Error analysis Definition and 100 Threads

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. J

    Error analysis of acousto-optic effect

    Homework Statement Hey guys, I have recently done an experiment in regards to the acousto-optic effect (which in itself is freaking amazing!). And i need to do an error analysis for my value of the phase velocity. I believe i have made a mistake but i can't find it anywhere. Firstly i have...
  2. M

    Error Analysis and Simpson's Rule to approximate integrals

    Hey there, This isn't exactly a homework question, but my question did arise while doing homework and I wouldn't know where else to post it, so here I am. I'm a Calc 2 student and covered approximations of integrals that I normally wouldn't be able to integrate today. I was going through the...
  3. G

    Measuring error analysis with 3 variables

    Homework Statement Consider the function F(xyz)=x^4+5y^4+2yz+3. Let the uncertainty in x be represented by the variable dx, the uncertainty in y be represented by the variable dy, and the uncertainty in z be represented by the variable dz. Find an algebraic expression for the uncertainty in...
  4. D

    Why do we report the standard deviation of the mean in error analysis?

    I've done a decent amount of reading on the subject, and I used this method of course when reporting errors during lab experience I got as an undergraduate, but it was never quite fully explained to me why exactly we report a value +/- the standard deviation of the mean as our result. Why not...
  5. E

    What are some recommended textbooks for error analysis in scientific research?

    I was recently told I needed to review some material and they recommended I look at Bevington: http://books.google.com/books/about/Data_reduction_and_error_analysis_for_th.html?id=0poQAQAAIAAJ I haven't had a chance to look at it yet, but I was wondering if anyone had any other...
  6. M

    How to Determine the Error on Magnetic Susceptibility?

    Homework Statement Alright so I'm writing a lab report and I am running into a problem of finding the error on this value. I am measuring the magnetic susceptibility of a couple of samples. My lab manual and instructor told me the error on the force is related to the error on the derivative of...
  7. B

    Error analysis, multiplying an error

    Equation: M (ΔT)= The question: If ΔT has an error of one degree, and i multiply it by the mass of an object (m) is the error in y still one Attempted answer: or is it proportional to M i.e Δt plus or minus 1 degrees so the error in y is 2M? P.S i need to be able to know the error...
  8. Z

    Measuring Error in Finite Difference Electrostatic Solutions | Tips & Tricks

    Hello everyone I am solving an electrostatic problem (with analytical solution) using a finite difference method and I want to plot the error of the FD against the analytical solution. What would be a good way to measure the error? I tried the relative and absolute error, but since values...
  9. C

    Simple error analysis for probabilities

    I'm dealing with a histogram and want to use poisson errors for each bin. For example, having 7 items in a bin gives that bin an error of sqrt(7). I'm comparing four different data sets, each with different sizes. I'm scaling everything in terms of probabilities so the four data sets can be...
  10. A

    Error analysis: significant figues

    Homework Statement I have three measurements for the L, W, H of a box: 40.4, 14.9, 17.0. the volume would then be 10233.32cm. each of my measurements has three sig figures, and it says in my book that with multiplication the product should have no more sig figures than the measurement with...
  11. Z

    Error Analysis: Check doop=1.021+-1.3e-3

    Homework Statement doop=a^{3}/(a^{3}-(b^{2}*d*s0/L) a=4.65+-0.03 b=4.60+-0.03 s0=3.987+-6.906e-3 d=5.05+-3.03 could someone please check that if they get the same answer as me: doop=1.021+-1.3e-3 Homework Equations The Attempt at a Solution Homework Statement Homework Equations The Attempt...
  12. Z

    Error Analysis of Sin(x) with x=2±0.2

    Homework Statement let x=2±0.2 y=sin(x) write y in the form mean±error i don't know how to perform error analysis on the sine function help please Homework Equations The Attempt at a Solution i looked through a physics textbook and saw something which might help me...
  13. B

    Error Analysis- Deriving Equations

    Homework Statement In this experiment, the acceleration due to gravity is related to the time, t, it takes the ball to fall to a distance , y, by Eq. (3). With this equation and Eq. (2), show that the fractional error, ∆g/g is ( (∆y/y)^2 + (2∆t/t)^2 ) ^1/2 Homework Equations Eq. (3) =...
  14. V

    Error analysis in log space: How to handle exponents in regression analysis?

