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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Measurement Uncertainty of Correlated Quantities
Using a Thorlabs S310C Detector with a calibration error of ±5%.
Let's say I do two measurements of laser power with this detector over a time period of 60s. The first measurement is bare input power, ...
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Calculating average from several independent physical experiments
If I have 2 experiments measuring the same thing. For example, I measure the voltage with 2 different tools (2 different voltmeters). I can calculate the final average in 2 different ways. For example,...
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Measurement paradox
When building electronics to measure usually it is asked what the bandwidth of the signal is and what is the frequency range usually done to limit noise bandwidth and thus have more SNR. To me it ...
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Significant figures in simple calculations
I have the resistivity of a material $\rho = 7.4 \times 10^{-7}$ $\Omega\cdot$m and I want to compute its conductivity $\sigma = 1/\rho$.
Straight forward calculation gives (up to 3 decimals) $\sigma =...
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Fokker-Planck: Uncertainty Propagation
I am interested in propagating the probability density function along the sampled trajectories having parametric uncertainty $a$. However I discovered that the fokker-planck equation for that system ...
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Definition of Uncertainty
I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
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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 ...
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From where does the uncertainty formula come from? [duplicate]
The uncertainty formula is the one used in the laboratories to find the uncertainty of a variable. Say $X$ is a function of $Y$ and $Z$ such that $X=X(Y,Z)$ then it's uncertainty can be found with: $$\...
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Why is the Accuracy in the measurement of Time so important in GPS?
I read in a physics book that
Without clocks of extreme accuracy, the Global Positioning System (GPS) that is now vital to worldwide navigation would be useless.
What would be effects on navigation ...
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How should I esteem the measurement error using an instrument with high precision and low accuracy?
I was performing an experiment about the Beer–Lambert law using a luxmeter I bought online. In the user manual it's stated it has "$Accuracy: \pm\,3\%\,reading\pm\,8\,digits$". During the ...
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Least Count Error is Random or Systematic?
There are so many articles on internet on Error analysis in measurement but some of them relate least count error with systematic and other with random error and some associate it with both of them. I ...
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Air resistance in the Cavendish Experiment
Would air resistance be an issue in the Cavendish experiment or are the velocities so low as to be irrelevant? Could it cause the experiment to fail?
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Why do we usually measure liquids and gases by volume?
Why do measure liquids and gases in volume rather than by weight? Isn't that comparatively more inaccurate since volume changes with temperature and pressure?
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Gaussian approximation integrated over a unit square, written in terms of error function?
So I am new here, and I apologize for my last question being badly formatted with too much extra information making it just painful to read. I am struggling with getting down a 2D Gaussian estimation ...
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Uncertainty principle, maybe it doesn't forbid simultaneous measurements of position and momentum?
Consider the single-hole diffraction of an electron. We can make the hole as small as we like and determine the electron's position with arbitrary accuracy. When it is in the hole, we can hit it with ...
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How error in a measurement is associated with least count [closed]
Error Analysis :-
Q. I want to know that how error in a measurement is associated with least count of measuring device ?
If I take a measurement with Milimeter scale what the Error I have to assume ...
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Temperature sensor in decimal accuracy in room temperature?
I am designing a device, in one of its parts there i need to collect any ticker of room temperature data for its local purpose of device in decimals counter recording such as 30 digits after 21 degree:...
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Median Uncertainty propagation
I have a data set of values each with a different associated error. If I take the mean, I can use standard error propagation to calculate a much smaller error. This will therefore incorporate the ...
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To what degree of precision are atoms electrically neutral?
It is said that if, say, the electric charge is not a Lorentz invariant, neutral atoms are no longer neutral, which is not experimentally valid. I want to know to what degree of precision atoms are ...
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Error analysis for counting experiments
i am trying to refresh my knowledge in error analysis and stumbled over an interesting question.
Suppose i have a radioactive compound and i want to measure the standard deviation of the decay count. ...
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Experimental errors and significant figures
Textbooks indicate that when reporting experimental results, the number of decimal places in the best estimate of the value (mean) should be the same as that in the standard error, e.g. 9.81 $\pm$ 0....
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Signficant figures of calculated values?
Consider the above table. The AS practical examination markscheme states that the signficant figures of calculated values should be the same or one more than the values it was calculated from. We also ...
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Error analysis via two different methods
We have a quantity $a$ expressed in terms of two quantities $b $ and $c$ as $a = b/c$.
It seems to me that there are two ways of estimating the error on $a$, the "physics" ...
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How to characterize the accuracy of a tensor value determined experimentally?
How to characterize the accuracy of a tensor value determined experimentally? I'm particularly interested in first and second rank tensor values.
For a first-rank tensor (a vector), measurements are ...
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Correct Way to Calculate Uncertainty [closed]
Given a function $f(x_1,x_2,...,x_n)$ of $n$ uncorrelated variables $x_1,x_2,...,x_n$, each of which has some small absolute uncertainty $\Delta x_1,\Delta x_2,...,\Delta x_n$, I know that the ...
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Relation between the 2 interpretations of the Courant–Friedrichs–Lewy (CFL) condition
In computational fluid dynamics, one tries to ensure that the Courant–Friedrichs–Lewy (CFL) number of the discretization scheme is less than 1. This is done to ensure that the errors made at a certain ...
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Certainty interval in physical measurements [duplicate]
Let we have the result of a physical measurement like this:
"Experiments have Dirac’s number at 1.00115965221 with
an uncertainty of about 4 in the last digit"
Is this gives any interval ...
