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19:21 Jun 22, 2010
This question was closed without grading. Reason: Answer found elsewhere
French to English translations [PRO] Science - Mathematics & Statistics / chemistry, metrology, chemometrics, measurement, uncertainty
French term or phrase:la loi de composition des variances
I work for a large industrial chemistry group, and I'm translating procedures relating to metrology and measurement uncertainty.
The term "loi de composition des variances" has come up several times now, and as yet I'm yet to come across a (verifiable/trustworthy/reliable) translation into English (my statistical knowledge is essentially nil). I've tried emailing a few experts in the field but as yet noone has come forward with an answer for me (apart from a couple of responses on another forum which I have been unable to check...). Anyone got any ideas ?
though this trip down statistical memory lane may be, the question remains: how to translate "loi de composition de variances". I'm not convinced that the law of propagation of uncertainty and the variance sum law (if you can call it that, since FR calls almost any mathematical relationship a "loi") are one and the same. As Christophe says, the most general form of the variance sum law includes correlated variables (ie not independent) and therefore also the covariances.
IMO, "composition" here refers to the sum of variances: more complicated than a simple sum on account of the weighting factors for each estimated variance, hence "composition". Presumably the boss knows what she means, so ask her!
It's not that hard, the only difference between the two formulas above is that the first assumes uncorrelated measurements, so the covariance part is zero.
No images supported, according to staff. My apologies for the inconvenience.
How does "la loi de propagation des incertitudes"equate to "la loi de composition des variances"? Evaluation des incertitudes de mesure - Exercice " Incertitudes de ...
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À l'aide de la loi de propagation des incertitudes, exprimer l'incertitude-type u(a). Solution. Le modèle est un modèle produit-quotient, on a donc ...
prn1.univ-lemans.fr/prn1/siteheberge/.../Exercice.html - Cached - Similar
Asker, are you certain the loi de composition des variances is synonymous in French with the loi de propagation des incertitudes? Better go back to your experts and check.
Found it! Apparently the "loi de composition des variances" is a real law, just a rather obscure one. I contacted a few experts in experimental protocol optimization and got the answer!
Thanks guys. The boss has asked me to translate it literally and see if our anglophone colleagues understand it (if not then we are going to change the source document... cheating, I know). I think it probably is the variance sum law, but without understanding stats properly I'm a bit stuck... Thanks everyone
Absolutely agree with rKillings on this - whether something can be broken down to its individual components or the various components added up to make the total it's all the same. It's just a question of perspective. The variance sum law specifies that this is only true if the variables are independent. I had a reference from a stat course that somehow did not make it on the posting
Combined uncertainty, pooled variance, whatever you wish to call the overall uncertainty of numerically dissimilar groups of measurements, Wiki has a good description: http://en.wikipedia.org/wiki/Pooled_variance
Maybe there is a "law of composition" in French, but not, as far as I'm aware, in English.
You're probably looking for the law of propagation of uncertainty, which says that the combined uncertainty of multiple measurements is the square root of the sum of the individual squared uncertainties.
Although one third of my first degree was statistics, this hardly qualifies me an an expert. However, during this time, which included all the multivariate and ANOVA stuff, I never came across a "law of composition of variances", unless the intended meaning is that of a pooled estimate of a population variance based on the variances of groups of unequal sizes. This may be the intended meaning, since such numerically heterogeneous groups are not uncommon where real measurements are concerned.
Are you 100% sure it is "composition" and not "décomposition"?
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Answers
57 mins confidence:
variance decomposition/the law of total variance
Explanation: Based on the lack of convincing evidence for "la loi de composition des variances" in French, and my comments below and the evidence found on English sites re statistics.
Variance: Definition from Answers.com
In statistics, a variance is also called the mean squared error. .... This property is known as variance decomposition or the law of total variance and ... www.answers.com/topic/variance-1 - Cached - Similar
liz askew United Kingdom Local time: 19:44 Native speaker of: English PRO pts in category: 8
Explanation: More generally, the variance sum law can be written as follows:
which is read "The variance of X plus or minus Y is equal the variance of X plus the variance of Y.
The formulas for the sum and difference of variables given above only apply when the variables are independent.
Explanation: Routledge French dictionary of telecommunications: ... - Google Books ResultStuart Wittering - 1997 - Reference - 437 pages
... fibre d'injection/ law a GEN loi /; - of combination of errors TEST loi de composition des erreurs/ lay1; - perso nn GEN profane m ...
books.google.com/books?isbn=0415133483...
Il s'agit à contrario de toute technique d'évaluation non basée sur un procédé statistique. Une telle évaluation s'appuie généralement sur un jugement scientifique porté à la suite d'une analyse physique de la manipulation, utilisant toutes les informations disponibles. Il faut en particulier cerner la part d'incertitude qui est due à chacune des corrections associées aux causes d'erreur identifiées, même lorsqu'elles n'apportent pas à priori de dispersion aux résultats. On applique le même formalisme que pour les méthodes de type A, à savoir évaluer l'incertitude sur la correction (correction qui peut être nulle!) par une valeur Uj qu'on peut traiter comme un écart-type. Cette valeur est déterminée à partir d'éléments tels que bibliographie sur les matériaux et capteurs, notices des fournisseurs et constructeurs, certificats d'étalonnage, rapport d'intercomparaisons, ... mais aussi à partir des connaissances et du savoir faire de l'analyste et de l'opérateur. Cette manière de procéder revient, dans certains cas, à postuler l'existence sous-jacente d'une loi de distribution pour la correction considérée.
Pour obtenir l'incertitude Uc (écart-type) sur la correction totale, on applique la loi de composition des variances qui s'écrit, dans l'hypothèse où causes d'erreur et corrections sont non corrélées,
-------------------------------------------------- Note added at 41 mins (2010-06-22 20:03:36 GMT) --------------------------------------------------
p.s.
if you open the last site you will actually find a formula at the bottom of the quoted text, which did not copy here...
-------------------------------------------------- Note added at 44 mins (2010-06-22 20:06:25 GMT) --------------------------------------------------
BTW
although the above site states "loi de composition..." I have only found about 3 French hits for "loi de composition", the great majority of refs = loi de DEcomposition des variances:)
liz askew United Kingdom Native speaker of: English PRO pts in category: 8
Note to reference poster
Asker: Hmm, I'd like to think it's decomposition, it would make my life a lot easier... It would certainly be logical. The frequency of the term and my boss' certainty that there is no other way to say it (she wrote the thing in the first place) suggest that it'd be a problematic assumption. I think I'm going to go digging in the standards documents the procedure is based on to see whether it'll clear things up...
The translation workplace 
peer agreement (net): +1