    Homework Statement Maybe, I am a little stupid, but I just can't understand what I am doing wrong here. I have 2 quantities which I have to convert to log (base 10) and perform a regression analysis. Quantity=1.235e9 error=3.4475e8 Homework Equations I have to express the above...
  15. R

    Error Analysis of Airfoil Experiment

    I have done a wind tunnel experiment on NACA 0015 airfoil for different angle of attack at a fixed velocity. Also calculated Cp, Cl, Cd and Cm for each angle of attack. Now I want to do an error analysis to find uncertainties in Cl,Cd and Cm. Please explain how I'm going to do that? I have...
  16. jegues

    First Order Error Analysis (Taylor Series)

    Homework Statement The equation for the velocity of a falling parachutist can be computed by, v(t) = \frac{gm}{c}(1-e^{-(\frac{c}{m})t}) Use a first-order error analysis to estimate the error of v at t = 6, if g = 9.8 and m = 9.8, c = 12.5 plus or minus 1.5. Homework Equations...
  17. R

    Integral Approximation and Error Analysis

    Homework Statement Approximation of e^(x^2+3x+1) from 0 to 3 within .2 of the actual integral. Homework Equations Riemann Sum or Trapezoidal. (We haven't learned Taylor yet). The Attempt at a Solution Last n value i found was 148068 which gave me a delta x of 3/148068...im very...
  18. V

    In immediate need of help with error analysis

    Homework Statement I have used excel to make a linearized fit of data - x and y variables - with no problem. But I must solve for a value that can only be extracted from my slope, also not a problem. My problem is I don't know how to calculate the uncertainty for my slope, based on the...
  19. H

    Calculating Average Error Uncertainty from a Large Set of Data

    Homework Statement Hi, I have this question that is bothering me. If I have a large set of data, each with its unique error uncertainty. How do I get the average error uncertainty from all the data points? Do I simply use the equation below: (∆ Z) ² = (∆A)² + (∆B)² And divide...
  20. H

    Error Analysis: Calculating Error from Radiation Counts

    Not sure if this is the best place for this post, if it isn't any recommendations would be appreciated. My qustion concerns calculating the error from a set of radiation counts. I understand that the error in a single radiation count is \sqrt{N} where N is the number of counts. My question is...
  21. M

    Understanding L2-Norm & Equation: Error Analysis Help

    Could someone please explain to me in fairly basic terms what the L2-norm is and what it does please. More specifically let me know what the following equation does, if possible... E(N) = 2*pi \int (U(N) - Uexact)2 r dr Where E is the error for a specific N. Ultimately I have values for an...
  22. Y

    Which Method Yields the Correct Mean in Error Analysis?

    Homework Statement This comes from the data analysis of a lab on the Michelson Interferometer. d1={.208 mm, .275 mm, .214 mm, .214 mm, .230 mm, .230 mm} d2={1.757 mm, 1.505 mm, 1.725 mm, 1.773 mm, 1.640 mm, 1.732 mm} r=5.13945\pm.11981 \lambda\approx\lambda'=599\pm23.7\ nm Homework...
  23. L

    How can I use calculus to analyze errors in angle measurements?

    URGENT URGENT ... Error Analysis in angle Homework Statement This is very urgent i could not find out how to find the error in my angles... using calculus this is not my level but i must do it somehow.. i would love to see some steps that i can follow. i know that for example E = mgh...
  24. L

    Error Analysis Trig: Diff theta w.r.t o & h

    Homework Statement d(theta)=1/sqrt(1-(o/h)^2) how would you differentaite the function of theta respect to o and h ? im very new to calculus, i would appretiate if someone giave me a very large step because im in a hurry to understand this and the sun is soon to rise please...
  25. P

    Newton's Method & Error Analysis

    Homework Statement (i) Use Newton’s Method and apparent convergence to solve x ln(x) = 5 accurate to 3 and 4 significant figures. Start out with x0 = 2. (ii) Directly approximate the absolute error on f, i.e. _f = f(x) − f(˜x). (iii) Use the difference between the 4 significant figures...
  26. B

