Combining Error Bars
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Combined Standard Error Formula
is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Sign up Here's how to calculate uncertainty in physics how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Multiple measurements of the same quantity - combining uncertainties up vote 7 down vote favorite 3 I combining uncertainties have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty. $$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm \Delta v_{2} $$ $$ v_{3} \pm \Delta v_{3} $$ $$ \vdots $$ $$ v_{N} \pm \Delta v_{N} $$ Since they're measurements of the same quantity, all the values of $v$ are roughly equal. I can, of course, calculate the mean: $$ v =
How To Calculate Error Bars
\frac{\sum_{i=1}^N v_{i}}{N}$$ What would the uncertainty in $v$ be? In the limit that all the $\Delta v_i$ are small, then $\Delta v$ should be the standard deviation of the $v_i$. If the $\Delta v_i$ are large, then $\Delta v$ should be something like $\sqrt{\frac{\sum_i \Delta v_i^2}{N}}$, right? So what is the formula for combining these uncertainties? I don't think it's the one given in this answer (though I may be wrong) because it doesn't look like it behaves like I'd expect in the above limits (specifically, if the $\Delta v_i$ are zero then that formula gives $\Delta v = 0$, not the standard deviation of the $v_i$). experimental-physics experimental-technique error-analysis share|cite|improve this question edited Mar 19 '13 at 12:07 asked Mar 19 '13 at 11:56 Benjamin Hodgson 528416 The answer from Pygmalion that you liked gives the correct (naive) treatment. Notice that in the average he has $N$ in the denominator, not $\sqrt{N}$. Also, you have not yet formed a standard deviation, which is not the same as a combined error (though in many cases there are useful relations between them). –dmckee♦ Mar 19 '13 at 15:41 Better than averaging, if each measurement has a different uncertainty, is to do a weighted mean, where the weights are $\frac{1}{\Delta\nu_1}$. –user40838 Feb 18 '14 at 9:34 add a comment| 2 Answers 2 active oldest votes up vote 3 down vote When you're combining meas
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Propagation Of Error Division
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Support Answers MathWorks Search MathWorks.com MathWorks Answers Support MATLAB Answers™ MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Ask Answer Browse More Contributors Recent https://www.mathworks.com/matlabcentral/answers/12946-plotyy-and-error-bars Activity Flagged Content Flagged as Spam Help MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Ask Answer Browse More Contributors Recent Activity Flagged Content Flagged as Spam Help Trial software Clement Wong (view profile) 5 questions 1 answer 0 accepted answers Reputation: 0 Vote0 Plotyy and error bars Asked by Clement Wong Clement Wong (view profile) 5 questions 1 answer error bars 0 accepted answers Reputation: 0 on 3 Aug 2011 Accepted Answer by Patrick Kalita Patrick Kalita (view profile) 0 questions 141 answers 62 accepted answers Reputation: 414 184 views (last 30 days) 184 views (last 30 days) I'd like to do a plotyy function, and I have confidence intervals for each point of my data. I can't seem to figure out a way to do both of how to calculate these at once. My x data is stored in an array RC, and the two y data are in arrays L and D. The confidence intervals are in ciL and ciD, and are not necessarily symmetric. Is there an easy way to add these as error bars to my plot? 2 Comments Show all comments Jan Simon Jan Simon (view profile) 57 questions 6,852 answers 2,076 accepted answers Reputation: 13,864 on 3 Aug 2011 Direct link to this comment: https://www.mathworks.com/matlabcentral/answers/12946#comment_28683 If you post the code you have currently, it would be easier to insert the changes. Clement Wong Clement Wong (view profile) 5 questions 1 answer 0 accepted answers Reputation: 0 on 3 Aug 2011 Direct link to this comment: https://www.mathworks.com/matlabcentral/answers/12946#comment_28850 The code looks something like this: x = 1; for rc = 1000:1000:10000 [beta,r,j,covb,mse] = nlfin(parameters including rc); ci = nlparci(beta,r,'covar',covb); L(x) = beta(2); D(x) = beta(3); ciL(x,:) = ci(2,:); ciD(x,:) = ci(3,:); x = x+1; end L,D,ciL,ciD are all preallocated for speed. But the idea is that now, I have the confidence intervals for all 10 data points as I sweep rc. RC goes from 1,000 to 10,000 in 1,000 step size. I'm plotting the values for L a
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