## English translation: square root of the sum of the squares

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
 English term or phrase: combined in quadrature English translation: square root of the sum of the squares Entered by:

 19:26 Nov 3, 2007
English to English translations [PRO]
Science - Mathematics & Statistics / uncertainty calculation
 English term or phrase: combined in quadrature "As set out in 5.1, the average flow is controlled to within ± 2%, while the flow meter is calibrated against a transfer standard with an uncertainty of less than 2%. These figures have been combined in quadrature to give an effective contribution in Table 1, for the uncertainty contribution to flow not covered by the field tests, of 3%." (EN 14907) Could somebody explain this expression please ? :)
 Jörgen SletEstonia Local time: 23:41
 square root of the sum of the squares Explanation:i.e. using something similar to Pythagoras. Thus in your example, a system error of 2% and a flow error of 2% combined in quadrature give an error of 2.818% e.g. a) dosimeter calibration uncertainty, scal b) dose mapping uncertainty, smap c) dosimeter reproducibility, srep d) machine variability, smach. stotal = sqrt(scal^2 + smap^2 + srep^2 + smach^2) http://www.irradiationpanel.org/docs/publications/Panel_SPC_...
Selected response from:

JohnGBell
Local time: 23:41
 Makes sense, uncertainty should be additive, thank you4 KudoZ points were awarded for this answer

4 +1square root of the sum of the squaresJohnGBell
4 +1square_root(a-squared times b-squared)/2Alexander Demyanov

23 mins   confidence: peer agreement (net): +1
square_root(a-squared times b-squared)/2

Explanation:
...where a and b are your "these figures"

Alternatively, it may mean that each individual measured value is squared, the results added to each other, the sq. root of the sum is taken and then divided by the number of values measured.

c.err : Rate errors combined in quadrature, i.e., it's sqrt{\sum{err^2}}/N, where N is the number of points in a given bin. Only calculate if err is input ...
space.mit.edu/CXC/analysis/SITAR/functs_reb.html - 12k

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Note added at 24 mins (2007-11-03 19:50:13 GMT)
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SOOORRRY!!!!! "plus", not "times"

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Note added at 29 mins (2007-11-03 19:55:15 GMT)
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Also, it appears that the "combined in quadrature" expression is a bit more loose and there can be other techniques for calculating the combination.

 Alexander DemyanovLocal time: 16:41Works in fieldNative speaker of: Russian
 Asker: yes, it is a loose expression indeed :)

agree  Nik-On/Off: It seems that the square root of the sums of the squares should not be divided by two// http://tinyurl.com/yrha99
 21 mins
-> Thanks, Dmitrii!//Then it wouldn't be "combined". What if we had 10000 values? Right, as e.g. combining forces at 90 deg. (the more forces you combine the greater is the resulting force). Like I said, the expression may be somewhat loose.

neutral  Ken Cox: with Nik-On/Off -- the formula you give is for calculating a form of mean error, but here the objective is to calculate the total error. (In the example, 3 is the approximate square root of 4 plus 4).
 1 hr
-> Thanks, Ken! As seen in the responses above, I don't insist on /N. I'm not 100% sure whether "eff. contribution" here should be a quadr-ed sum or quadr-ed mean. Unfortunately, I didn't make up the formula: got it at the mit.edu site.

2 hrs   confidence: peer agreement (net): +1
square root of the sum of the squares

Explanation:
i.e. using something similar to Pythagoras.
Thus in your example, a system error of 2% and a flow error of 2% combined in quadrature give an error of 2.818%

e.g.
a) dosimeter calibration uncertainty, scal
b) dose mapping uncertainty, smap
c) dosimeter reproducibility, srep
d) machine variability, smach.
stotal = sqrt(scal^2 + smap^2 + srep^2 + smach^2)

 JohnGBellLocal time: 23:41Native speaker of: EnglishPRO pts in category: 4
 Makes sense, uncertainty should be additive, thank you

agree
 20 hrs

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