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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Propagation Of Error Calculation Of Incompressible Continuity Equation

Hello I am having trouble deriving the correct equation for error in vertical velocity from the incompressible continuity equation. We are trying to estimate vertical velocity ($w$) from the ...
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Experimental design and precision for calculating moment of inertia

Here is the experiment: A hanging mass is placed on one end of a three-step pulley. The pulley rotates a rod with masses, $m_1$ and $m_2$, on each end. Now, we know the moment of inertia of the two ...
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What if the resulted error is so large?

Suppose that we need to do the error analysis for the quantity: $$F = \frac{1}{A-B}$$ with $A=1.08\pm0.02$ and $B = 1.05\pm0.03$. As usual, it could be evaluated by $$\bar{F} = \overline{A}-\overline{...
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How to interpret the Uncertainty Principle... between measurements?

The insight to understanding why electrons do not spiral into the nucleus was provided by the uncertainty relation between position and momentum - at university, this was described to me as follows: &...
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Uncertainty of the coefficient of friction

We all know the experiment in which one raises the angle of an inclined plane until right before the block begins to slide, in order to establish the static coefficient of friction. The result for ...
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Does Heisenberg's uncertainty principle also apply to measuring velocity? Can we measure velocity at an exact time and point?

There will always be an error in measuring velocity because it is average velocity in some range of time not the exact time. So the physical quantity velocity doesn't exist at a moment. So how come ...
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Minimum $\chi^2$ fit of experimental data in absence of fluctuations of one variable

I know how to make a minimum-chi square fit when I have two variables both affected by statistical error. But how do I perform the fit when one of them has no statistical error, just the uncertainty ...
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Intuition/reason behind method of rounding numbers with significant figures [duplicate]

Edit: Just found another answered question which is an exact copy of my question, check that if anyone has the same doubt. Why was this convention for Significant Figures set up? My teacher taught us ...
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Rules of significant figures, precision, and uncertainty

In the physical sciences (which are physics, chemistry, astronomy, materials science, etc.), we learned that the uncertainty is +/- the smallest unit (which is 1) of the last significant figure if the ...
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3 votes
2 answers
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Is there a fundamental lower bound to resistor precision?

The resistor noise index provides a lower bound to how precise a resistor can be measured, even using ideal instrumentation. Effectively, it even makes no sense to define the resistance any more ...
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Multiplication and significant figures

What is point of rounding off to significant figures in multiplication. e.g. $3\times123456789=370370367$, if I round off the answer to least sig fig it becomes $400000000$ which has a large error. So ...
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Significant figures in standard and scientific notation

I know that standard notation can be changed into scientific notation and vice versa while preserving the number of significant figures, like $100=1\times10^2$ which has one significant figure, or $...
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Uncertainty of a measuring cylinder which is scaled & calibrated using another low volume measuring cylinder

Consider we want to prepare a bigger measuring cylinder (in which the scale division would be 10 liters i.e. 0,10,20,30, 40) We want to do it with a smaller measuring cylinder in which the scale ...
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Understanding the readings of Force Torque sensor based on accuracy and precision

I am working with a 6-axis force-torque sensor to measure the thrust and moments of a model jet engine. I want to understand the significance of the accuracy (measurement uncertainty) and precision (...
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What is a "cycle time" in Allan deviation formula for atomic clock instability? And why does having more independent atoms reduce $\sigma_y(\tau)$?

