The statistics tag has no wiki summary.
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1answer
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Standard Deviation in Particle Physics
I'm familiar with sigma, and how its usually calculated and used, but would like to know how it's applied to particle physics. I recall reading that the discovery of the Higgs would only be credible ...
7
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2answers
1k views
How do we know that some radioactive materials have a half life of millions or even billions of years?
If a radioactive material takes a very long time to decay, how is its half life measured or calculated? Do we have to actually observe the radioactive material for a very long time to extrapolate its ...
7
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2answers
220 views
How to predict how much data to collect
The same question on CrossValidated
Apologies if I'm being a bit vague in what follows, I've been asked to keep certain aspects of the experiment confidential for the time being.
An analogous ...
6
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2answers
286 views
Use of Monte-Carlo simulation in High-energy Physics
I've been doing some research into the analysis used in particle physics when determining the significance of a finding (e.g. the recent Higgs candidate was announced as a boson in the 125-126 ...
5
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6answers
790 views
Why don't experimental physics groups have statisticians in it?
Perhaps someone can clear up a bit a cognitive dissonance I am experiencing. Pollsters are under constant scrutiny of statisticians for even the most mundane of survey topics. With so much riding on ...
5
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3answers
845 views
How to combine measurement error with statistic error
We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times.
I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction ...
5
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1answer
5k views
How do you find the uncertainty of an 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 ...
5
votes
1answer
176 views
Finding coefficient of proportionality
Recently in my AP Physics class I did a lab in which I measured k for a spring by setting up an oscillating system with it, and timing the period, repeating for different masses. Since ...
5
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2answers
157 views
statistics for photon counts in photomultiplier
It seems that a common statistical model for the count numbers of a photomultiplier is a Poisson distribution whose parameter $\lambda$ equals to the square-root of the number of counts.(e.g. ...
5
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2answers
110 views
Averaging decibels
Wikipedia:
The decibel (dB) is a logarithmic unit that indicates the ratio of a
physical quantity (usually power or intensity) relative to a specified
or implied reference level.
If I ...
5
votes
2answers
279 views
Photon statistics of an incandescent light source
We usually calibrate the cameras on our microscopes by capturing 20 images of a blurry (not sharp) fluorescent particle. For each pixel in this stack of 20 images we calculate the intensity variance. ...
4
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3answers
259 views
why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero?
Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the ...
4
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92 views
What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?
What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $?
Where $\left\langle ...
4
votes
2answers
192 views
What do “local” and “global” mean when talking about standard deviations in experimental particle physics?
I found the following sentence:
The excess is most compatible with a SM Higgs hypothesis in the vicinity
of 124 GeV and below, but the statistical significance (2.6σ local and 1.9σ
global after ...
4
votes
1answer
143 views
Products of Gaussian stochastic process variables
In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
4
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0answers
148 views
What statistical test should I use?
I have two differential cross sections $d\sigma_{1,2}/dM$ ($M$ is some invariant mass) corresponding to different hypothesis. What I want is to calculate how well the appropriate experiment would do ...
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3answers
348 views
Calculating uncertainties for a final result
Say you are dividing 2 times with uncertainties:
$$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$
After doing the calculations you get:
$$\frac{t_1}{t_2} ~=~ 0.774 \pm ...
3
votes
1answer
845 views
How to combine the error of two independent measurements of the same quantity?
I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$.
$k$ is just the mean of $k_1$ and $k_2$. I thought ...
3
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3answers
258 views
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
3
votes
1answer
953 views
Is there a stable numerical algorithm for FWHM that isn't 2.35*sigma?
This is a question that should have a simple answer, but which I can find no proper discussion of in the literature or on the internet.
I start from the assumption that I have a noisy numerical ...
3
votes
2answers
119 views
Question about uncertainty
Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values?
The answer is yes, but I do not clearly see why this is so. I appreciate ...
3
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3answers
1k views
What are distinguishable and indistinguishable particles in statistical mechanics?
What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
3
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2answers
284 views
Relating the power to weather variables [closed]
Could you please help me in this problem?
I have 3 independent variables, (T,H,t) , as inputs and one output P ( I have all data for these inputs and the output, done experimentally measured every ...
2
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3answers
78 views
Statistics software for basic undergrad lab
I'll have to perform some simple experiments, like measuring the period and damping of a pendulum, focal length of a lens, …
As a result I will end up with some X, Y data points and need to calculate ...
