# Uncertainty calculation in measurements.jl

**URL:** <https://discourse.julialang.org/t/uncertainty-calculation-in-measurements-jl/94637>\
**Category:** General Usage\
**Tags:** question, measurements\
**Created:** [February 14, 2023, 5:24pm UTC](https://discourse.julialang.org/t/uncertainty-calculation-in-measurements-jl/94637 "2023-02-14T17:24:15Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![CurioMath](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/curiomath/32/43603_2.png) [@CurioMath](https://discourse.julialang.org/u/CurioMath)\
**Post date:** [February 14, 2023, 5:24pm UTC](https://discourse.julialang.org/t/uncertainty-calculation-in-measurements-jl/94637/1 "2023-02-14T17:24:16Z")

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Hi,  
It was really amazing to see Measurents.jl handling uncertainty propagation … However I would like to know what is the level of confidence used in the uncertainty calculation  
in measurements.jl.

Does that takes into account only expanded uncertainty with 95% confidence?

Can I find expanded uncertainty with 99% confidence in measurements.jl? And how?

Thanks in advance!

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**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [February 14, 2023, 8:51pm UTC](https://discourse.julialang.org/t/uncertainty-calculation-in-measurements-jl/94637/2 "2023-02-14T20:51:31Z")

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According to one of the Measurements.jl references ([JCGM, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement”, BIPM, September 2008](https://www.iso.org/sites/JCGM/GUM/JCGM100/C045315e-html/C045315e_FILES/MAIN_C045315e/AE_e.html#A_E_3)), the linear error propagation theory used, seems to be formulated in terms of standard deviations, but it also applies to the propagation of multiples of these with the following caveats:

“_If each standard deviation σi is replaced by a multiple k\*σi, with the same k for each σi, the standard deviation of the output quantity z is replaced by k\*σz. However, it does not apply to the propagation of confidence intervals. If each σi is replaced with a quantity δi that defines an interval corresponding to a given level of confidence p, the resulting quantity for z, δz, will not define an interval corresponding to the same value of p unless all of the wi (input uncertainties) are described by normal distributions._”

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**Author:** ![CurioMath](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/curiomath/32/43603_2.png) [@CurioMath](https://discourse.julialang.org/u/CurioMath)\
**Post date:** [February 15, 2023, 4:29am UTC](https://discourse.julialang.org/t/uncertainty-calculation-in-measurements-jl/94637/3 "2023-02-15T04:29:51Z")

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That was indeed really informative! Thanks for your time…