NPAE - Brief instruction on how to present results of your measurements with error bars

Brief instruction on how to present results of your measurements with error bars

Sometimes authors present results of their measurements with e.g. 6 digits (or even more) after point (or comma in the Ukrainian version) while uncertainties (error bars) could be e.g. 10%. This is incorrect: number of digits in presenting your values depends on your uncertainties.

General rules of presentation of values and their error bars can be found in textbooks. Below three example instructions are given: from AMDC (Atomic Mass Data Center), PDG (Particle Data Group) and JCGM (Joint Committee for Guides in Metrology). You can use one of these examples as a guideline for presenting your results.

(1) Politics in Atomic Mass Evaluation 2020 (Chin. Phys. C 45 (2021) 030003, open access, see page 5):

"In cases where the furthest-left significant digit in the uncertainty was larger than 3, values and uncertainties were rounded off, but not to more than tens of keV.
(Examples:
2345.67 ± 2.78 → 2345.7 ± 2.8;
2345.67 ± 4.68 → 2346 ± 5;
but
2346.7 ± 468.2 → 2350 ± 470)."

(2) Review of Particle Physics 2020 by the Particle Data Group (Prog. Theor. Exp. Phys. 08 (2020) 3c01, open access, see page 17):

"The basic rule states that if the three highest order digits of the error lie between 100 and 354, we round to two significant digits. If they lie between 355 and 949, we round to one significant digit. Finally, if they lie between 950 and 999, we round up to 1000 and keep two significant digits. In all cases, the central value is given with a precision that matches that of the error. So, for example, the result (coming from an average) 0.827 ± 0.119 would appear as 0.83 ± 0.12, while 0.827 ± 0.367 would turn into 0.8 ± 0.4."

(3) Joint Committee for Guides in Metrology (Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM), open access, see page 26):

"... estimates should be rounded to be consistent with their uncertainties; for example, if y = 10.05762 Ω with u_c(y) = 27 mΩ, y should be rounded to 10.058 Ω."