication and division, the result should have the same number of significant figures as the quantity with the least number of significant figures entering into the calculation.

2. For addition and subtraction, the answer can contain no more decimal places than the least-precise measurement.

See also: https://en.wikipedia.org/wiki/Significance_arithmetic

the usual "measure one more than the lines on the ruler" rule https://chem.libretexts.org/Courses/University_of_British_Columbia/CHEM_100%3A_Foundations_of_Chemistry/02%3A_Measurement_and_Problem_Solving/2.03%3A_Significant_Figures_-_Writing_Numbers_to_Reflect_Precision

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Here's a physics lab that sort of does Monte Carlo error prop: http://openbooks.library.umass.edu/p132-lab-manual/chapter/monte-carlo-error-propagation/

NIST Uncertainty Machine https://uncertainty.nist.gov/ article about it https://pubs.acs.org/doi/10.1021/acs.jchemed.0c00096

Here's a calculator app that does some sort of error prop: http://physics.gac.edu/~huber/error_calc/

Nice all-normal error prop calculator: http://www.julianibus.de/

Nice old ref: https://www.jstor.org/stable/27951340 "Significant Digits in Computation with Approximate Numbers" (1931)

"crank three times" http://www.av8n.com/physics/uncertainty.htm#sec-crank3 (best, min, max)

"interval arithmetic" for bounds propagation https://en.wikipedia.org/wiki/Interval_arithmetic

mathier (closes form) error propagation https://en.wikipedia.org/wiki/Propagation_of_uncertainty

[ajschumacher]

https://stats.stackexchange.com/questions/52646/variance-of-product-of-multiple-independent-random-variables/52699

[ajschumacher]

"Significant Figures" are wasteful

[ajschumacher]

“All the certain digits and the one uncertain digit” https://brilliant.org/wiki/significant-figures-and-precision/

[ajschumacher]

12.4 - 12.3 = 0.100 is silly

[ajschumacher]

ugh rounding of final results vs. intermediary results is so gross

[ajschumacher]

oh also f92b935