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Questions tagged [error-analysis]

Techniques and methods for computing, estimating, or placing bounds on the errors of expressions (formulas) based on knowledge of error distributions, error intervals or bounds of variables and parameters entering those expressions, and of methods used in the computations.

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Estimating error in perturbation theory

Is there a simple way to estimate the error in the eigenvalues when approximating a hamiltonian by its $n^{th}$ order perturbation expansion?
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22 views

Uncertainty Decomposition in velocity signal

I have a timeseries with repeated measured velocity signal (almost periodic signal). To find the mean time-varying velocity, I have decomposed the signal and computed the ensemble-average and the RMSE ...
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32 views

Propagation of error for identical values

I know that if I am given $$f=a+b$$ then $$\sigma_\text{specific} = \sqrt{\sigma_a^2 + \sigma_b^2} \tag1$$ which is a direct result from the more general $$\sigma_\text{general} = \sqrt{\left( \frac{\...
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Uncertainty and percentage uncertainty formulas

So I am curious how does one derive the following relations for uncertainties: Let $p=cxy$ or $p = c\dfrac{x}{y}$ and $r =z^n$ where $c=constant$ $\dfrac{\Delta p}{p} = \dfrac{\Delta x}{x}+\dfrac{\...
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Change in momentum from de Broglie

From $p=\frac{h}{\lambda}$, the textbook concluded that $\Delta p=\frac{h\Delta\lambda}{\lambda^2}$, where did this come from? I've considered $\frac{\Delta p}{p}$ being of the same magnitude of $\...
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Uncertainty on ultrasound velocity in water! [closed]

How do I calculate the uncertainty on the ultrasound velocity in water considering the room temperature? Best
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22 views

''Answered in the comments'' Interpretation of accuracy notation

I have come across the following notation for accuracy of a multimeter: $\pm (+0.03\%\ rdg\ + 4\ digits)$ How should I interpret it? For example, what would be the error for a reading of $3.21$?
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33 views

Uncertainty of $\theta$ in Malus's law

Malus's law can be rearranged to this form $$\theta = \arccos\sqrt \frac{I}{I_0}.$$ $I_0$ is constant. $I$ has a variable uncertainty while $I_0$ has an uncertainty of 1. How can I find the ...
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1answer
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Magnetic susceptibility error by binning Monte Carlo

I am studying the 2D Ising model using Monte Carlo simulations and I have learned the binning (or batching) method for the error statistical analysis. Following this discussion https://books.google.it/...
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1answer
41 views

Redrawing circuit rules

Take a look at this circuit: Is it allowable to redraw the circuit like this ? Can I move cd wire until it merge with b junction ? Can I move e point like what I did in the figure ?If yes why this ...
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1answer
30 views

What is the error in the potential energy calculation of an elongated rod (if any)?

When we calculate the energy stored in the rod after elongation by an external force, we only consider longitudinal expansion. My question is that according to Poisson, there is also a sideways/...
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Calculating uncertainty from $\ln$ equation [duplicate]

I am using an equation $\theta=\theta_0 e^{-\beta t}$, which rearranges into the equation $\ln(\theta) = \ln(\theta_0) - \beta t$ in order to plot a linear graph. I know the error for both $\theta$ ...
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Uncertainty in the measurement tools

There is a question which states, find the percentage uncertainty when the measured value of an object is $6\text{cm}$, given that a vernier caliper is used. $$60.0\text{mm} \pm 0.1\text{mm}$$ Hence ...
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1answer
28 views

Logarithms in uncertainties

I'm looking at the following plot: The vertical lines show the upper and lower frequency bounds for each of the bands W4, W3, W2...and I'm trying to convert them to wavelengths using $\lambda=\frac{c}...
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1answer
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Question on finding the relative error

The question is as under: Find the relative error in Z if Z= A/B Z= A(B^-1) Relative error in A is ΔA/A and in B is ΔB/B My solutions are : As A and B are being ...
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1answer
32 views

Monte Carlo error propagation

I want to assign an error to the standard deviation computed with a Monte Carlo error propagation method. Now, I explain better. If we have a random variable $x$, with mean value $x_0$ and standard ...
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1answer
30 views

Poisson statistics & ratios

The rule of thumb I know for the error on a count for random sampling is that it goes as the square root of the count. For instance, if I observe a radioactive source for $1$ minute and measure $100$ ...
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1answer
32 views

What is the meaning of true value and uncertainty from a measurement?

I am taking the following example: Lengths of an object are measured as : 5cm , 5.2cm , 5.1cm , 5.5 cm. Calculate the true value and the error . The answer is True value = 5.2 cm error = 0.15 ...
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Why there are 3 significant figures in 86400 but 5 in 86400 s ( because of Unit)

My book states one rule for determining the number of significant figures as under: All zeroes to the right of a non zero digit but to the left of an understood decimal point are not significant . ...
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115 views

Why is the resolution or measurement uncertainty of $G$ so bad?

I sorta know how the Cavendish apparatus works, and I know that "Gravity is an extremely weak force" for subatomic particles in comparison with the E&M or nuclear forces that act on these ...
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1answer
19 views

Calculating percentage error with significant figures

I have a problem with significant figures. In an assignment, the paper gives us data to $3$ significant figures to calculate some values but afterwards requires us to calculate the percentage ...
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1answer
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Tipler & Mosca on “accuracy”

In the Tipler & Mosca textbook we are shown how numerical integration (the Euler's method species of it) is done using a spreadsheet program. The authors then go on to say on page 138 that the ...
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What to do if in an equation there are uncertainty on both sides when solving for a variable?

