# What is Error analysis: Definition and 100 Discussions

In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics.

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1. ### Error running example ICRP145_HumanPhantoms in Geant4

Dear experts , when I run the ICRP145_Human Phantoms example following the instructions in the user manual, I get this error response [ VirtualBox:~/Geant4/share/Geant4/examples/advanced/ICRP145_HumanPhantoms/build\$./ICRP145phantoms ./Internal -i 9500 -m example.in -o example.out Usage...
2. ### Error of a graphical approach

As part of my studies, I'm obliged to take an experimental course at the moment, where I have to conduct experiments and write a composition. Today we examined spectral lines of helium with a prism. As part of the evaluation, I had to plot the measured diffraction angles of different colors /...
3. ### I Measurement Error Analysis in Gaussian distribution

I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet which I am not able to grasp. image Source Q. In this graph(above) if...
4. ### Error propagation leads to different uncertainties, which do I choose?

I understand how to compute and propagate errors but have trouble with conceptualizing all things put together. I have performed an experiment to determine a value for some quantity. This quantity depend on two variables. The first one depend in turn on some other quantities as well but I think...
5. ### I Error of the WKB approximation

hello everyone I tell you a little about my situation. I already found the approximate wavefunctions for the schrodinger equation with the potential ##V(x) = x^2##, likewise, energy, etc. I have the approximate WKB solution and also the exact numeric solution. What I need to do is to calculate...
6. ### I Alternate expressions for the uncertainty propagation

I have seen that there are two different formulas that we can use when calculating the propagation of uncertainty in a measurement. If ##X=f(A, B, C, \ldots)## is the quantity whose uncertainty we want to estimate, which depends on the quantities ##A,B,C,...##, then we could calculate the...
7. ### Computing Errors when Data Sets are Given

This is for the lab report I have to submit. ##n## is the refractive index. ##L## is the length of a gas chamber and ##m## is the number of fringes passed as the pressure in the gas chamber changes by ##\Delta p##. We are already given the error in ##L##. I performed the experiment and obtained...
8. ### Puzzled about the non-teaching of Monte Carlo method(s) for error analysis

Say you have measured several quantities and you can calculate the value of a physical quantity as a sum/product of the several measured quantities, and you are interested to calculate the uncertainty of that physical quantity. I have just learned about the Monte Carlo method applied to error...
9. ### I Statistic uncertainties in cross section plots - how to calculate?

Hi there, I hope I chose the right forum for my question. So, basically, I'm doing an analysis measuring the number of signal particles in a certain momentum bin i, and doing two corrections: Nsig, i=M*(Nmeas, i-Nbkg, i) Here, M is a matrix covering PID correction and PID efficiencies, and...
10. ### Half-life error analysis

What is meant by the constant background and how would one deduce the half-life IF not from the fit?
11. ### I Error analysis: simple but confusing matter

Dear all, We learn students to work with significant figures. I guess we all know those rules of thumb. Now imagine I have an expression like L = 2x, where x is a length a the 2 is an amount, i.e. the value of a discrete 'function'. If x=0,72 m (2 significant figures), then L = 1,44 --> 1,4 (2...
12. ### Uncertainties in a set of measurements

Suppose I measure the distance between two objects for three trials. The two objects then get farther away, and I measure the distance between them again for three trials. I repeat this for 3 more different distances, getting a total of 15 measurements (3 trials for 5 distances). I then compute...
13. ### How to compare two measurements with uncertainties in terms of sigma?

Perhaps that statement is just saying how big the t-value is. Like, in this case: t = (1.0 - 0.98) / 0.1 = 0.1 So we can say that our measured value is within 1 sigma from the other measured value. In this case, do we just ignore the uncertainties of the other measured/reference value? It's...
14. ### B Questions Regarding the Fundamental Rules of Error Analysis

(A)My textbook states the following : (1) The example explaining the italicised statement is rather confusing. My understanding of the statement is that we need to include one extra significant figure than what the relevant rule requires us to round off to, for intermediate...
15. ### Trivial question on differentiating logarithms

My Question : Shouldn't differentiating ##-log B## give ##\frac{-\delta B}{B}##? (Note : A, B and Z are variables not constants) By extension for ##Z=A^a \,B^b\, C^c## where ##c## is negative, should ##\frac{\Delta Z}Z=|a|\frac{\Delta A}A+|b|\frac{\Delta B}B-|c|\frac{\Delta C}C##?
16. ### Error analysis: propagation of error

Homework Statement The following may appear to be a rather strange question but I have no access to a lab to conduct experiments so I have to rely on my imagination, and questions from textbooks, to contrive questions that will hopefully improve my understanding of a topic. I have recently...
17. ### Error of an instrument

Homework Statement For my lab report I am asked to calculate the error of a couple of measurements which I did with a lux meter. I know that the lux meter has tolerance(or accuracy?) 5%. The instrument is digital and it's last digit is 0.1. The maximum reading is 47.5 lux. Homework Equations ...
18. ### Uncertainty of a chosen value

Homework Statement I have taken 5 sets of readings of voltage against angle for an experiment to determine specific rotation. (I'm using the maxima to determine the phase shift) So, having averaged these values and determined the maximum, I can then trace back to the angle at which this...
19. ### B Difference Between Trueness & Bias Measurement

Can someone explain the difference between trueness and bias, as used in measurement?
20. ### Using STdev wrong or apparatus error?