The usual formula for clock instability is given as $\sigma_y(\tau)\approx\frac{\Delta f}{f_0\sqrt{N}}\sqrt{\frac{T_c}{\tau}}$ First off what do each of these symbols really mean? What is $T_c$? The ...
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Subtracting background from a radioactive measurement

To measure the activity of a certain sample, we need to also measure and subtract the background. An experiment I attended had explicit instructions that the background should be measured before AND ...
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2 answers
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Error calculation for a relative difference with only one standard deviation (STD)

I have a quantity that is calculated with two measurements, but I only have a tabulated standard deviation for one of the measurements. How would I calculate the error on the calculated quantity? The ...
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Equivalent Formulation of Least Squares Method in Terms of Entropy

I have learned that people in the field of machine learning and statistics often use the least squares method. Is there any alternative formulation of the least squares method using entropy? (It might ...
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How do I calculate the standard uncertainty? Task on determination of energy gap width of semiconductors

I am creating a report for my physics class and all I have left to do is calculate the standard uncertainty for this formula. $$ \ln \left( \frac{R_{T}}{R_{\infty}} \right) = \ln \left( R_{T} \right) -...
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Ambiguous propagation of uncertainty

Suppose I have a voltage versus current graph with various "peaks" in current at given voltages. For example, this is what is seen in a Franck Hertz experiment. I can measure the value of ...
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Different fitmodels for different intervals

A number of points were measured and plotted on an XY graph. I want to have the best fit line for this graph. The best fit model for the first part of the graph is described by some function $f_{1}\...
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2 answers
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How to quantify the uncertainty of the time series average?

Usually, we measure a fixed physical quantity, then we simply average MEAN on the measurement results and calculate the standard deviation STD, then the measurement result can be written as MEAN±STD. ...
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3 answers
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Total standard deviation for a set of measurements

I have a doubt about the calculation of the standard deviation for a set of measurement. To explain better what I mean, I will illustrate what I am doing in my experiment. I am collecting the spectra ...
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Finding the uncertainty in angles that need to be changed to radians, when dealing with trigonometry ratios?

I just wanted to ask about how we are supposed to do uncertainties in our experiment since in they y-axis is acceleration/cosx and on the x axis is tanx. Are we supposed to place error bars on both ...
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Non-terminating values of physical quantities in reality

My question is: Can the true value of a physical quantity be non-terminating? It is not possible to measure the true value of a physical quantity due to error (also called uncertainty) in the ...
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What is the theoretical limit on accuracy of an idealized photon detector?

I know that Heisenberg's Uncertainty Principle and the Observer Effect mean there is a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of particles (...
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How to compute errors from a fit?

I have a set of data with errors, how do I compute the error for the fit $f(x)=a$? I remember there are formulas for the errors in parameters for fit $f(x)=ax+b$, i.e. $\delta a$ and $\delta b$. Where ...
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Error propagation for the mean of time-series

From what I have read, when measure repeatedly the same quantity X N times and the measurements follow a normal distribution the uncertainty of the mean is $σ_{mean} = \frac{σ}{\sqrt{N}}$ where σ is ...
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3 votes
3 answers
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What is the meaning of an object having an uncertainty of velocity of 2 $\rm m/s$?

In several questions we are given the uncertainty in velocity of an object and are asked to calculate the uncertainty in position of an object? Well my doubt is that,as when we say that the ...
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1 answer
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How to plot the 95% CLs exclusions when working with MG5/MA5?

So I am a complete noob to phenomenology and I need to plot CL contours for a model I am working on. My model looks kinda like this $$\mathcal{L} = g_{1}\{Fields\} + g_2\{Fields\}$$ and I need to plot ...
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How to correct for periodic errors in data set (worm motor)

I have a monochromator produced by Bentham which I am using for my physics experiment. This runs through the wavelengths in steps of what I thought were exactly 1nm. To calibrate the monochromator I ...
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4 answers
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In a least squares fit, is the resulting error in the fit parameters considered statistical/random error or systematic error?

