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
2answers
46 views

Why do Repeat Measurements Result in a Reduced Error?

I'm currently reading "Concepts in Thermal Physics", and in the chapter on independent variables it has the following example: If we have $n$ independent variables $X_i$, each with a mean $\...
0
votes
1answer
29 views

Test $Z$ and uncertainty

I am having some problems when I need to calculate the test $Z$. Suppose I got a value, by a measurement, of $x = 3.44433$ with uncertainty $0.00003$. And, for example, it is given to me a "...
0
votes
0answers
23 views

Add factor $Δℓ$ or $Δℓ^2$ in the expression of variance for integrated over multipole the spectroscopic Shot noise

I have the following expression for standard deviation on $C_\ell$: $$\sigma(C_{\ell,X})=\sqrt{\dfrac{2}{(2 \ell+1)\Delta\ell \,f_{\mathrm{sky}}}}\left[C_{\ell,X}+N_{X}(\ell)\right]$$ where $X$ ...
4
votes
2answers
55 views

What does it mean that uncertainty can be calculated by the "smallest division on a scale"?

I have been reading everywhere a little bit to understand the concept of uncertainty but I cannot understand exactly how to find the uncertainty value. On this explanation it says that the uncertainty ...
1
vote
2answers
67 views

Can adding two numbers increase the significant figures?

I am having a question regarding significant figures in calculating average of two masses. For example adding two masses 7 kg and 8 kg gives 15 kg, both inputs 7 and 8 have only one significant figure ...
5
votes
2answers
134 views

Calculating uncertainty from significant figures of a value

A question in Giancoli's Physics for Scientists and Engineers (2. ed) has me confused. Here it is (Ch 1, Problem 3): What is the area, and its approximate uncertainty, of a circle of radius $2.7 \...
0
votes
1answer
49 views

Adding point (0,0) to data set and its uncertainty?

This question assumes only Classical Mechanics. I am conducting a simple experiment to determine the relationship between the force applied to a spring and the displacement of the spring from its rest ...
1
vote
2answers
36 views

What is the 'correct' way of determining uncertainty of an average value from multiple measurements?

I am very confused as to what the correct way is to calculate the uncertainty of the average of values ($x_{avg}$) in a data set of measurements $(x_1 ... x_N)$. I have found at least four different ...
1
vote
2answers
31 views

Usage of $t$-test in HEP experiments

I was brushing up on some statistics and thinking about what I'd learned in my undergraduate degree, which is what led me to this topic: Is the (Student's) $t$-test, and $t$-distribution used anywhere ...
0
votes
2answers
38 views

Relative measurement error in addition / subtraction formula

if the Absolute Measurement Error = Wrong Value - Correct Value positive/negative sign is neglected since a posisitve calculation error is as bad as a negative calculation error. and if the Relative ...
0
votes
2answers
43 views

On regressing data, should the $y$-intercept be forced to a value according to the model?

I have a theoretical model of the form $$y=kx$$ Say I experimentally measure the data pairs $(y,x)$, from which I want to determine the value of $k$. I am using the curve fitting feature of MS Excel (...
0
votes
3answers
71 views

What is meant by precision?

I've found two different meanings of precision: Meaning 1 (from Grade 11 Physics textbook,India): Precision tells us to what resolution or limit a quantity is measured. Meaning 2 (from Grade 11 ...
1
vote
0answers
43 views

Fractional error in time period

The length of a pendulum is measured using a meter scale which has 2000 divisions. If the measured value L is 50cm, the accuracy in the determination of g is 1.1% and the time taken for 100 ...
0
votes
1answer
32 views

How to account for nominal resolution in calibration measurements?

I have a real world question but I think it'll be clearer if I phrase it like a "homework" question so here goes*: A physicist is trying to use a laser measuring device to determine the ...
0
votes
1answer
27 views

Maximum error in a measurement?

