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.
1,050 questions
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Is the measured value of G a true constant, or an average affected by internal structure and attenuation? [closed]
The gravitational constant G has been measured in various experiments since Cavendish, but nearly all assume that macroscopic bodies (like test masses or the Earth) act as uniform sources of gravity. ...
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Confused with Vernier Calipers [closed]
I've been lied to about the correct method to read vernier calipers by my teacher. And I realised it 10 years later when I myself become a teacher!
Sorry, for the rant, but I have to make sure, which ...
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How should you handle uncertainties of when determining mean count rates of radioactive sources?
When taking count rate measurements, I get a mean of 572.41 #/s. I have taken one measurement per second, totalling 596 measurements. After consulting Glenn F. Knoll's Radiation Detection & ...
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Is there any general principle for why small deviations in models give only small errors in predictions?
I have a question regarding the pragmatic heuristic that goes something along the lines of
"Small deviations from reality in a model yield small errors in the predictions of the model"
Is ...
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Scientific notation with/vs. complete integers
I got into a fight on the zsh forum over the fact that zsh uses '5.' to indicate the integer 5 but stored as a floating point number. I protested that '5.0' would be better since the trailing dot is ...
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What are the main sources of systematic uncertainty in $Δα/α$ measurements from quasar absorption lines?
Studies like Webb et al. (2011) and King et al. (2012) have reported small deviations in the fine-structure constant, α, using quasar absorption spectra at high redshifts. These rely on precise ...
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How can I determine the error for assuming earth is and using Cartesian coordinate system
While I was reading through HRK came across this problem
at the last picture it's asking
"Can you estimate the distance d that the airplane must fly before the use of flat Cartesian coordinates ...
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Does this spring work with Hooke's law or not? [closed]
In the table is the data from the spring. In the y axis is the force in Newtons, and in the x axis is the extension in meters.
Edit: I found out the reason why this spring did not work as initially ...
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Statistics for Theoreticians
I'm a theoretician, and as the years pass, I notice my knowledge of statistics and my memories of experimental physics classes fading and becoming more and more uncertain. Thus, I'd like to ask for ...
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Is it okay if your signal and noise have the same statistical distribution?
Please bear with me if this seems like a very basic question. Let's say you want to detect a signal by measuring a variable $x\in[0,\infty)$. Let's say you know the variable $x$ follows a probability ...
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Questions about calculations of significant figures
Essential Physics 4/e by Richard Wolfson states this:
In addition and subtraction, the answer should have the same number of digits to the right of the decimal point as the term in the sum or ...
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To what extent can we trust a measurement and its uncertainty?/Is there a rigorous framework for measurement?
The underlying driving question here is really just "How do I trust a measurement?"
Ultimately, I'd like an answer(s) that applies to any measuring device (be it a voltmeter, telescope data, ...
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Triangulation, how, by drawing triangles schemes, does one control the error of the measurements? [closed]
I am trying to understand triangulation, especially I am focused on the triangulation Méchain and Delambre achieved in the end of the 18th century, in order to measure the distance between Dunkirk and ...
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Length of an object
Usually, when we measure the length of an object in reality, we determine the end point and measure it. But if you look at the boundary between the object and the vacuum, you can't know exactly how ...
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Numerically marginalizing over a parameter
I am working with gravitational waves data. I have done a Bayesian parameter estimation using dynamic nested sampling. So I have posterior distributions for several parameters. Now I want to ...
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When to average measurement results?
What do I want to do?
I want to measure the gravitational acceleration $g$.
To do so I measure the fall time
of an object from a height $h$, which I have measured previously up to a uncertainty $\...
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How is $\pm$ notation taught / actually used by professionals?
When using notation like $5.7 \pm 0.2$ to indicate a measurement and error, it seems like there are many standards to what this could mean. Is there a standard taught to students? Is there a standard ...