So i did an experiment which requires me to calculate the specific heat capacity of copper. To do that i equate the quantity of heat loss by copper and quantity of heat gained by water. (heated copper ...
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Why is the Standard Quantum Limit (SQL) in Interferometers added as that of mass $m$ and not $2m$?

We write $$(\Delta z)^2 = (\Delta z)_{PC}^2 + (\Delta z)_{RP}^2 + (\Delta z)_{SQL}^2$$ to indicate the contributions to the total error from photon counting error, radiation pressure error and the ...
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Uncertanty in Chi-squared measurements, spectra-like

Let's say I have some observational data. For example: in a certain wavelength interval I measure the flux, 10 000 points, and I have the uncertainty for each one of them. For example: ...
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How to find the standard error of calculated results in comparison with experimental data

Given two sets of data, experimental frequencies and calculated frequencies from some theoretical model: In an article underneath that table, one can find the statement that the "standard error for ...
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30 views

Raising 10 to the power of a value with an associated error

If I raised, for example 10, to the power of a value with an uncertainty, how would that error be propagated?
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1answer
16 views

Error propagation in cone width for kinematic neutron imaging

I'm trying to figure out the error in the opening angle for a cone created with kinematic neutron imaging. The angle is defined as: $$ \theta = \sin^{-1}\left(\sqrt{\frac{Ep}{E}}\right)\,. $$ And I ...
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1answer
44 views

Why was this convention for Significant Figures set up?

In my textbook $3$ rules have been stated for rounding off digits for maintaining the same level of precision as in the provided experimental values, or simply for maintaining the number of ...
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2answers
33 views

Uncertainty for a given value

While including a data table for a lab report, the guidelines asked to include an uncertainty value for each raw data. In this particular lab where we used slotted masses the masses were already given ...
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Subtractive cancellation errors in the lab

I am quite familiar with the problem associated with loss of significance in numerical analysis. This problem seems to be an even bigger problem in the science lab, where subtracting one physical ...
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0answers
28 views

Errors of indirect measurments

Having some troubles with calculating the errors of indirect measurements. Any help is appreciated! I calculated the mass absorption coefficients for different materials and now I need to evaluate ...
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Error in FFT (Sectrum) analyzer Instrument

Recently I performed an experiment on finding the natural frequency of vertical cantilever. I used accelerometer and FFT analyzer instrument for measuring it. First I kept the accelerometer near the ...
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Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator?

Background I: Suppose the commonly used non commuting operator $\hat p$ and $\hat x$. The uncertainty principle told us that $\sigma_p\sigma_x\geq \frac{\hbar}{2}$. In standard quantum mechanic ...
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A theoretical limit of accuracy?

Is there an agreed upon/conjectured theoretical limit to our ability to resolve the accuracy of time?
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1answer
20 views

Length and velocity of a pulse of particles

We are given a pulse of protons of duration $10^{-7}s$ and energy $2KeV$. I know I am supposed to use the uncertainty principle to solve this. I need to get the length and the indetermination of the ...
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1answer
37 views

Least count of Vernier

Is least count not always 1 main scale divsion-1vernier scale divsion or is it always least reading possible on main scale/ no of vernier divsions. question: 1 main scale reading be 1 mm Lets say 5 ...
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1answer
26 views

The difference in using a predetermined error or standard deviation for calculations

Please edit the thread's tags and content if there are mistakes. I am not sure where If I'm posting my question with the right tags. This is a simple question regarding the study of Linear Motion by ...
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2answers
54 views

What is the proper way to combine two different errors for the same measurement?

We did an experiment in the lab (regarding magnetic domain walls) that yielded some pictures that we later on analyzed and manipulated in Matlab (we took an RGB image made it into grayscale one and ...
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Why -20dB is taken as the standard rejection ratio for optical mode rejection in multimode waveguide?

In case of multimode waveguide to demonstrate perfect mode rejection, I saw researchers use boundary of -20dB. If mode power at output is less then -20dB, it is considered as fully rejected/filter out....
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1answer
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Error propagation and data linearization

I am fairly new to teaching error propagation to students but came across a question I couldn’t answer myself. Say we have a set of data that produces a parabola. In order to linearize the data and ...
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1answer
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Intuition behind swapping the known and unknown resistance in a slide wire meter bridge

Today I was learning about wheatstones and balanced meter bridges. But while learning about the sources of error while working with the meter bridge (measuring unknown resistance), I couldn't ...
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60 views

When is the order of magnitude not equal to the exponent of scientific notation?

Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
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2answers
28 views

Would equipment that is wrongly used by a person be considered as a systematic error?

Would equipment that is wrongly used by a person be considered as a systematic error or a random or both? I would say a systematic error because a person could don't know how to use a ruler and starts ...
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How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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854 views

Significant figures while finding errors

The question which arose my confusion: Two resistors with resistance $R_1 = 100\pm 3 \ \Omega$, and $R_2 = 200\pm 4 \ \Omega$ are connected in (a) series, (b) in parallel. Find the equivalent ...
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3answers
128 views

Is this the definition of significant figures?

In a thread I posted recently about significant figures, someone said that they are defined as follows. I will use an example to save time trying to generalize the definition. The person said, for ...
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3answers
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Uncertainty in ripetitive measurements

Good afternoon everyone, I have a question which is puzzling me and I did not found an acceptable answer yet. Suppose you have acquired some data from a measurement and you have the following numbers: ...
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1answer
23 views

Uncertainty estimation of a quantity after its calibration

I have to calibrate power output of a diode to its input voltage. The voltage source has negligible error but the power meter has significant uncertainty (a couple %). I take a number of power ...
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10answers
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Why aren't the 0's significant figures in 0.002?

I understand that significant figures is a term used for "reliably known digits". However, what I don't understand is why the 0's are not counted among these in numbers such as 0.002. Surely, if we ...