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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
22 views

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 ...
user avatar
3 votes
1 answer
42 views

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 ...
user avatar
0 votes
1 answer
39 views

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 ...
user avatar
1 vote
0 answers
15 views

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) -...
user avatar
0 votes
2 answers
66 views

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 ...
user avatar
  • 1,028
0 votes
0 answers
34 views

Where does the error from Origins fitting come from? [closed]

Im using Originpro to do some linear fitting of my data points. Origin calculates the gradient and gives an error. Where does this error come from? Ive assumed its how much the data points are ...
user avatar
1 vote
2 answers
56 views

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}\...
user avatar
1 vote
1 answer
39 views

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. ...
user avatar
  • 11
2 votes
3 answers
31 views

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 ...
user avatar
  • 21
0 votes
2 answers
36 views

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 ...
user avatar
  • 11
0 votes
1 answer
40 views

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 ...
user avatar
0 votes
0 answers
17 views

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 (...
user avatar
  • 285
0 votes
2 answers
80 views

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 ...
user avatar
0 votes
1 answer
36 views

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 ...
user avatar
3 votes
3 answers
90 views

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 ...
user avatar
0 votes
1 answer
28 views

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 ...
user avatar
0 votes
0 answers
17 views

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 ...
user avatar
0 votes
4 answers
55 views

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/...
user avatar
1 vote
1 answer
46 views

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 =...
user avatar
  • 111
1 vote
1 answer
22 views

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 ...
user avatar
  • 442
0 votes
1 answer
39 views

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 ...
user avatar
0 votes
0 answers
34 views

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 ...
user avatar
0 votes
3 answers
96 views

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 ...
user avatar
0 votes
2 answers
82 views

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 ...
user avatar
2 votes
3 answers
198 views

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 "...
user avatar
  • 1,015
1 vote
2 answers
120 views

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 ...
user avatar
  • 11.4k
27 votes
19 answers
11k views

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 ...
user avatar
2 votes
1 answer
81 views

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 ...
user avatar
  • 55
3 votes
2 answers
85 views

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}...
user avatar
  • 723
11 votes
2 answers
3k views

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, ...
user avatar
  • 438
-4 votes
1 answer
70 views

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?
user avatar
1 vote
3 answers
86 views

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-...
user avatar
-2 votes
1 answer
89 views

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 ...
user avatar
  • 1,672
1 vote
1 answer
55 views

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 ...
user avatar
2 votes
4 answers
135 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. ...
user avatar
  • 303
0 votes
1 answer
23 views

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 ...
user avatar
-1 votes
1 answer
47 views

Uncertainty in the relativistic energy [closed]

Relativistic energy is given by formula, $$E^2 = P^2+m^2$$ according to this is it correct to denote the relation between uncertainty in the energy and momentum by, $$E\Delta E = P \Delta P$$ $$\...
user avatar
  • 17
0 votes
1 answer
52 views

What is the total signal strength of the Higgs?

Dealing with the signal strength modifier of the Higgs, a few things escape my grasp : 1/ In the PDG booklet the combined result is presented with an uncertainty, although some of the measured signals ...
user avatar
0 votes
2 answers
43 views

Is there concurrency or is it just missing precision?

Imagine I measure the time of two balls hitting the ground. My stopwatch displays 5.5 seconds for both of them. Then I could say, that both balls hit the ground at the same time. But if I add a few ...
user avatar
-1 votes
1 answer
29 views

How do I calculate the uncertainty of a fraction raised to a power? [closed]

What is the uncertainty of: $y=(\frac{a}{b})^{n}$ Would it be: $\Delta y = n (\frac{\Delta a}{a}+\frac{\Delta b}{b}) y $
user avatar
3 votes
4 answers
175 views

How large does $N$ need to be for statistical mechanics to be a good approximation?

About how many components ($N$) does a system need for statistical mechanics to apply to that system? I took stat mech and biophysics from the same professor in undergrad and I distinctly remember him ...
user avatar
  • 95
6 votes
2 answers
208 views

Uncertainty notation: I am unsure of how the parentheses notation works

If I have a value of $5.868709...×10^{−7}$, and an uncertainty of $7.88431...×10^{−12}$, is it correct to write this as $5.86871(8)×10^{−7}$ or $5.8687(8)×10^{−7}$? A problem I have with the first is ...
user avatar
0 votes
1 answer
22 views

Splitting the line and SNR of optical signal

In this lecture on optical resonance at around 5:28, the professor has drawn two plots, the top one is the time domain plot of pulse amplitude for a short duration of time while the bottom plot shows ...
user avatar
  • 450
1 vote
1 answer
39 views

Poisson error for detected photons

Assume that there are photons arriving at a detector according to a Poission distribution. Let's say we detect 100 photons over 10 seconds. Now I see two ways to calculate the statistical error $s$, ...
user avatar
0 votes
0 answers
31 views

In the uncertainty principle, are $\Delta x$ and $\Delta p$ uncertainties? [duplicate]

I was thinking about a very old exam where the UP was expressed as $$\Delta x\Delta p\geq\frac{\hbar}{2}.$$ From what I understood in my measurement course, the uncertainty of a measurement model $Y$, ...
user avatar
0 votes
1 answer
38 views

Uncertainty propagation time difference

So for an experiment we gathered time data. It a rolling object, where t2 and t1 are measurements of one whole roll of circumference. We estimated time uncertainty at 5 ms. ​ So then estimation of ...
user avatar
1 vote
1 answer
52 views

Fitting of experimental data affected by different kinds of errors

It is quite easy to evaluate the best-fit curve for a set of n data points when the dependent variable is affected by a statistical error (namely when you have n triplets $(x_i,y_i,\sigma_{y_i})$. I ...
user avatar
0 votes
3 answers
594 views

How do I calculate the uncertainty (error) of an oscilloscope measurement?

I currently have a lab report to write and nobody taught use how to calculate the error of our measurements with an oscilloscope could somebody explain it to me? EDIT: We are measuring the Voltage ...
user avatar
  • 1
2 votes
1 answer
71 views

Good book/resource/chapters on the foundations and science of accuracy, precision, and measurement?

I guess measurement and accuracy is a science, and thus, I assume there's foundations and universal theory that can be learned from scratch, independently of international conventions used, just like ...
0 votes
2 answers
68 views

How do I know which linear fit is better?

Let's say we have a simple mass/string harmonic oscillator. Measuring the period of the movement, I can calculate the angular frequency. Knowing that $$\omega = \sqrt{\frac{k}{m}} \qquad \text{and} \...
user avatar
  • 45

1
2 3 4 5
17