Suppose a quantity $Z$ is given by $Z = x \pm \Delta{y}$, then what is the maximum error in the quantity $Z$? Is it $\Delta{y}$ or 2$\Delta{y}$?
12
votes
2answers
903 views

Why don't we use absolute error while calculating the product of two uncertain quantities?

I've found a rule that says, "When two quantities are multiplied, the error in the result is the sum of the relative error in the multipliers." Here, why can't we use absolute error? And why ...
0
votes
1answer
38 views

Error in thermal time constant from measurement

I would like to know how to calculate the error in thermal time constant ($\tau$) based on temperature measurements. For example, lets say I have a plate with a thermocouple and I provide it with a ...
1
vote
0answers
23 views

Statistics for analysis in Physics

While I am well aware of the branch of physics called statistical physics my question does not pertain to this. My background is bioinformatics which very rarely uses causal modelling instead we tend ...
1
vote
1answer
33 views

Accuracy of known constants versus precision

I am wondering if the community could comment on the accuracy of the known constants versus their precision. What I mean is while many values like the electron magnetic moment are known to ...
0
votes
1answer
48 views

Error in measurement

A part of my question says "...measured value of L is 20.0 cm known to 1mm accuracy..."; in the solution thereafter Del L is taken as 1 mm. The least count of the metre scale is 1 mm right? ...
0
votes
1answer
29 views

Needed precision for detecting effects in experiments

I did a bayesian fit to experimental data with a physical model. I notice that some effects cannot be detected due to the precision of the data and the physical model doesn't fit in the best way. So I ...
-1
votes
2answers
174 views

What is the meaning of $O(10^{-14})$?

What is the meaning of the symbol,O(1),O(10^-4),in the picture above the text box? I am not a computer engineer or a computer language major. Please tell me simply. I don't want an explanation with ...
1
vote
1answer
165 views

Demonstration: Integral (discrete summing) of $C_\ell$ has a better variance than one single $C_\ell$

I am working in a cosmological context where I use the $C_{\ell}$ quantities coming from Legendre transformation. I am faced to a issue to prove the gain that we get by computing the variance of an ...
0
votes
2answers
58 views

Does 'Full width at half maximum' include ~76% of values or about 97.5%? Within its area?

From Wikipedia: If the considered function is the density of a normal distribution of the form $${\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}\exp \left[-{\frac {(x-x_{0})^{2}}{2\sigma ^{2}}...
0
votes
0answers
37 views

Numerical Problems Based On Vernier Callipers

I watched a video on Vernier Calipers which gave me an understanding of how it works and how to read a Vernier Caliper. I also tried the GeoGebra simulation. But I am not able to understand the ...
2
votes
1answer
53 views

Creating a map of energy from gravitation measurements

There are some devices which used supercooled falling atoms to measure gravity in order to weakly find large regions of different density. Would it be possible with current technology to measure ...
0
votes
1answer
44 views

Difficulty bounds in a white noise model

Suppose we make a measurement in a real/virtual experiment for which the noise is given by a white noise (Gaussian) model. Suppose also that we have a very good filter or machine learning (ML) model ...
0
votes
1answer
23 views

Relationships between G magnitude, Johnson V magnitude, and spectral type of stars?

I'm simulating a population of binary stars for a summer research project. I'm adding uncertainties to my simulated observables such as angular position and radial (line of sight) velocity. I'm using ...
0
votes
1answer
31 views

How are 'margin of error' and 'sigma' (standard deviation) combined in a particle physics experiment?

If a particular experiment is done to determine a particular value, say the charge radius of a particle, and they give a 'sigma' of two and a 'margin of error' of a femtometer, does that mean there is ...
-1
votes
1answer
31 views

Confidence in COBE, WMAP, and PLANCK measurements of the CMB?

