Questions tagged [statistics]

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6 views

Statistical distribution for “volume exchange”?

The Boltzmann and Gibbs distributions are derived from the assumptions that our system exchanges energy (canonical ensemble) or both energy and particles (grand canonical ensemble) with the ...
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20 views

Analytical derivation of the distribution of dependent quantities

The problem I am facing is the following. I do have two physical quantities, $x$ and $y$, and I know the analytical relation between the two $$y = g(x)$$ Now, I know that $x$ is well represented by a ...
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2answers
41 views

Momentum uncertainty in Uncertainty principle

In my physics textbook, to estimate atomic and nuclear energies, they used the Uncertainty principle. In this problem, $\Delta p=p-(-p)=2p.$ But in many different problems, people just defined the $\...
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0answers
47 views

Pink noise and averaging

Disclaimer: I am aware this is somehow at the boundary between physics and statistics, but I have the impression that it is more likely that somebody doing/studying physics, rather than statistics, ...
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1answer
31 views

A question on probability and expectation concepts

Let A be an observable event. If the expectation of A is zero, does it imply that the probability of A is zero?
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37 views

How to find the integrated luminosity for a 5$\sigma$ discovery?

I was thinking about the procedure needed for the discovery of a new particle. Suppose a data-analysis aims at searching for a new resonance X decaying to two electrons after collecting 20 fb$^{-1}$ ...
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3answers
64 views

Should we include instrumental uncertainty when calculating the uncertainty of a measurement?

Imagine we are measuring the period $T$ of a pendulum using a stopwatch The stopwatch has an inerent instrumental uncertainty (e.g. 0.1s) let's keep this fact in mind Due to random error (let's ...
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0answers
23 views

What is a Figure of Merit in statistics? [migrated]

Papers published on the arXiv often mention the notion of Figure of Merit (FOM). Can you explain what a Figure of Merit is, how it is used and what are its relations to statistics?
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4answers
991 views

Help interpreting “five sigma” standard?

So, I am coming from a math/stats background. I was just wondering about this in the abstract, and tried Googling around, and came across this article which says the following regarding some ...
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1answer
19 views

Polynomial regression and errors weighted with square root of reduced chi square

I conducted a polynomial regression of the form $y(x) = A+Bx + Bx^2$, and would like to obtain parameters $A$, $B$ and $C$ and their respective errors/confidence level. The reduced chi square is less ...
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1answer
56 views

Error Propagation of Variable raised to Variable

I am an environmental scientist and it's been too long since I've taken a math class. In my research I've had to use this equation for gas loss constants, but I am going back to assess my ...
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4answers
100 views

Is the Least Squares Fit always the accepted Fit in Physics?

Is the Least Squares Fit always the accepted Fit in an experiment? Suppose you have $N$ data points and a function $f$ with some parameters. There is a one Least Square sum, it may be obtained for ...
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25 views

Intuition re. log scale versus linear scale

I have a dataset with the speed of movement of two sets of particles (the red, slower, and the blue, faster) as calculated by the diffusion constant. Below is a histogram, on the left on linear scale ...
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1answer
45 views

Average value and confidence interval with different precisions of a measurement [closed]

Imagine you have to measure thickness of a paper sheet using only a caliper which provides a precision to $\Theta $ mm. You start with a stack of 10 sheets and the caliper reads ${{l}_{1}}$ mm. Then ...
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3answers
21 views

How to display an measurement results with error bar given huge number of digital measurements? [closed]

I need to measure the flow rate using a flow meter. This flow meter collects 6000 data points over the course of 5 minutes for every temperature of our experiments. I repeat this experiment at ...
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3answers
41 views

If radioactive decay is measured by halflife does it mean that few atoms of a radioactive material are practically stable?

If radioactive decay is measured by halflife does it mean that few atoms of a radioactive material can be considered practically stable? If we try to measure the time when 0,1% of the atoms of the ...
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0answers
40 views

Compute the variance of the squared ratio of 2 observables with noise

I have to compute the variance of the squared ratio of 2 observables (here cosmological bias $b_1$ and $b_2$). The random variable represented by this squared ratio is noted "observable O". ...
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1answer
27 views

Computing correlation between two time series: confusion regarding nonlinear relationship and nonlinear data

I am trying to understand if correlation can be computed between two time series generated from two different initial conditions for chaotic dynamical systems. In general, correlation is applicable ...
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3answers
46 views

What is the probability distribution for the detection times of radioactive emissions from a radioactive sample?

