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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21 views

What's role of signal-to-noise ratio in the quantum measurement? [on hold]

Recently, I've been watching videos of MIT opencourse (http://www.youtube.com/watch?v=TcvY8Nt0ZGA&list=PLUl4u3cNGP62FPGcyFJkzhqq9c5cHCK32&index=2) taught by Nobel laureate Wolfgang Ketterle. ...
1
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1answer
24 views

Best way to estimate a coefficient when data have errors

I am a little bit confused about some tecniques concerning error-analysis.Consider this situatiuon: During an experiment I collected a $x,y$ table of data that are expected to satisfy a linear ...
8
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4answers
1k views

Can the accuracy in Planck's constant ever be increased?

I guess I am having some confusion about the history of calculating Planck's constant. I see the mass of the electron may come into the equation here but isn't the measurement of mass based mostly ...
2
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2answers
40 views

Standard convention for $x$ error bars

What is the standard convention regarding the error bars of the independent quantity in a graph? In what situations should I show the $x$ error bars? In case both $x$ and $y$ uncertainties are ...
1
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0answers
8 views

How can I estimate meta-uncertainty?

A type A uncertainty estimate is derived from repeated measurements. For example, I may estimate the uncertainty on a measurement by repeating the measurement $N$ times and then calculating some ...
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19 views

How is this procedure of error propagation called?

I'm calculating the error on $\theta$ from given PDG values for $f(\theta)=sin^2(2\theta) \pm \sigma_{f}$ Question: I'd like to calculate the errors (from the inverse function) as $$\sigma_{\theta}^{...
2
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1answer
40 views

propagation of error - sin^4

I am currently working on an analysis of a Rutherford scattering and encountered a somehow strange behaviour for the errors. It basically boils down to the behaviour of: $$\sin(\theta/2)^4$$ For ...
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27 views

Is there a standard in the manner in which significant figures are used?

I have always understood significant figures to be those figures which we know with certainty. Wikipedia (https://en.wikipedia.org/wiki/Significant_figures) provides a related but less rigid ...
3
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1answer
68 views

Uncertainty in the distance between Sun and other planets

I have read about the orbit distances between Sun and the planets and have come to know for example: Earth is around 150 million km away from the Sun. However I have seen that tht value is only an ...
0
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0answers
16 views

Cathode Ray Tube: Nonuniform Magnetic Field

For an experiment, I found out that the charge to mass ratio of electron was 1.91x10^11 C*kg^-1. So, I overestimated from the theoretical quite a bit. I used a cathode ray tube with Helmholtz Coils ...
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1answer
73 views

Home Work Help: Calculating Entropy for Melting Ice - Clarification on answer

The question states: What is the change in entropy for the process to completely melt 8.0 kg of ice at 0°C? The formulas for Entropy we've been introduced to are: ...
1
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2answers
74 views

Error Analysis involving random errors

The question goes like this: In an experiment, the time period of an oscillating object in five successive measurements is found to be $0.52$s, $0.56$s, $0.57$s, $0.54$s, $0.59$s. The least count ...
4
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2answers
61 views

Combining two data points with different uncertainties

I have two separate algorithms (call them "A1" and "A2") which reconstruct the $(x, y)$-position of an event in a particle detector. I can test both of these algorithms on simulated events from a very ...
1
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1answer
30 views

Systematic+Random Uncertainty for velocity measurement

I have a question regarding systematic and random uncertainties. I have to measure the mean value of a velocity measurement in flow field at a point. I've recorded say 1000 samples in time, which I ...
0
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2answers
64 views

Least Squares Fitting - 68% Confidence Interval

I am fitting a linear polynomial to some data and I have derived the errors for each of the best-fit parameters from the covariance matrix. I would expect these errors to correspond to a $1\sigma$ 68% ...
16
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2answers
897 views

How to deal with zero uncertainties?