I'm heavily unfamiliar with error analysis in astrophysics and have been curious about how confident we are about the measurements of the CMB by the respective satellite missions COBE, WMAP, and then ...
2
votes
0answers
81 views

Computation of standard deviation on $C_\ell$ with fraction of sky $f_{\text{sky}}$ and $\Delta\ell$

I try to demonstrate the expression of error on a $C_{\ell}$. Below the expression of standard deviation on a $C_{\ell}$ that I would like to get: $$\sigma_{C_{\ell}}=\sqrt{\dfrac{2}{(2 \ell+1) f_{\...
1
vote
1answer
25 views

What does $\Delta m_s$ mean in regard to meson and quark decays? And what are (syst) and (stat) in regard to margins of error?

From Wikipedia, B meson: The neutral B mesons, B0 and B0 s, spontaneously transform into their own antiparticles and back. This phenomenon is called flavor oscillation. The existence of neutral B ...
0
votes
0answers
11 views

Compute the variance of spectroscopic Shot Noise in cosmology context

I would like to know the right expression for the expression of variance of Shot noise in spectroscopic probe. Sometimes, I saw $$\sigma_{SN,sp}^{2} = 1/n_{sp}$$ with $n_{sp}$ the average density of ...
1
vote
0answers
32 views

Why do we add an error of 0.1 to a measurement by an instrument of least count 0.1

If the measuremnt comes between 2.3 and 2.4 why do we write as 2.3 ± 0.1. Why can't we write it as 2.35 ± 0.05. I understand this gives a wrong idea about precision, but why not create a new ...
0
votes
2answers
51 views

How to add these in accordance with the rules of significant figures?

$2300$ has 2 significant figures (2,3). Thus $2300+123 = 2423$. However, we can also write this as $100\cdot(23+1.23) = 100\cdot( 24.23 )$ since 23 has no decimals, 24.23 is rounded to 24. The answer ...
0
votes
0answers
39 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$^{-1}$ ...
0
votes
1answer
62 views

Position of the wavefunction's collapse

When a wave function is said to "collapse" to a single point during a measurement, is there uncertainty about the point's position or is it known infinitely precisely?
0
votes
3answers
219 views

How does the number of significant figures change when a unit is added?

This (foolish) doubt on significant figures is giving me sleepless nights. Say, A given number is 20000 I would say it has 1 significant digit right? But Now, Say The value given is 20000 m (metres) , ...
1
vote
2answers
543 views

Why are there two vernier scales on a prism spectrometer?

Why are there two vernier scales on a prism spectrometer and why are they 180 degrees apart? Example image (source): I have some idea that it reduces the error in measurements but I don't exactly ...
0
votes
1answer
41 views

Measuring sum of angles of triangles on different curvature

I was reading Richard Feynman’s Six Not so Easy pieces where I came across the concept of measuring geometric shapes drawn on different curved surfaces like the ones with negative and positive ...
4
votes
3answers
76 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 ...
0
votes
1answer
37 views

Uncertainty in data from star databases

I have students who are pulling data from various astronomical databases like SIMBAD or the Binary Star Database and then using that data to determine correlations between certain properties. My ...
7
votes
4answers
1k 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 ...
0
votes
2answers
32 views

Why is least count error like this?

For a measurement of 4.6 (between 4.6 and 4.7 ) with a least count of 0.1 we write the measurement as 4.6 ± 0.1 . Why can't we write it as 4.65 ± 0.05. My guess is this gives a false sense of ...
0
votes
1answer
21 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 ...
1
vote
2answers
46 views

Why Signal-to-noise ratio (SNR) is measured in $\rm dB$?

I understand that the signal to noise ratio is $$ \text{SNR}=\frac{P_\text{signal}}{P_\text{noise}} =\left(\frac{A_\text{signal}}{A_\text{noise}}\right)^2 $$ My question is why SNR is measured in $\rm ...
1
vote
3answers
61 views

How to take the reading of voltmeter if the needle falls between 1.6V and 1.7V?

What value should I take based on this voltmeter reading as shown in the picture? Is it 1.6V or 1.7V? I believe there is a parallax error in this case. Therefore, the reflection on the mirror would be ...
0
votes
1answer
68 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 ...
1
vote
4answers
109 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 ...
0
votes
0answers
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 ...

1
2 3 4 5
16