Homework Statement I have 3 (n) measurements of the radius of a capillary tube, and I'm wondering whether I should take the STDev of these values and then divide by sqrt(n-1) to obtain a standard error, and use this as my error on the mean... or Do I propagate the apparatus error through and...
21. ### Graphing Data in Excel: Error Bar Confusion

I'm currently writing a paper over an experiment I did for class and I have a very stupid question over I need clarification on before I continue. I am using excel to graph out data, and I have determined that the error in my Length is .001 m. However, I am graphing the inverse of length to...
22. K

### Error analysis E/M experiment -- help please

So I am doing the charge to mass experiment and determining the relationship between: 1. accelerating voltage and radius formed by the electron beam 2. magnetic field strength and radius formed by electron beam Theoretically I should obtain an equation of the form: r = (1/B) *sqrt(2mV/e) where...
23. ### MATLAB Weighting data points with fitted curve in Matlab

Hi all, I'm currently in the middle of performing an experiment for the final project of my MSc, and I have a question about how I should go about weighting the data when fitting a curve to it using the MATLAB fitting tool. Firstly, a bit of background about the problem. I am seeing how low...
24. ### Error Analysis of wall thickness

Homework Statement The internal and external diameter of a hollow cylinder are measured with the help of a vernier calipers. Their values are (3.87 ± 0.01) cm and (4.23 ± 0.01) cm respectively. The thickness of the wall of the cylinder is ?Homework Equations Thickness of cylinder wall= 1/2...
25. ### How do I use the number of oscillations given?

Homework Statement The length of a simple pendulum is about 100 cm known to have an accuracy of 1 mm. Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g? (a) 0.2%...
26. ### How to make a hardware setup for monitoring BER of modbus

I have to devices in communication with modbus protocol. Master is PC and slave is compressor(100ft line,RS485 standard, modbus RTU protocol). I have to build a setup which will show how much the error in communication. I am coupling some white noise to the line and some burst signals too. I...
27. ### I Linear regression on data collection error

Hi I've collected few sets of data and obtained significant different linear regression (R^2) in 2 particular sets of data . Does that indicates the 2 sets of data is not validated which might due to data collection error? For example, 20 sets of data contain linear regression of 0.900+...
28. ### Significant Figures & Error Analysis

Hi, I've just had my first lab in physics and I'm having a bit of trouble understanding how to determine the significant figures of my final answers and transforming them in scientific notation. For example: Homework Statement [/B] I had to measure three sides of a parallelepiped with a...
29. ### Error Calculation Homework: Can I Kill 1 Bird with 2 Shots?

Homework Statement I have to shot 100(±5) to kill 50. how many shots I need to kill 1 bird? Homework EquationsThe Attempt at a Solution 100±5/50 = 2±0.1 this solution is so simple, I think it is not right - is it? :rolleyes:
30. ### Best Method of Analyzing Experimental Percent Error

Homework Statement I have performed a chemistry experiment where I analyzed how the diluting of two reactants with the same volume and initial concentration impacts the percent yield of a precipitate product. Thus my IV was concentration and my DV was percent yield. My question is what is the...
31. ### I Why is the standard deviation the error on the singular meas

I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation ##\sigma## of a series of data. There is one fundamental thing about ##\sigma## that I read but I could not understand. >In a series...
32. ### Calculating the error in <x^2> from the error in <x> (Molecular Dynamics)

Hi, does anyone know of an easy way to calculate the error in <x^2> from the error in <x>? I am running a molecular dynamics simulation and trying to work out the error in the fluctuation of kinetic energy <dEk> = <3/2NT^2> - <3/2NT>^2 from the error in <T>. Thanks in advance
33. ### I Error propagation estimation

I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}## where B, M, N and relative uncertainties are given. And M and N are dependent on B. Could you show me how to calculate and estimation for the uncertainty on A? Thanks a lot
34. ### Calculating errors after curve fitting (linearizing) graphs

Homework Statement I did a lab this week measuring periods of swings of a simple pendulum. We need to curve fit the equation T=k*l^n and we got ln(T)=n*ln(l)+ln(k), and we need to plot the data we collected into the linear graph, meaning out y axes is ln(T) and our x axes is ln(l). So far all...
35. ### I in deciding what my error bars should be

So, we did an experiment to find the dissolved oxygen concentration in % over time in a stirred tank reactor at 2 different flow rates and at 3 different agitator speeds. We did not do any repeat measurements, it was just one reading per condition. Now I am confused what sort of error bars I...
36. ### Error Propogation for Half-Life

In this homework question we are told to calculate the half-life of an isotope based on count-rates before and after a given time interval, the relevant equation is given below. Half-life = t1/2 = tln(2)/ln (A/A0) The second part asks to determine the standard deviation of the half-life due...
37. ### Another Error Analysis Question - how to go about it?

