# 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.

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 (...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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$\Delta{y}$?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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?
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### 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) , ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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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### 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 ...
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### 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 ...