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Physical implications of the inexact value of circumference of a circle
Since $\pi$ is an irrational non-terminating non-repeating fraction therefore if it is multiplied by any real number that cannot be represented as a product of $\pi$, the result will be a non-...
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To what extent is gravitational wave “observation” a function of model-matching?
I'm asking about the epistemic structure of the detection process — not whether gravitational waves are real, but how we decide that what we've seen is a specific event, given that the match is ...
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Error on Integral of a Gaussian given Amplitude, Mean, and Width Errors [closed]
I am fitting physics data with a gaussian function. The gaussian function has a mean(where it sits along the nsigma axis), width, and amplitude, along with corresponding errors for these parameters.
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Should I apply a non-linear formula before or after averaging repeated measurements?
I have to perform an experiment in my university where I have to determine the refractive index of a lens using the non linear formula, $\mu = 1+ \frac{R}{2 f}$. Now, after taking a repeated ...
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Is the magnitude of error in a measurement inversely proportional to the number of observations taken?
I came across the following question.
A research worker takes 100 observations in an experiment. If he repeats the experiment by taking 500 observations, how is the probable error affected?
The ...
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Monte-Carlo error propagation in divergent function
I have a function
$$
f(a,b)=\left(\frac{a}{b} - 1\right)^{-1}
$$
I have obtained values for $a$ and $b$ from two independent linear fits including errors on $a$ and $b$.
Now I wanted to calculate the ...
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Why do we use $\hbar$ instead of $\hbar/2$ for uncertainty principle? [duplicate]
my question is regarding finding momentum from uncertainty principle (I was trying to find Bohr radius from UP).
We normally state the uncertainty principle as follows:
$$\Delta{x}\Delta{p}\geq \hbar/...
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Does taking a picture mean that time is not continuous? [closed]
If we assume that a picture is a static moment in time, then if time is continuous and can be represented by real numbers, it would be impossible to take a picture, since we can't pinpoint a real ...
user476068
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Which of the two error propagation methods may be regarded correct?
Consider the following problem.
Two resistors of resistances $R_1=(100±3)\Omega$ and $R_2=(200+4)\Omega$ are connected
(a) in series and
(b) in parallel.
Find the equivalent resistance of the (a) ...
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Standard deviation on particle detector efficency
First time posting here, so indulge with me if I do not respect yet the formatting.
In the context of a particle physics work, I am studying the efficency of a detector. More precisely, its efficency ...
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Determination of Ohmic Resistance from Characteristic Curve [duplicate]
When trying to determine the ohmic resistance from measurements of current $I(U)$ at different voltages $U$ of a circuit with the ohmic resistance built in, which of the following methods evaluate the ...
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Why macroscopic/classical objects can't probe small distances? [duplicate]
The usual explanation given to understand why high energies are required to probe very small distances is that we need the de Broglie wavelength of the probe to be comparable/smaller than the length ...
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How does a GPS manage to achieve a precision of about 1m?
I am wondering how it is possible for a GPS to get such a high precision. Looking at the signals sent by GPS satellites, it seems that their bandwidth is about 10 MHz. Based on this, I would expect ...
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What is $Δx$ in Heisenberg's principle? Standard deviation or absolute error (I have 2 sources saying opposite things) [duplicate]
In the statistics of such measurements, we can view, say,
x
and
px as the spread (actually, the standard deviations) in the measurements.
Fundamentals Of Physics Extended, 10th Edition
by David ...
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Uncertainty Propagation
I have recently encountered a question which I am a bit confused about.
The question asks to calculate the uncertainty in $V$ if $R$ has an uncertainty of $2$ and by using a graph for which the ...
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Addition v/s multiplication in significant figures
Say, I measured the length of a rod to be 2.5 units, now I place 4 such rods in line, what will be the length of the new rod?
will it be:
a)10
b)10.
c)10.0
My dilemma:
If I multiply $2.5\times4$, as 2....
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What is the point of using a least squares fit for experimental data points when almost all data points have varying errors in $y$?