Suppose you measure quantity $x$ with an uncertainty ${\rm d}x$. Quantity $f$ is related to $x$ by $f=x^2$ . By error propagation the uncertainty on $f$ would be ${\rm d}f=2x{\rm d}x$. If a certain ...
0
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1answer
35 views

Error analysis / propagation : trigonometry

If the hypotenuse of a triangle is (1536 +- 3)m long, and the (non right-angle) angle measured from the ground is (22.2 +-0.1) degrees, what is the height of the triangle, and the error in this? sin(...
0
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1answer
36 views

Why is the standard deviation the error on the singular measurement?

I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation $\sigma$ of a series of data. There ...
0
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1answer
55 views

What is the accuracy when firing an electron at a target?

Consider firing an electron at a target. Let the target be at a distance $d$ and the electron be travelling at a non-relativistic speed $v$. How can we estimate the maximum possible accuracy ...
0
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1answer
48 views

Propagation error for a third grade equation

I am trying to find the value for the roots$\pm$error for a set of experimental data. The function that fit the best is $$\epsilon(t)=a+bt+ct^2+dt^3.$$ Which is the best way to calculate the roots $\...
0
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0answers
44 views

Can we calculate the point on Earth nearest to the Moon?

We have the ability to calculate the Moon's orbit in order to predict Lunar and Solar eclipses precisely. Using our known calculations of the Moon's orbits, can we calculate the closest point (city ...
0
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0answers
26 views

Question about errors, Hubble's constant

I am just looking through some old notes I have from for cosmology, and theres something cropped up that i can't seem to figure out: Say I have two (or more) values for $H_o$ each with errors such as:...
3
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1answer
88 views

Measuring very long half lives accurately

There are already some questions about long half life times for radioactive elements, explaining how to calculate the half life time. Now I am wondering: When you have some radioactive material and ...
0
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0answers
25 views

Total uncertainty of multiple stereo camera depth measurements

I have a stereo camera that measures depth for a rectangular area of pixels in a single image. Each depth measurement is obtained independently (this goes back to the stereo matching algorithm used). ...
4
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60 views

Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical ...
2
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1answer
28 views

Correction for uncertainty of multiplications and divisions

The conventional means of obtaining uncertainty of $c$ where $c = a \cdot b$ is adding percentage uncertainty of $a$ and $b$. This method seems to have a flaw as shown below (please excuse me if I am ...
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0answers
37 views

Difference between Theoretical and Experimental Errors

When performing an experiment to find a certain value $f(x_1,x_2,..,x_n)$, we can find the error for each measured $f_i$ using partial derivatives, and we can find the experimental error $|f_i-\langle ...
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3answers
110 views

Given 2 values with different significant figures, how many significant figures do you take the final answer to?

A random example from the top of my head: Given a mass of $m=1.12\:\mathrm{kg}$ accelerated by $a=99.87465\:\mathrm{m\:s}^{-2}$, find the force $F=ma$. Now, how many significant would I take ...
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0answers
22 views

How to calculate error in a function using partial derivative method?

I don't have error calculation using partial derivative method in my text book. Can someone explain me this method as it is quite useful in calcution of error in a physical quantity which is a ...
2
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2answers
31 views

How do I find uncertainties in an intensity plot created from a photograph?

I have a photo of a laser beam (taken by sending the laser into a CCD). I then took the image and ran it through an image reader that gave an intensity surface plot. I then took a single cut from that ...
0
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1answer
57 views

Error propagation estimation [closed]

I have a physical quantity A defined as $A=(74.5 B^2*(M+N))^{1/3}$ where B, M, N and relative uncertainties are given. And M and N are dependent on B: $log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)$...
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25 views

Goodness of fit for two different properties of the same model?

This is a question about statistics and optimisation. I have a model which produces two different distributions of the same dimension. Let's say they are the mean velocity distribution $\langle v(r) \...
0
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1answer
178 views

What will be the percentage error in measurement of time?