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Accuracy of finding electron's magnetic moment
In the little book QED, Feynman says:
"experiments have Dirac’s number at 1.00115965221 (with an uncertainty of about 4 in the last digit); the theory puts it at 1.00115965246 (with an ...
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Hidden rules in uncertainties?
Lets start with the EMF equation, $\epsilon = I(r+R)$, where $\epsilon$ is EMF, $R$ is the resistance of the circuit, $r$, internal resistance and finally $I$, current.
If we are given the values, $I =...
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How to calculate accuracy of a calculated (predicted) coordinate (latitude, longitude)?
Given GPS data that consists of:
Latitude
Longitude
Bearing (degrees)
Speed (meters per second)
Accuracy (radius of the circle around the coordinate where true position can be found with 68% chance, ...
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(Uncertainty propagation) Should variance of log radiated energy be scale invariant?
I need to propagate the error from the measure of the bolometric fluence $ S_\text{bolo}$ to the $\log_{10} $ of the isotropic-equivalent radiated energy $E_\text{iso}$ which is related to $S_\text{...
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How the accuracy of a meter bridge is increased?
It is said that the accuracy of a meter bridge is increased if the null point is nearly in the middle. Why is it so? How to prove it mathematically?
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Understanding uncertainty calculations?
When adding or subtracting quantities I am told to add absolute uncertainties while for multiply and dividing quantities, we add percentage uncertainties. I am trying to gain intuition for why this is ...
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Approximations in physics
I have a very abstract at the same time awkward question. In many formulas across physics we need to take several approximations and often we derive formula from previous formula which had certain ...
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Unexplainable discrepancy between the centripetal force calculated directly and by linear regression
The centripetal force $F_C$ of a uniform circular motion can be expressed as,
$$F_C=\frac{4\pi^2mr}{T^2}$$
where $m$ is mass, $r$ is the radius, and $T$ is the time interval for one revolution (the ...
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Adding absolute uncertainties with different significant figures
I have to add two measures with their respectiuve absolute uncertainties, given by the instruments I have used to measure them. The measures are:
x = 0.486 +- 0.001 m
y = 0.01230 +- 0.00001 m
They ...
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Model with very high chi squared reduced
I've done a latent heat experiment and measured the mass of nitrogen over time while applying heat. These are the results::
Which looks fine, most of the measures are in the linear fit. But when I ...
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Can the standard errors in the slope and the intercept of a linear regression be used to get the uncertainty in the dependent variable?
I have bought a resistor that works as a heater when a voltage is applied to it, and the seller provided me these $ \left(V (\mathrm{V}), T (\mathrm{°C})\right)$ points: $(6.20$, $200)$, $(7.75$, $250)...
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How to include instrumental uncertainty in the uncertainty of a measurement?
Imagine to calculate the period of a pendulum using a software which takes his data from a cronometer that has an inerent instrumental uncertainty of 0.0025 s. In another discussion on this topic I ...
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Significant figures and multiplication
Suppose the volume of a cylinder with diameter $d=$11.92 ± 0.01 mm and height $h=$38.06 ± 0.02 mm. Calculating $\frac{\pi d^2h}{4}$, the volume is 4247.282773 mm^3, without rounding off. Now, I read ...
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Which will be the experimental error in this ripple tank experiment?
I am having some issues while setting my experimental error in a ripple tank experiment where we are studying the interference in multiple slit.
I already know that it is not the most accurate ...
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Why do the uncertainties for a data set of natural logs have the same error?
I am attempting to plot the natural log of a set of values against another set of data on the x-axis in Python.
However when I code the error propagation, as the error for $\ln(\alpha)$ is given by ...
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Is 10/3 Coulomb charge possible? [closed]
I think 10/3 Coulomb of charge is not possible because 10/3 / (1.6 * 10^-19) gives 2.083333..... * 10^19 and after many digits before decimal point we will get point 33333.. at the end and that will ...
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How much does mass center of satellite oscillates about elliptic orbit as its spinning around the Earth?
I would like to know how much the real orbit of satellite can differ to the elliptic one.
Some perturbation of mass center position of the satellite must occur - Earth gravity accelaration changes as ...
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Uncertainty propagation: formulas with average errors vs standard deviations [duplicate]
Suppose that $y=f(x_1,x_2,...,x_N)$, with $x_1,x_2,...,x_N$ a set of $N$ independent variables. If $\Delta x_i$ represents the error in the $x_i$ variable, then, as described here, there would be two ...
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Significant figures and angles
We measure an angle to be -55 degrees (2 sigfigs).
Let us take the sine of this angle. We get sin(-55) (2 sigfigs). Now, since sin(-55)=sin(305), then we can also take the sin(305) (3sigfigs). Now, ...
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Error analysis in measuring wavelength using diffraction grating [closed]
If $\alpha_m$ are the diffraction angles where the diffracted wave has maxima, then the wavelength is given by the following
$$d\sin{\alpha_m} = m\lambda.$$
In order to find $\lambda$, I've run a ...
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Reporting machine resolution as experimental error
I'm doing a measurement with a machine that has a resolution of $0.14 \mu\textrm{m}$. I can do said measurement many times and then calculate the average of measurements, which comes to $52.0094 \mu\...
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Uncertainty measurements done with multiple devices
so I need to calculate the volume of a cylinder. I have measured both the radius and the height with three different devices (ruler, calipers, micrometer), each of them 10 times (total 90 measurements)...
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Uncertainty Calculation: Applying Product Rule instead of Power Rule
I use $\delta$ to represent absolute uncertainty. The power rule for the calculation of relative uncertainty in $t^2$ is
$$\frac{\delta (t^2)}{(t^2)}=2\left(\frac{\delta t}{t}\right).$$
But if I treat ...
