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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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
863 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 ...
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1answer
33 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 ...
2
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1answer
440 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - ...
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1answer
40 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 ...
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1answer
28 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? ...
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1answer
27 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 ...
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1answer
52 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 ...
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3answers
3k views

Error calculation in parallel resistances

This is the question: There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination. According to what I've ...
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3answers
671 views

Theoretical uncertainty of a circuit's total resistance when made entirely of resistors

My question in short(ish) is: Will the fractional uncertainty of a circuit made entirely of resistors with equal fractional uncertainties be the same as the fractional uncertainty of those resistors. ...
1
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1answer
198 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
3
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1answer
66 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 ...
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3answers
157 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 = ...
2
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1answer
24 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

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 ...
3
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1answer
76 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 ...
11
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2answers
18k views

How do you find the uncertainty of a weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
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0answers
25 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 ...
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3answers
107 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
18 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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0answers
44 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 ...
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0answers
34 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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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 ...
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0answers
18 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 ...
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1answer
54 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 ...
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1answer
49 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?
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21 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) ...
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0answers
37 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 ...
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1answer
49 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 ...
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1answer
45 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
45 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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2answers
31 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 ...
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1answer
20 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 ...
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1answer
69 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
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3answers
90 views

Significant figures

How to calculate significant figures of a number? I got confuse as the number 28600 has 3 significant figure instead of 5. Anyone can explain?
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0answers
20 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 ...
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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 $b\pm \sigma_b$ ...
-1
votes
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 ...
2
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4answers
119 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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0answers
24 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 ...
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3answers
141 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
votes
1answer
68 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
109 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 ...
0
votes
1answer
52 views

Precision of the edge of a cube versus the volume of a cube [closed]

The edge of a cube was measured with 1% precision. How is the precision of the volume of same cube calculated on the basis this measurement? Is it true that precision of the measurement would be 3%?
0
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1answer
63 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
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1answer
91 views

The confusion of fractional error calculation

I need to find the focal length of a lens by using equation 1/u + 1/v=1/f I have: u= 50+-3 mm v= 200+-5 mm I calculate the value of f as 40mm. Now i need to find the uncertainty in this value. ...
6
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1answer
2k views

The uncertainty of a metre ruler?

I have been taught that the uncertainty in the measurement of a metre ruler is +-1 mm. However , I was also taught that the uncertainty is half of the smallest division in the measuring instrument. ...
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2answers
49 views

Error propagation without analytical expression

I have an algorithm $f$ that takes two inputs $x,y$ and gives one output. I say algorithm because I don't have the analytical expression for $f(x,y)$ (it's a black box in a computer, surely a ...
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1answer
87 views

error propagation of a quantity [closed]

I have $e =$ 0.015 $\pm$ 0.005. How would I use error of propagation to calculate the uncertainty on $$ \frac{1}{( 1 - e^2)^{\frac{1}{8}} } $$ EDIT Since the question was put on hold then I will ...
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1answer
664 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...