2
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1answer
150 views
Maxwell-Boltzmann velocity PDF to CDF [closed]
I asked on Math.SE and was advised to try here instead.
I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
2
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1answer
224 views
Is $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement?
I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$.
But in ...
2
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1answer
287 views
Astronomical detection significance from magnitude error
At this website:
http://heasarc.gsfc.nasa.gov/docs/swift/analysis/threads/uvot_thread_afterglows.html
The passage at the bottom states that a V-band magnitude of 17.62, with an error $\pm$0.02 is a ...
2
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2answers
159 views
Average Neighbouring Impurity Separation in a Random 1D chain [closed]
I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...
2
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1answer
61 views
Experimental measurement of volumetric flow rate
The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
2
votes
1answer
54 views
Underlying physical basis of an exponential distribution
My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies ...
2
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2answers
99 views
What is the relation of the release time of fossil fuel emissions to climate change? [closed]
This question presupposes that
The amount of fossil fuels on earth is limited
Mankind will burn all of its fossil fuels eventually
Based on these presuppositions, the total amount of CO2 released ...
2
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2answers
122 views
Wave Function Statistical Interpretation vs Oscillation Interpretation
Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the ...
2
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1answer
131 views
How do you determine the degree of localization of a wavefunction?
Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
2
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2answers
66 views
Error in variance
I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
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1answer
122 views
Peak deconvolution [closed]
I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample.
The two ...
2
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0answers
69 views
Randomly sampling a “well-mixed” solution of Brownian particles
I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
2
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2answers
513 views
Combining multiple theories with 5 $\sigma$ confidence level
Sadly I am not a physicist but I am interested in the topic. Please have mercy with me if you find my question trivial or dumb. Here it comes:
As far I understand physicist express their certainty ...
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5answers
220 views
Are Uncertainties in Measurements Important?
In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...
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4answers
231 views
Statistics in physics
What are the uses of statistics in physics? I am about to embark upon a study of statistics and I would like to know what the particular benefits I gain in physics.
1
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1answer
108 views
Lacking of scale and distribution moments
Given a physical random variable x, $E(x)$ and $E((x-<x>)^2)$ defines mean and variance. From a statistical point of view variance represents the statistic error (isn't it?). If variance is not ...
1
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1answer
90 views
How to interpret a negative failure rate?
In statistical engineering the "hazard rate" of a distribution is defined as:
$$r(x)=\frac{f(x)}{1-F(x)}$$
where $f(x)$ and $F(x)$ are the PDF and CDF. Basically $r(x)$ is the odds that, having ...
1
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2answers
69 views
What is the Schechter luminosity function's domain of support?
I'm trying to fit a Schechter luminosity function to some data points, but it's not clear from this definition what the domain of support of the PDF should be. I'm familiar with the standard Pareto ...
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2answers
122 views
How to decide convergence of the ensemble average in a Monte Carlo process
I am simulating electromagnetic scattering off a rough surface. The usual process is to do a Monte Carlo simulation, which is briefly described as follows.
Generate a randomly rough surface, and ...
1
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1answer
81 views
Variance of Nested Experimental Uncertainty
I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for ...
1
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1answer
57 views
How to properly read a measurement result if it is a number?
If the result of a measurement is i.e. $3.2 \pm 0.7$, what is 0.7? At which confidence level we know that the real result is inside of this interval?
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2answers
203 views
How do derive this result in stat-mech style
I'm going through (well, at least I'm planning to) Rief's book about statistical mechanic (I want to improve my knowledge). I want to be serious about this so I'm trying to solve as much problem as I ...
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2answers
686 views
Physical interpretation of y-intercept in a Current vs Voltage graph
So I collected current and voltage data from a simple circuit with a power source and a resistor, using a multimeter. I created a graph for this data using excel and got the y-intercept (which is ...
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1answer
69 views
Computing an average escape distance for a particle
Somewhere in a two dimensional convex bulk of particles (pic related) on a random position a reaction takes place and a particle is sent out in a random direction with a constant velocity $v$.
What ...
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0answers
30 views
is log-Laplace ever an optimal model for physical phenomena?
In the financial world, the log-Laplace distribution almost perfectly models many phenomena such as price changes.
Does this model best fit any physical phenomena?
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0answers
171 views
Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