    How to do error analysis in this lab on linear motion

    Okay so I did a lab on Linear Motion using the glider with the air track and a spacer. This is the information I have about the glider and spacer. glider mass = (468.7 +/- 0.02) g thickness of spacer =(14.8 +/-0.05) mm I'm stuck on doing the error analysis and I don't know how to go on...
  27. B

    Error analysis using partial derivatives (wrong forum, can this be moved?)

    edit: Totally put this in the wrong forum on accident. Can it be moved to the Calculus and Beyond forum? Thanks. Homework Statement calculate the error associated with stress and strain Homework Equations First equation is stress, second equation is strain. P is load, A is...
  28. L

    Improving Error Analysis Techniques for Physics Students

    I am a First year Physics Student going into Second Year in a few weeks. I've been coping very well with all the work and theory. However Along with tight and Limited Lab schedule my sessions feel rushed and unfurfilling, particularly the analysis section. Although we are given a lab manual...
  29. A

    How Do Derivatives Estimate Measurement Errors?

    Homework Statement I have a resistor which has value written as 5K\Omega and I measured the value and it is 4.8K\Omega. I want to work out the error. 2. The attempt at a solution I can use simple percentage calculation to get \frac{4800-5000}{5000} \times 100 = -4% error but I've been...
  30. N

    Error Analysis of Experiment Data: Calculating Percentage and Absolute Error

    Homework Statement In my latest experiment, I have found two sets of data from the data processing. Normally, the values in the data sets should be equal, but they are not as a result of the error of the experiment. How can I do the error analysis? (Percentage Error, absolute error...)...
  31. R

    Mass momentum of inertia in lab, error analysis

    Homework Statement Hi, I've a lab assingment, and the labwork must be planned beforehand, but I have some trouble figuring out some parts of my error analysis. So, I'm supposed to measure (as in not use integrals to find out) the mass momentum of a ball. The plan is to place the ball on an...
  32. X

    Error Analysis for Moles of Calcium Ions in 250mL

    Just a quick question about error analysis. Moles of Calcium ions in 10 mL = 6.0 x 10-4 ± 0.5 x 10^-5 mols I'm suppose to scale this number to Moles of Calcium ions in 250mL. So when I multiply by 25, do I multiply the error value as well? Or does it remain the same?
  33. T

    Solving Coupled Flow and Diffusion in COMSOL: Error Analysis

    Hi, I am not sure if this is the right place to post a COMSOL question. If not I apologise, could you point me to the right place. I have a 3D geometry in COMSOL shape like a "T" where I want to model flow using navier stokes and a chemical diffusion using convection and diffusion. Both...
  34. B

    Estimating Error in Titration Results Using Second Derivative Analysis

    I have an error analysis question...I carried out a titration, and I have error for each measurement, but I then took the second derivative of the data and graphed it. The actual value I am reporting was estimated from the x-intercept of this graph. The curve was not fit to anything. How do I...
  35. G

    Troubleshooting Gradient Errors in Linear Graphs: Tips and Techniques

    I am trying to work out the error in the gradient for a linear graph. I have worked out the the RMS error for the y-values, but since I am using excel to determine the graident of the graph I am a little unsure about how to work out the percentage error in my gradient from the RMS error. Am i...
  36. B

    Error Analysis On Excel Questions

    Homework Statement The error part of my physics labs have been takin up a lot of time lately. Anyways, say I have 10 numbers for time measurements like 3.53 s, 5.32 s, 3.57 s, 4.89 s, 3.24 s, etc... and my reaction time is say +/- 0.20 s. I want to average these 10 values out but I have to...
  37. S

    Kepler's Law: Error Analysis & Mass of Earth

    hello everyone, I have a couple of questions from my astonomy course that are confusing me. 1. Which do you think would cause the larger error: a 10% error in "p" (period of orbit) or "a" (length of semi-major axis in units)? I would think that the "p" would produce the larger error, because...
  38. $

    Error Analysis Help: Line of Best Fit with Error Bars

    Homework Statement I am trying to work out if there is an elegant way to do a line of best fit(straight) through a set of points (3) while taking into consideration their error bars? Clearly I'm looking for a piece of software that can do this. Obviously excel, etc can do a standard straight...
  39. R

    How Do You Calculate the Error in the Y-Component of Force?

