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.

Measurements and uncertainties

All measurements in physics have some uncertainty attached to them. The uncertainty is a measure of how well a scientist knows the "true" value of the measured quantity.

Propagation of uncertainties

Least-squares fitting

Common statistical distributions in physics

Poisson distribution

Gaussian (normal) distribution


External Resources

Taylor, An Introduction to Error Analysis is a commonly used text book appropriate for introductory undergraduate lab courses.

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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 and atomic clocks. These instruments are many…
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How exactly do you avoid fooling yourself?

In cargo cult science Feynman writes: "Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a little bit off, because he had the incorrect value for the…
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What reference clock is an atomic clock measured against?

I looked at a few of the other posts regarding the accuracy of atomic clocks, but I was not able to derive the answer to my question myself. I've seen it stated that atomic clocks are accurate on the order of $10^{-16}$ seconds per second. However,…
zrbecker
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Are random errors necessarily Gaussian?

I have seen random errors being defined as those which average to 0 as the number of measurements goes to infinity, and that the error is equally likely to be positive or negative. This only requires a symmetric probability distribution about zero.…
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Why does the speed of light in vacuum have no uncertainty?

I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we measure other stuff using the physical definition of…
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In nuclear physics, what length year in seconds is used?

So I'm working on a nuclear physics problem and am looking at radioactive decay. The common unit used for very long decays is years within the literature. Is this the sidereal or tropical year? I want to use units of seconds but seeing as how these…
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Looking for an old physics lab meme (early 2000s)

I’m trying to track down a mock physics lab report / figure that circulated online in the early 2000s. It showed very noisy, essentially meaningless data, a clean straight-line (or simple) fit drawn through it, and a deadpan or profane caption along…
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Why is a leading digit not counted as a significant figure if it is a 1?

Reading the book Schaum's Outline of Engineering Mechanics: Statics I came across something that makes no sense to me considering the subject of significant figures: I have searched and saw that practically the same thing is said in another book (…
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To what degree of precision are atoms electrically neutral?

It is said that if, say, the electric charge is not a Lorentz invariant, neutral atoms are no longer neutral, which is not experimentally valid. I want to know to what degree of precision atoms are measured to be electrically neutral and what would…
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Why aren't the 0's significant figures in 0.002?

I understand that significant figures is a term used for "reliably known digits". However, what I don't understand is why the 0's are not counted among these in numbers such as 0.002. Surely, if we know that the units digit is 0, and that the tenths…
Raghib
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What does the notation $8.9875517923(14)$ mean?

The number $8.9875517923(14)$ appears in Coulomb's constant. I have read that it has something to do with the uncertainty of the accuracy of the number but answers have been unclear. Can somebody define the meaning of such notation?
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Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How should I understand this uncertainty? Does it mean $\pm 44$ on…
Steeven
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What is the minimum temperature difference which can be measured?

All real things have temperature. Temperature can be measured in various ways. We have reached to a great precision in measuring change in time and space , however I am not sure to what extent change in temperature can be measured? I searched the…
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Why should a clock be "accurate"?

Having read that atomic clocks are more accurate than mechanical clocks as they lose a second only in millions of years, I wonder why it is necessary for a reference clock to worry about this, if the definition of the second itself is a function of…
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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 time. If I now measure, say 40, 41 and 39 seconds in…
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