Hi folks, apologies if this is in the wrong forum. I'm a new undergrad physics student and I'm having trouble figuring out how to 'do' error analysis. (I had a quick look through some similar posts here & am still none the wiser.) I'll use my recent lab experiment on Resonance in a Tube as an...
38. ### Maxwell 2D (ANSOFT): Error analysis

Dear all, I've done many analysis in Maxwell, but in the last ones I'm paying special attention to the error plots. I've been ploting Energy Error and Time Error, but I've got the feeling that I don't know how to properly interpretate it. Fist of all, to validate one simulation, should I...
39. ### Error Analysis of Modern Gram Schmidt Technique -code bug

Hi all, I am to compute A = QR using the Modified Gram-Schmidt algorithm. I need to find the error using the one norm of : (Q transpose * Q) - I. Here is my code: %Modern Gram Schmidt p=zeros(5,5); e=zeros(5,5); g=zeros(5,5); for k=1:n; p(:,k)=(A(:,k)); end %j=k, i=u, r=g, q=e, v=p for...
40. ### How to round in error analysis

Hi, to start with my questions I will show you what I have done so far. (23.56+/-0.05) km/h x (56.3+/-0.4) h So I ended up with (1326.428+/-12.234) km But I know the real answer is (1330+/-10) km What I don't understand is how I would round to that answer. I do not know what I have to look...
41. ### How did error analysis evolve over time?

Hello, all, I am wondering if anyone can provide me information on the historical origin of error analysis; that is, with the quantification and mathematical manipulation of uncertainties in measurement. I find that all the textbooks I have stumbled upon provide a narrative of physical...
42. ### How is the error in the gradient calculated?

Homework Statement A series of 5 measurements of Y are recorded with increasing X. (i.e. gradient has units Y/X) The error in measurement of Y is ±0.05 The error in measurement of X is ±0.005. How is the error in the gradient calculated? Homework Equations - measurements[/B] Y | X...
43. ### Error analysis of a function

Hi guys, I have a silly question, but I seem to be confused about it. Let's say I have a function of Newton's cooling law. I measured the exponential drop of the temperature of some system and now I want to make an error analysis. Do I treat this function as a two variable function of tau (time...
44. ### Calculating Experimental Error

Homework Statement I am writing a lab report for an X-ray diffraction. I have been attempting to come up with an equation for the error using formulas some people from college gave me and also some I found on wikipedia but I am quite sure I am doing it wrong. The only variable is the angle...
45. ### Charge to Mass Lab Error Analysis

In a lab measuring the charge to mass ratio of an electron I am having trouble with the error analysis. Specifically, this lab measured the radius of a curved path of an electron in a magnetic field (generated by Helmholtz coils with a a current 'I' running through them) with the velocity of the...
46. ### Statistical error analysis of Geiger counter?

1. Homework Statement An average value of N measurements is defined as: ravg = 1N ∑ ri where i = 1 and it sums up to N measurements By using this expression in the master formula for a general function z = (x1, x2,...) error propagation, we find the δravg error propagation: (δravg)2 =...
47. ### Help with error analysis ly needed

Help with error analysis! urgently needed Homework Statement Using the theoretical prediction of t, find the errors of both t and x, . The problem is based on an experiment I did in Labs, In which a small metal ball was fired at 40° (uncertainty 0.5°) to the horizontal, at a height,y= 1.095m...
48. ### Error analysis and propagation

Hi folks, I have a rather simple question on error propagation - I have 2 sets of models, where the results from model are used as variables in the next model. I need to know how to carry forward errors from one to another. Case - Model 1: Y = a*exp(b*X) + c The errors on X (which is a...
49. ### Simple question about Error Analysis

I'm doing a report on a set of lab data and am supposed to find the mean and mean's standard deviation \bar{x} + \sigma_{\bar{x}} The mean is given by \displaystyle{ \bar{x} = \sum_{i=1}^{N} w_{i} x_{i} } Where \displaystyle{ w_{i} = \left( \frac{\sigma}{\sigma_{i}} \right)^2...
50. ### What is the Standard Deviation of the Mean for Lab Homework Data?

Homework Statement Using 5 different ammeters, you get the following data (all measured in Amps): I_{A} = 128 ± 2 I_{B} = 121 ± 1 I_{C} = 114 ± 8 I_{D} = 120 ± 3 I_{E} = 122 ± 4 Calculate the mean current and the standard deviation of the mean. Homework Equations Standard...