Talk:Propagation of uncertainty/Archive 1

message: The errors should add in quadrature. So square each element and take the square root. Take the example Y=A+B. Then the error is \sqrt(dA^2+dB^2), not dA+dB. That is what you get when you use the equation right above the example problem.  —Preceding unsigned comment added by 132.163.47.52 (talk) 23:21, 4 July 2010 (UTC)
thread_title: The Resistance example is wrong, I think.

message: I genuinely think that this article is important for the whole of science.  Too many scientists (including myself) graduate without becoming confident with error calculations, and I suspect that many scientists never do so.  I see here an opportunity to improve the quality of a whole body of scientific work.
Currently, the approach is too mathematical (and not even rigorous), and does not deal with the subtleties of error calculations, like the difference between using errors and standard deviations, and which situations it is ok to use approximations.
When the equations are approximations, why not use the "is approximately equal to" instead of the equals sign?  The fact that it is an approximation should be clearly marked, in any case.
I suggest the article should clearly delineate the different possible approaches - perhaps this could even become the basis for standardisation of error calculations in future publications.  Thanks, MichaelR 83.72.194.27 11:12, 7 October 2007 (UTC)
thread_title: This article is extremely important, and needs improving

message: Is it necessary to use both i and j as indices for the summation of the general formulae? it appears to me that i only appears in the maths whilst j only appears in the english. True? If not, it could be more clearly explained as to the reasons for the change / use of both.
Thanks Roggg 09:35, 20 June 2006 (UTC)
thread_title: i or j

message: Example application: the geometric mean? Charles Matthews 16:33, 12 May 2004 (UTC)
replies: text: From the article (since May 2004!): "the relative error ... is simply the geometric mean of the two relative errors of the measured variables" -- It's not the geometric mean.  If it were, it would be the product of the two relative errors in the radical, not the sum of the squares.  I'll fix this section. --Spiffy sperry 21:47, 5 January 2006 (UTC)
thread_title: Geometric mean

message: In my experience, the lower-case delta is used for error, while the upper-case delta (the one currently used in the article) is used for the change in a variable.  Is there a reason the upper-case delta is used in the article? --LostLeviathan 02:01, 20 Oct 2004 (UTC)
thread_title:  Delta? 

message: Can we get some caveats placed in here? i.e. a statement that these formula are only valid for small sigma/mean and that the formula for the quotient particularly is problematic given Hodgson's paradox and the discussion in ratio distribution. The Goodman (1960) article has some exact formula that modify the approximate forms here as well.169.154.204.2 01:17, 23 August 2007 (UTC)
thread_title:  Caveats? 

message: I searched for this page to remind myself of one of the formulae, which I use on a regular basis.  (When I'm at work, I flip to a tabbed page in my copy of [Bevington].)  I could see that the table contained many errors, mostly due to confusions between \Delta A\!\, and \left(\Delta A\right)^2 \!\,, and some of the table entries included extra terms, presumably for correlations between A\text{, }B\text{, }C\!\,, though they are stated in the caption to be uncorrelated.  I didn't notice it right away, but the table had a third column with \Delta A\!\, replaced with an undefined (but commonly used) \sigma_A\!\,.
In its current form, the table is (exactly, not approximately) correct for uncorrelated,  normally-distributed real variables.  Hopefully, it also gives an indication of how these rules can be combined.  (Some are special cases of others, but they all derive from the general rule in the previous section, anyway.)
So what about formulae for correlated variables?  I don't know much about that because I always use the general derivative method for problems with correlations.  I only use the example formulae for simple cases. Jim Pivarski 23:25, 7 October 2007 (UTC)
thread_title:  Re-wrote example table 

message: There is an important exception to the usual treatment of error propagation. That is when a power series expansion of the function F(x) to be calculated breaks down within the uncertainty of the variable x. The usual treatment assumes that the function is smooth and well-behaved over a sufficiently large domain of x near the measured value x_0. Then one expands in a power series about x_0 and takes only the first linear term. However, if F is not well-behaved (for example if F(x) goes to infinity at some point near x_0) the correct uncertainty on F(x) may be completely different from the usual formula Delta F = F'(x_0) Delta x.
The simplest example is the uncertainty in 1/x. If we measure x=100 with an uncertainty of 1%, then 1/x has an uncertainty of 1% also. If we measure x=100 with an uncertainty of 100%, then 1/x has an *infinitely* large uncertainty, because x may take the value 0!
Is this effect treated in any known texts? --Tdent 15:09, 24 October 2007 (UTC)
thread_title:  Pitfall of linear error propagation: eg dividing by zero 

message: I put in a couple of references to problems with ratios alluded to above, but what is required is a better quantification for when these issues are important. The Geary-Hinkel transformation has limits of validity and they can be used to show when that formula (which reduces to the standard case in favorable circumstances) is useful. Hopefully someone can add to that? 74.64.100.223 (talk) 16:07, 29 November 2007 (UTC)
thread_title:  caveats added, but more details needed 

message: Been trying to understand this for a while (and how the formula are derived) and not that easy to understand from this page. Finally found a useful reference which then makes the rest of this page make sense so thougt I'd share. The reference is 
Taylor, J. R., 1997: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd ed. University Science Books, 327 pp.
and section 9.2 helps make things clear.
Added a comment here as I don't have time to edit main page.  —Preceding unsigned comment added by 139.166.242.47 (talk) 11:44, 29 February 2008 (UTC)
thread_title:  Useful Reference? 

message: In the caveats section, the formula
:y=mz+c: \sigma^2_y=z^2\sigma^2_m+\sigma^2_c+2z\rho \sigma_m\sigma_c
is written, but the variable \rho is not defined. Please fill in its definition.
Zylorian (talk)  —Preceding undated comment was added at 17:04, 6 October 2008 (UTC)
thread_title:  Undefined variable in caveats section 

message: The third equation for M^f_{ij} is wrong or inconsistent
with itself. The term A_{ik} should have its subscripts
reversed, right? 
Likewise, the same error in the next equation down.
This is my first post on wikipedia, I leave this to
the author to correct it if it needs to be done.
In agreement with the comments above, I found the section "Partial
derivatives" a bit contradictory or at least lacking explanation.
It is contradictory because in the third paragraph \Delta x
is said to be commonly given to be the standard deviation \sigma,
which is the square root of the variance \sigma^2,
yet in the section "Partial derivatives" the square root of the
variance is not equal to the absolute error in the table. It was
precisely this issue for which I had consulted wikipedia. However
there is enough information here to have helped me solve my problem.
Dylan.jayatilaka (talk) 05:23, 7 January 2009 (UTC)
thread_title:  Errors in section 1 and confusions in section "Partial derivatives" 

message: ...rather than try to edit this one. Take a look: Experimental uncertainty analysis. Right or wrong, I believe it to be far more "accessible" than this one is. How to reconcile my new article with this one and with Uncertainty analysis remains to be seen. Please give me a week or so to produce the table at the bottom of "my" article- it will go beyond the table in this article, and I think it will be a very useful thing for many readers. Also I have a mention and a reference related to the 1/x thing I see above here- the solution of course is to use a higher-order expansion, and the necessary eqns are in that book. Regards... Rb88guy (talk) 18:30, 12 March 2009 (UTC)
thread_title: Created new article on this subject