    Homework Statement What is the error in calculating the y-component of the force created by a hanging mass (m=432.23g) at an angle of 28º? Take g=9.81m/s^2)Homework Equations Fg = mg The Attempt at a Solution Fg = mg = (0.43223kg +/- 0.000005kg)(9.81m/s +/- 0.05m/s) = (0.43223 +/-...
  40. E

    Finding Velocity & Error Analysis from Position vs Time Data

    Homework Statement I have a physics lab due and need help finding a velocity vs time graph from a position vs time graph. I also need help finding the Mathematical error analysis from the data. here is the data for the position vs time graph time(sec) position (cm) 0.0000 0 0.4084 10...
  41. N

    Error Analysis: Solving 2a^2 + b^2 with Uncertainty (a=6.0+/-0.1, b=17.5+/-0.3)

    given that a=(6.0+/-0.1) and b=(17.5+/-0.3) what is 2a^2 + b^2 i'm having so much trouble with this i think we first go (6.0+/-0.1)^2 then times it by 2, and add (17.5+/-0.3)^2...i tried this but couldn't get the right answer...what am i doing wrong? ...ANY help would be greatly...
  42. R

    Methods for correlation and error analysis (statistical)

    1. A system of 7 objects each have one measurement taken of them. These measurements are to be compared with two theoretical models, which theoretical model does the data fit best?[br]The machine used to measure the values has an extremely small error, so the data gathered does not have...
  43. D

    On error analysis of my practical

    [Urgent]On error analysis of my practical Homework Statement well, the aim of the practical is to calculate the speed of light using LED, oscilloscope and varying fiber optics cable. i have my results as follows : L /m t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 taverage 5.00 (28 30 28 28 28 28 28 28...
  44. D

    How Do You Represent Error in a Log-Log Magnetic Field vs. Distance Graph?

    Hi, I'm investigating the variation of Magnetic Field with Distance. The investigation requires me to plot lnField against lnDistance. My question is, say the quantities had an error of +/- 0.01 mT for the Magnetic Field. How would I represent this on the ln Field v/s ln Distance graph? I...
  45. F

    Why is the calculated ∆S error 0.0007m instead of 0.0005m?

    i have 5 values of slit width S 0.0015m 0.0158m 0.00191m 0.0021m 0.00257m the standard error is plus or minus 0.0005 however my teacher says she wants us to calculate ∆S error she says its ∆S=S(subscript 2) - S(subscript 1) she says the answer is 0.0007m WHY IS THIS SO...
  46. M

    Optimizing Subgroup Selection in Gaussian Distribution for Error Analysis

    Here is a question I can not seem to get from an error analysis course. Assume that you have a box of resistors that have a gaussian distribution of resisances with mean value mu=100 ohm and standard deviation sigma=20 ohm (20%resistors). Suppose that you wish to form a subgroup of resistors...
  47. bayan

    My Report on Experiment & Error Analysis

    This is my report on an experiment that I have done and I really needed the latex codes to generate the equations. I have done the other parts of the report on other PC. Do they seem to be ok? (the errors, like the max possible value and min possible value) no help is really needed, rather...
  48. I

    Is this error analysis equation correct for a simple geometric mean?

    Any error analysis gurus out there? I'm trying to work out the uncertainty for the following equation: C = \sqrt{(A-B_A)(P-B_P)} A and P are counts from a radioactive source from two opposing detectors. B_P and B_A are background counts with no source present. It's a simple geometric...
  49. J

    Understanding Lagrange Error Analysis

    In my BC calc class, we just finished working through most of series and sequences, and as we were reviewing years past free response questions on the topic, and in 2004, they dropped a lagrange error analysis. I've been looking at different explanations, but I'm not getting the concept. It...
  50. F

    Solving Error Analysis for Acceleration: Troubleshooting with Simple Formula

    I'm having a problem with something I know should be simple, but my answer is off so I'm doing something wrong. I need to find the amount of error for an acceleration that was found using the formula a=2d/t^2. Where d represents distance travelled. There is no uncertainty in the distance...
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