Assume I have a radioactive sample composed of $N$ atoms of some type A. I know that if I measure at time t the number of atoms not already decayed, this number will be given by $$ N(t) = N_0 \exp^{-t/...
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3answers
133 views

How radioactive dating works? [duplicate]

Often in geology & archaeology we listen that they calculated the age of things (bones, pots) using radio active dating. Radioactive dating works using half life of unstable isotopes. And what ...
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1answer
22 views

Definition of RMS deviations from mean w.r.t. $|u(x,0)|^2$ and $|A(k)|^2$ in Jackson

In chapter 7 of Jackson’s Classical Electrodynamics (page 323) he speaks of ‘‘rms deviations from mean, $\Delta x$ and $\Delta k$, defined with respect to $|u(x,0)|^2$ and $|A(k)|^2$’’. I do not ...
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5answers
3k views

Why can't the Uncertainty Principle be broken for individual measurements if it is a statistical law?

The Heisenberg Uncertainty Principle is derived for two operators $\hat A$ and $\hat B$ as $$\Delta \hat A\ \Delta \hat B \geq \dfrac{1}{2}|\langle[\hat A, \hat B] \rangle|$$ where $\Delta$ denotes ...
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1answer
21 views

Combinatorics: what is the total number of fermionic microstates?

This might be pretty basic but, say we have a fermionic chain with $L$ sites which can be occupied by one fermion. One possible macrostate is to have 1 fermion in the chain which in turn may be ...
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1answer
32 views

Intuition behind order of speeds in kinetic gas theory

In kinetic gas theory, we have the following result for the order of speeds $v_{rms}>v_{av}>v_{mp}$ i.e: the ratio of $1:1.128:1.224$ for the speeds $v_{mp}:v_{av} : v_{rms}$. Definitions (...
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1answer
48 views

How to calculate the amount of standards deviations a measure is from another value

I have a theoretical value $\gamma_t$ and a measured values $\gamma_m$, with uncertainties $\sigma_{\gamma_t}$ and $\sigma_{\gamma_m}$ respectively. If the errorbars of $\gamma_m$ is inside of $\...
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1answer
62 views

Sigma Significance in Particle Physics and Beyond [closed]

Why is a 5 sigma confidence level enough to solidify an experimental result as not being a statistical fluke in particle physics? Other branches of science have different sigma values for which they ...
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1answer
81 views

What is the strongest result that has subsequently been shown to just be a statistical glitch?

While reading up on the $g-2$ result, I noticed that the authors stopped short of announcing a definitive result because they only had 4.2 sigma of confidence rather than the 5 that is the standard ...
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2answers
125 views

Why is it legitimate to use the Poisson law for likelihood computation in particle physics? (background events are not rare)

In experimental particle physics at colliders, there are a high number of collisions of incoming particles, for example protons at LHC. Once protons collide in a given collision event, those protons ...
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0answers
42 views

How to compute the covariance error term in cosmology context?

Below the error on photometric galaxy clustering under the form of covariance : $$ \Delta C_{i j}^{A B}(\ell)=\sqrt{\frac{2}{(2 \ell+1) f_{\mathrm{sky}} \Delta \ell}}\left[C_{i j}^{A B}(\ell)+N_{i j}^{...
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2answers
57 views

Are these histograms stacked or overlapping?

How do I read these histograms because the interpretation seems ambiguous. https://profmattstrassler.com/articles-and-posts/the-higgs-particle/holiday-higgs-hints-confidence-inspiring-or-not/ Are ...
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3answers
59 views

Calculate the slope of a straight line from experimental points [closed]

Draw a straight line from the experimental points so that the scatter of the experimental points is minimal. Having determined the slope of the resulting straight line. How should I do it? I ...
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0answers
28 views

Resource request for experimental physics and data handling

When solving questions in olympiad physics, I come across problems on experiments, data, errors, drawing graphs and extracting information from given graphs, etc. Is there any good book/resource for ...
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0answers
25 views

Long term and short term sensitivities

I am currently studying rotation sensing, specifically, rotation sensors using matterwave interferometry that operate on the Sagnac effect. I have noticed a few units being used when discussing the ...
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1answer
125 views

How can sub- and super-Poissonian statistics be distinguished from bunching and antibunching?