The least count of a stop watch is 0.2 s .The time of 20 oscillationsof a pendulum is measured to be 25.What will be the percentage error in measurement of time?
3
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1answer
68 views

What does the direct sum symbol (i.e. $\oplus$) mean in the context of uncertainties

I've noticed the symbol $⊕$ used in a context I'm unfamiliar with. In several papers about the the calculation of the uncertainty of quantities measured with hadron colliders. For example the ...
1
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0answers
49 views

Uncertainties propagation with complex numbers [closed]

How would one go by to estimate the uncertainties on the result of a calculation when it is done with complex values ? For example I am trying to calculate the impedance of a quadrupole and the ...
0
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1answer
38 views

Is fractional error computed using the actual value or the best estimate?

I'm trying to figure out which is the best way to do error propagation for situations when you have a product. For instance, for $F(x,y) = xy$, we can use Taylor expansion and keeping 1st order terms:...
1
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1answer
46 views

Which procedure is correct? [closed]

A problem is given in my textbook pg.no-191 as Example 5.10 A solenoid has a core of a material with relative permeability $\mu_r=400$. The windings of the solenoid are insulated from the core and ...
1
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1answer
58 views

Are residuals supposed to have error bars?

Hopefully I'm asking this in the correct section. So I've got a graph with a linear trend of data and a best fit line plotted. The data points on the main graph obviously each have their own error ...
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1answer
52 views

Uncertainty in Range of Projectile [closed]

If we are given that a projectile is launched with velocity 10m/s at an angle of $45^\circ$ and uncertainty in angle is of $0.5^\circ$ . What is the uncertainty in the range of projectile. The problem ...
0
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2answers
33 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
1
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1answer
24 views

How to find the error of all the counts within the Full Width Half Maximum (FWHM)?

We've been doing Gamma ray spectroscopy and have peaks from various sources. We'd use Poisson statistics, but obviously the detector doesn't have a resolution of zero, thus we are summing the counts ...
0
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0answers
29 views

How to round up percentage uncertainties

Let's assume that the absolute error of some value is, say 0.4. The value itself is 6.0. To calculate the percentage error one is to divide the absolute error by the value. I get 6.7% However, my ...
0
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0answers
17 views

Influence of measures errors on the average value error with three or less measures

Suppose to take three measurements of the same thing. Say for example of the area of the surface of a table. In this situation we have the bases and heights values and errors like $b\pm \sigma_b$ $h\...
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1answer
18 views

Proper significant digits in terms of a characteristic scale

Suppose I have a defined quantity in a paper $$g = 20\ \mathrm{meV}$$ and I wish to express the following equivalence (where $k_{B}$ is the Boltzmann constant which easily has more than 3-digit ...
0
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0answers
37 views

error calculation with a variable error

I have to calculate the error on the following quantity: $$f(\epsilon^M,\epsilon^S)= \sqrt{ \frac{1}{N}\sum_{i=1}^N (\log{\epsilon_i^M} - \log{\epsilon_i^S})^2 } $$ Usually I would use this standard ...
2
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4answers
129 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
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3answers
144 views

Is it correct to calculate the propagation of error in this way? [closed]

I conducted an experiment and measured the values of $R$ and $H$ to calculate $v_i$. The equation used is: $$v_i=\sqrt{{gR^2}\over{2H}}$$. My average values ($v_i$ is calculated only for the average ...
0
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1answer
80 views

What does error order $O(t^2)$ mean? [closed]

What does it mean if something is $O(t^2)$? And more importantly, how would I check for this relationship? I thought it meant error proportional to $t^2$, and that this could be tested by plotting a ...
2
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1answer
110 views

Why do length measurements apparently have zero uncertainty?

In order to estimate the length $L$ of an object the distance from its edges to the $0$ of a graded ruler are measured. Assume this object has its edges at $x$ and $y$ (mean values) with standard ...
4
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3answers
167 views

Why are significant figure rules in Multiplication/Division different than in Addition/Subtraction?

I've never understood specifically why this is. Here's what I mean. In Addition/Subtraction, what matters are the digits after the decimal point. So for example: 1.689 + 4.3 = ...