In a least squares fit, if there is no error estimate on the input data points, is the resulting error in the fit parameters $\sigma_y$ (which is calculated from residuals) considered statistical/...
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1 vote
1 answer
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Uncertainty of output current in voltage-current converter

I have a problem comprehending some things about uncertainty in electrical measurements. Here is illustrative example from my textbook. We use voltage-current converter for measurement. U1 = 10V, I2 =...
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1 vote
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Error propagation in measurement of photon rate

A detector is measuring photons coming from a known source $D$ and a background $B$ which produce photons respectively with rates $F_D$ and $F_B$. Suppose we want to measure $F_D$ by performing two ...
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Propagating systematic error on slope and offset of linear regression

Assume you measure a fluctuating voltage on a photodiode on which a beam of fluctuating power is incident. Or any other pair of values (U, P) with statistical uncertainty. You estimate the statistical ...
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Uncertainty of frequency from tone generator app on phone

If I were to download a tone generation app (sonic) on my phone (Iphone 13) and use it to generate a sine-wave of a certain frequency, what would the uncertainty of the frequency be? How can it be ...
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3 answers
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What is the precision of number 4.03100?

Trailing 0s occurring after decimal are significant. Like 0.302000. Suppose I got the measurement reading of 4.03100, with clearly 6 significant digits.What's the precision of my measurement? Isn't it ...
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2 answers
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Uncertainty derived from assumptions

When determining certain quantities experimentally, we sometimes make theoretical assumptions. For example, we might assume some variable remains constant during the measuring process (when in fact ...
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3 answers
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Is there any exact law in physics? [closed]

Even for maybe the most fascinating computation in physics, about anomalous magnetic moment of the electron, theoretical physics gives: $$a = 0.001 159 652 164 ± 0.000 000 000 108$$ which is not "...
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Is the accuracy of atomic clocks about engineering limits?

I read that a microwave with specific wavelength is shone on a bunch of atom to make them change energy state from ground to excited state, then they measure this difference in energy to determine its ...
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27 votes
19 answers
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Why should a clock be "accurate"?

Having read that atomic clocks are more accurate than mechanical clocks as they lose a second only in millions of years, I wonder why it is necessary for a reference clock to worry about this, if the ...
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2 votes
1 answer
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Uncertainty of a PT100 temperature calibration

Description of the Problem: I have a PT100 that is calibrated by an external lab and used in our lab as a reference for calibrating thermocouples. In the end, I would like to have a complete ...
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3 votes
2 answers
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Determining the appropriate number of significant figures to report in least squares analyses

I'm tasked with fitting a set of data to a line using Excel's $\text{LINEST}$ least-squares fitting routine. The data are $l$ and $m$ values, assumed to follow the relationship: $$l = l_0 + {g\over k}...
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11 votes
2 answers
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If a measurement has 5% error, can we say it has 95% accuracy?

Most often when, in a numerical problem, it is demanded that we calculate the accuracy of the final result, we write the final result in terms of the error. So I want to know if, in a measurement, ...
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Are the blur pictures of black hole a proof of Heisenberg's uncertainity principle?

I wonder that are the blur pictures of black holes due to Heisenberg's Uncertainty principle because the velocity of black holes is unpredictable that's why we couldn't take better pictures of them?
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1 vote
3 answers
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Validity of power law fit (and analytical fit choice)

Context I am carrying out molecular dynamics simulations of trapped ions in a radio-frequency field of amplitude $U_{RF}$ + DC (see details https://arxiv.org/abs/2102.04098). I am studying radio-...
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-2 votes
1 answer
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Do perfectly periodic motions (perfect clocks) exist in nature?

Periodic motions are used in clocks to measure time quantitatively. If we position a pendulum next to process, we can measure how long the process lasted. If the pendulum executed 3.78 periods it took ...
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1 vote
1 answer
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h-bar limits measurement precision. What limit arises for h-bar itself?

The question is simple. h-bar, or $\hbar$, limits the precision of every measurement, books tell us. For example, length measurements are limited by the Compton wavelength. What limit for the ...
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2 votes
4 answers
154 views

Height of a table: what's the uncertainty?

I would like to introduce high school students to error analysis with a simple experiment: find $g\pm \Delta g$ by measuring the time a ball takes to fall from a table, repeating many times. ...
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Significant number and Measurement resolution

It would be kind if anybody could explain how many significant numbers do we have in 0.00034 if the resolution is 0.001? Without the special mention of "the resolution" my answer was 2, But ...
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