Sorry if this is a silly question - 1st year Physics undergrad here. My question is, why does the method of least squares fitting seem so ubiquitous, given that it is always emphasised that where ...
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Understanding Measurement Accuracy in a Temperature Control System
I’m setting up a small experiment for a personal project. The goal is to control the temperature in a water basin using a PT100 sensor, a PID temperature controller, a Solid State Relay, and an ...
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Uncertainties on negative mass spec intensities
I'm developing mass spectrometry (specifically, RGA-QMS or residual gas analysis mass spectrometry with a quadrupole) data reduction software and have encountered an issue with handling negative data.
...
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Why should we not round off in the middle of calculations? [duplicate]
Does rounding off in the middle of a calculation end up giving you wrong answers at the end of calculations?
Why should we not round off in the middle of calculations?
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Is there a concensus on the reason behind the discrepency of neutron decay times?
As some may know, there is a discrepancy of about 10 seconds for the measurement of the decay time of a neutron. This discrepancy exists between 2 methods: the "beam" and "bottle" ...
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Does uncertainty mean fixed, but unmeasurable underlying value, or a measurable value that fundamentally fluctuates? WRT specific question
Consider the following question from Eisberg and Resnick's "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles," pg 84, #4.34
A boy on top of a ladder of height $H$ is ...
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Difficulty fitting a curve with many parameters in SciPy [closed]
I am trying to fit a curve to some data points, however the fit is not as good as I'd like. The function I am fitting too is a ZBL type screened coulomb potential.
This is my code:
...
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Propagation of errors and uncertainty calculations
Looking at an MIT note on propagation of errors, the error of a product $m\cdot v$ works out to the sum of the percentage errors, so we can report the range of values as $m \cdot v =m\cdot v ~(1 \pm ~(...
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Clock uncertainty / building a better clock
Let's say, hypothetically, I've built the best (lowest uncertainty) clock in the world. How is this proven?
We can bring my new clock in the next room to a caesium fountain, optical lattice, whatever, ...
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Error analysis in trigonometric functions
I have a question, here it is -
Given $Y = \sin(\theta)$, find percentage error in $y$ if percentage error in $\theta$ is $2\%$ at $\theta = \dfrac{\pi}{6} \ \text{rad}$.
Our teacher did this ...
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Can I change $4 \ \text{cm}$ to $4.000 \ \text{cm}$ if I want to divide it by $0.127$ to make it appear in $4$ sig figs?
I need to write a report on angle and length. Can I change, for example, $4 \ \text{cm}$ to $4.0 \ \text{cm}, \ 4.00 \ \text{cm}$ or $4.000 \ \text{cm}$ as I like if I want to make the division sig ...
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How many significant digits could the fine structure constant have?
The fine structure constant 1/137,035999... (at low 4-momentum) is a famous quantity of nature.
How many significant digits could it have?
More specifically, could it have more than 62 significant ...
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Is integration physical, but differentiation is not? [closed]
There are electrical (e.g. analogue computers), and even mechanical (ball-pen) methods to generate the integral of a given function.
On the other hand, naively differentiating a physically given ...
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Are there any theoretical reasons why we cannot measure the position of a particle with zero error?
In experimental laboratories, every measurement of the position of a particle always returns an error, which can be very small, but is never zero.
Is this because our measuring instruments are ...
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Combination of line profiles
When combining two line shapes (for example a Gaussian and a Lorentzian), the effect of Both of them combined is the convolution of both (with a Gaussian and a Lorentizan,this is the Voigt function). ...
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Noise in gravitational wave detections
I'm reading a paper (https://doi.org/10.1103/PhysRevD.49.2658) in order to understand the use of Fisher Matrix in gravitational wave detection. I'm a bit confused with the assumptions they do about ...
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Why aren't there approximation signs before some of the values in this table?
Why aren't there approximation signs (~) before some of the values in this table?
This list is from Physics for Scientists and Engineers, 5th edition, by Serway and Beichner.
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