This is my first post here, so I apologize if there's something wrong. I am studying quantum optics and I found myself in trouble with the difference between bunching/antibunching and super poissonian/...
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0answers
38 views

What did Freeman Dyson mean when he said this? [duplicate]

In this video, Freeman Dyson, when speaking of Fermi said the following thing, "...what does he think about the numerical agreement, and he said, 'How many parameters did you use for the fitting?...
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1answer
28 views

Marginal characteristic function from a multivariate charateristic function

[I am posting this question here and not in Mathematics Stack Exchange because I will be using conventions as they are usually used in statistical physics (especially the notation is more involved in ...
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1answer
98 views

Calculating the $p$-value with Wilks' Theorem

I am stuck at understanding the following: According to Wilks' Theorem, the test-statistic $$q_0 = -2\cdot \ln\frac{\mathcal L\left( S = 0\right)}{\mathcal L\left( \hat{S}\right)}$$ follows a $\chi^{2}...
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2answers
59 views

How do you combine the errors resulting from measuring one instrument with another?

In a recent lab, we were asked to find the time constant, $\tau$ by timing the discharge of a capacitor through a resistor. The voltage on the capacitor was measured with a DMM whose instrumentation ...
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0answers
32 views

CMS Paper of Higgs Discovery: Exclusion Plots [duplicate]

In the discovery paper of CMS of the Higgs boson, on page 24, we can find the following plot: Question: What is the dashed line really representing? After all, it says in the caption that this line ...
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1answer
35 views

Is there any significant scale nuclear transmutation currently in practice?

There was a similar question in place but the details of the answer may suggest another solution. So I am aware that transmutation is used to reprocess radionuclides in nuclear waste to render them ...
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1answer
38 views

Calculating basic systematic error

My lab partner and I are in disagreement about what the systematic error of our temperature measurement is. The digital temperature gauge measured to one decimal place (i.e 20.3°C). We took a number ...
162
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20answers
11k views

How do you make more precise instruments while only using less precise instruments?

I'm not sure where this question should go, but I think this site is as good as any. When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras ...
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1answer
67 views

What does $\Delta p$ in uncertainty principle mean?

What does the $\Delta p$ in uncertainty principle mean? Is it standard deviation? I have seen few videos on youtube as well as in our high school textbooks, it was proved that the electrons don't ...
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3answers
128 views

What does the $\langle \rangle$ notation mean?

I have what I think is a very simple question, basically, what does the notation "$\langle \rangle$" stand for? My background is in math and I am not familiar with physics notations. I am ...
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0answers
35 views

Decoupling noises

This is an experimental physics problem: Say I have 3 random variables $P_1, P_2, P_3 $ such as : $\Delta P_i=\Delta_Q P_i +\Delta_0P_i \ \ \forall i$, where $\Delta$ is the variance, this equations ...
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3answers
186 views

Why do physicists, in quantum mechanics, call average an expectation value, not expected value? [closed]

I guess there is a specific reason for this - calling the expected observation $$\langle\psi|\hat{Q}|\psi\rangle$$ (for a normalised wavefunction) an expectation value. I heard somewhere that, in ...
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1answer
76 views

Exponential rule for propagation of errors

I'm struggling to follow what feels like it should be a simple method. I often see that for if you want to find the error of an exponential, it follows: if $y = x^{n}$ we have $\frac{\Delta y}{y} = n\...
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1answer
32 views

How to calculate uncertainty of rounded data [closed]

I have been seriously confused with the following text for a short while. Suppose that three teachers have timed the school 100 m sprint race and have recorded times of 12.3, 12.5, and 12.6 s for the ...
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1answer
28 views

How is measurement uncertainty defined / calculated (of a sensor or measurement)?

Textbooks and online sources often say the industry standard for uncertainty is given at a confidence interval of 95 %. This means out of 100 measurements, 95 would achieve the specified value and ...
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8answers
14k views

Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute?

I wondered this since my teacher told us about half life of radioactive materials back in school. It seems intuitive to me to think this way, but I wonder if there's a deeper explanation which proves ...

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