I used to teach my students: "In error propagation, you express errors of intermediate results with two significant digits (to avoid the extra error of rounding up) and you express the error of the final result with ONE significant digit. Then you round up the main number accordingly". This means if the numbers given by you are final results they should be expressed as (25±3)*10 and 8±1. Regards.

I agree with you ...Grazyna

and I beleive that authors/ referees should give more attention in this issue.

Regards

Mira

When the most significant digit of the error is 1 it is recommended to specify two significant digits for the error, as in 35+-14, to avoid the rounding up error.

This rule applies for the intermediate results, but not for the final result.  And why 1 is supposed to be so special?

I think that the Dariusz recommendation is aimed to avoid that the rouding could considerably increase or reduce the actual uncertainty. This effect of rounding is largest (in relative terms) when the first digit is 1.

I would like to thank Mirofora for having highlighted this issue, which affect many submitted papers and also several published papers.

In addition, I would like to mention that in many cases the probability associated to the uncertainty (i.e. 68%, or 90%, or 95%, or 1 sigma, or 2 sigma, or else) is not reported at all. This missing information is also important to evaluate the uncertainty.

Dear Francesco

I aggree that is important to mention whether the uncertainty used is 1σ οr 2σ  etc

I never heard about the second significant digit .....that is recomended when the first digit is one. I neither understand the example 35+-14

Could you sent me the refference please?

Finaly,

My experience is mainly from educational labs, where the final uncertainty in all cases can not have more than one significant digit.

I would like to hear an example of a measurement, in which the final combined uncertainty can be given with 2 significant digits

Thanks

Mirorora

dear Dariusz

I never heard about the second significant digit .....that is recomended when the first digit is one. I neither understand the example 35+-14

Could you please sent me a refference?

Thanks 

Dear Mira,

the main reference about the expressions for measurement uncertainty is the Guide to the Expression of Uncertainty in Measurement (the so-called GUM).

The chapter 7 (Reporting uncertainty) contains specifically what you interested to.

I hope this can be useful.

Best wishes

Francesco

Dear Francesco

Thanks a lot

Mira

Estimation of measurement   Uncertainty should be a quadrature sum of  the systematic uncertainty and random uncertainty associated with the  measurement process. The confidence limits should be stated.ISO document INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, Guide to the Expression of Uncertainty in Measurement, ISO, Geneva (1995) and IAEA TECDOC -1585 are  useful documents to consult.

dear Mirofora

also useful is the latest ISO11929-2010, about declaring uncertainities

can be found / bought on https://www.iso.org/standard/43810.html

regards - Michel

Thank all of you!

The main problem for me is how to apply the "Guide to the Expression of Uncertainty in Measurement" in a specific type of measurement and how to decide for the appropriate number of significant digits in the final total uncertainty .

Im still straggling to understand ....but I'm confused from the way the results are presented in several pubications .

I wiil return soon with more specified question since I realised that a lot of people is interested for this issue

(even among the same team there are different approaches)

There is no ISO standards, but I recommend LNHB publication "Arrondissage des resultats de mesure - Nombre de chiffres significatifs":

http://www.nucleide.org/DDEP_WG/Arrondis_NT04-13.pdf

Regards!

GUM 7.2.6: The numerical values of the estimate y and its standard uncertainty uc(y) or expanded uncertainty U should not be given with an excessive number of digits. It usually suffices to quote uc(y) and U [as well as the standard uncertainties u(xi) of the input estimates xi] to at most two significant digits, although in some cases it may be necessary to retain additional digits to avoid round-off errors in subsequent calculations.

http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315e-html/C045315e_FILES/MAIN_C045315e/07_e.html#L_7_2

I think that most of nuclear systems can give the uncertainty of measurement.

Hello everybody, since I realised that a lot of people is interested in this issue, I'm sharing with you the following:

Exploring the literature for the issue of uncertainty evaluation and its expression in a measurement, I found that there are recommendations for keeping one or two significant digits in the final expression of the final uncertainty.

I'm sharing with you the articles and also give a copy of what explicitly is written for this issue

A) Concerning the expression of the final uncertainty measurement

• Ø Recommendations for the significant digits and the format, in some resources

1. IAEA-TECDOC-1585 Measurement Uncertainty (A Practical Guide for Secondary Standards Dosimetry Laboratories) May 2004

&3.10 , P25 “”In many cases, one significant digit in the uncertainty is enough. Only where the leading digit is a 1 or 2 is there a strong case for greater precision in the uncertainty. Rounding should only be applied to the final result and its uncertainty, not at intermediate steps in the analysis.”

2. JCGM100201X CD Evaluation of measurement data — Guide to the expression of uncertainty in measurement

3.6.2 “The uncertainty, u(y) should generally be stated to two significant decimal digits unless there is a technical reason for doing otherwise (12.2.1.2)….”

3. Multi-Agency Radiological Laboratory Analytical Protocols (MARLAP) “MEASUREMENT UNCERTAINTY” 19.3.7 Significant Figures

“The number of significant figures that should be reported for the result of a measurement depends on the uncertainty of the result. A common convention is to round the uncertainty (standard uncertainty or expanded uncertainty) to either one or two significant figures and to report both the measured value and the uncertainty to the resulting number of decimal places (ISO,1995; Bevington, 1992; EPA, 1980; ANSI N42.23).

MARLAP recommends this convention and suggests that uncertainties be rounded to two figures. “

• Ø Reporting standard uncertainty (recommendation of MARLAP and also in NOTES EURACHEM / CITAC Guide CG 4 Quantifying Uncertainty in Analytical Measurement)

“The plus-minus format may be used to report an expanded uncertainty, but it generally should be avoided when reporting a standard uncertainty, because readers are likely to interpret it as a confidence interval with a high coverage probability. A commonly used shorthand format for reporting a result with its standard uncertainty places the one or two digits of the standard uncertainty in parentheses immediately after the corresponding final digits of the rounded result. For example, if the rounded result of the measurement is 1.92 and the standard uncertainty is 0.14, the result and uncertainty may be shown together as 1.92(14). Another acceptable reporting format places the entire standard uncertainty in parentheses. The result in the preceding example would appear in this format as 1.92(0.14). The laboratory may also report the standard uncertainty explicitly…..”

B) For the evaluation of the uncertainty in gamma ray spectrometry I found useful the following articles

1. IAEA-TECDOC-1401 2004 Quantifying uncertainty in nuclear analytical measurement (C. DOVLETE, P.P. POVINEC QUANTIFICATION OF UNCERTAINTY IN GAMMA-SPECTROMETRIC ANALYSIS OF ENVIRONMENTAL SAMPLES)

2. CALCULATION SPREADSHEET FOR UNCERTAINTY ESTIMATION OF MEASUREMENT RESULTS IN GAMMA-RAY SPECTROMETRY AND ITS VALIDATION FOR QUALITY ASSURANCE PURPOSE Alessia Ceccatellia* , Ashild Dybdala , Ales Fajgeljb , Aurelien Pitoisa Applied Radiation and IsotopesVolume 124, 1 June 2017, Pages 7-15

Dear Miro,

thank you again for having promoted this discussion. Moreover, thank you for this last contribution summarizing the discussion.